Perspectives

Restricted Boltzmann machines are simple yet powerful neural networks. They can be used for learning structure in data, and are used as a building block of more complex neural architectures. At the same time, their simplicity makes them easy to use, amenable to theoretical analysis, yielding interpretable models in applications. Here, we focus on reviewing the role that the activation functions, describing the input-output relationship of single neurons in RBM, play in the functionality of these models. We discuss recent theoretical results on the benefits and limitations of different activation functions. We also review applications to biological data analysis, namely neural data analysis, where RBM units are mostly taken to have sigmoid activation functions and binary units, to protein data analysis and immunology where non-binary units and non-sigmoid activation functions have recently been shown to yield important insights into the data. Finally, we discuss open problems addressing which can shed light on broader issues in neural network research.

Attosecond microscopy aims to record electron movement on its natural length and time scale. It is a gateway to understanding the interaction of matter and light, the coupling between excitations in solids, and the resulting energy flow and decoherence behavior, but it demands simultaneous temporal and spatial resolution. Modern science has conquered these scales independently, with ultrafast light sources providing sub-femtosecond pulses and advanced microscopes achieving sub-nanometer resolving power. In this perspective, we inspect the challenges raised by combining extreme temporal and spatial resolution and then highlight how upcoming experimental techniques overcome them to realize laboratory-scale attosecond microscopes. Referencing proof-of-principle experiments, we delineate the techniques' strengths and their applicability to observing various ultrafast phenomena, materials, and sample geometries.

This paper comprehensively reviews the research progress on reputation evolution mechanisms within the framework of network-based evolutionary game theory. It first summarizes the typical strategy learning mechanisms used in evolutionary games. Next, it provides an overview of traditional reputation evolution mechanisms and their associated mathematical models, highlighting recent research findings. Furthermore, the paper presents experimental evidence from several key studies, including mechanisms like reputation-based incremental heterogeneity and reputation-based discount accumulation. It identifies the limitations of current research on reputation evolution mechanisms and proposes future research directions. The aim is to empirically verify the role of reputation in promoting cooperative behavior by exploring more accurate reputation evaluation mechanisms and developing reputation evolution models across diverse network structures.

Network controllability refers to the ability of a networked system to drive its state to any desired configuration through control inputs. Controllability robustness ensures that this capability is maintained or retained under structural variations, such as node or edge failures caused by malicious attacks or random perturbations, which is critically important for real-world networks. This paper reviews existing metrics, evaluation methods and optimization strategies for controllability robustness, introducing also modeling techniques for attack processes. Analytical techniques, empirical simulations and machine-learning–based approaches are presented, highlighting their respective advantages and limitations. Finally, some future directions are briefly discussed in four key areas: metrics design, evaluation refinement, optimization algorithms, and attack process modeling. By addressing these challenges, it is expected to develop more robust and stronger resilient networked systems.

Recent advancements in quantum technology have highlighted the potential of nitrogen-vacancy (NV) centers in diamond. However, realizing this potential requires overcoming challenges associated with the size, complexity, and cost of current optical systems. In this Perspective, we present a compact and portable confocal setup designed for efficient detection, initialization, and readout of single NV center photoluminescence signals, enabling coherent spin control and nanoscale-resolution magnetic field sensing.

In this Perspective article, we introduce a new framework for the global non-equilibrium thermodynamics of stationary states. This theory uses the spatial distributions of temperature, density, velocity, and other variables in stationary states as its input. It outputs the global state parameters to describe the system's energy exchange with the environment. The number of state parameters is determined solely by the type of substance in the system and external potentials, regardless of the number of boundary conditions, fluxes within the system, or its specific geometry. The theory offers a second law of non-equilibrium thermodynamics for stationary states, predicting the direction of spontaneous processes between them. When all macroscopic fluxes reach zero, the theory reduces to equilibrium thermodynamics.

The "Swampland Program" aims to discriminate consistent-looking effective field theories that do not admit a UV completion in quantum gravity from those that do. While most often developed under the umbrella of string theory, several swampland criteria have been explored also in other contexts, especially asymptotically safe gravity. A comparison between different approaches can help to clarify the dependence of low-energy constraints on UV physics and thereby shed light on the universality of quantum gravity itself. In this perspective we summarise what is known about three important swampland conjectures in string theory and in asymptotic safety. We point out future lines of research that can help to understand to what extent swampland conjectures are absolute, i.e., hold in quantum gravity in general, or relative, i.e., belong only to a specific UV framework.

Human mobility serves as a fundamental component in shaping the contact networks through which infectious diseases propagate during pandemics. It significantly influences the spatial and temporal patterns of disease transmission among individuals. Traditional epidemic models often struggle to capture the complexity of these heterogeneous contact patterns. In contrast, models incorporating human mobility, which account for the movement of individuals across regions, offer a detailed perspective on micro-level interactions and their impact on disease spread. The discussion highlights four types of epidemic models that integrate human mobility, including compartment models, complex network models, agent-based models and machine learning models, emphasising their crucial roles in epidemic prediction and control. Additionally, it provides insights into the broader implications of human mobility on dynamic-modelling and decision-making within the context of epidemics.

Over the past decade, the digital twin brain (DTB) has emerged as a transformative brain science paradigm, integrating multimodal data to construct dynamic models closely simulating biological brain function. This approach has advanced understanding of structure-function relationships, cognitive behaviors, and disease mechanisms, while supporting personalized therapies. Recent progress highlights DTB's potential in capturing functional heterogeneity, simulating information integration, and predicting individual cognitive and pathological variations. Looking forward, the development of a high-precision DTB is expected to drive breakthroughs in understanding brain mechanisms and enabling precision medicine. This perspective summarizes DTB modeling strategies, including multimodal data integration and optimization, while addressing challenges such as model granularity, and biological interpretability. Future efforts should focus on refining modeling techniques and integrating with brain cognition and disease. We believe these advancements will pave the way for breakthroughs in brain science and precision medicine, ushering in a new era of neuroscience and personalized healthcare.

Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources such as fluctuating environments, behavioural errors or incomplete information. Incorporating uncertainty into evolutionary models is essential for enhancing their relevance to real-world problems. In this perspective article, we survey the relevant literature on evolutionary dynamics with random payoff matrices, with an emphasis on continuous models. We also pose challenging open problems for future research in this important area.

In this short review article, we present recent progress in quantum thermodynamics in the framework with a correlated catalyst. We examine two key properties of thermal operations, the Gibbs-preserving property and the covariant property. The state convertibility of a Gibbs-preserving operation is fully characterized by the second law of thermodynamics with the nonequilibrium free energy. The state convertibility of a covariant operation is shown to be free as long as an initial state has finite coherence. We finally show that these two findings can be combined in the enhanced thermal operation (covariant Gibbs-preserving operation).

Fairness stands as a pivotal element in maintaining social stability. It is still a highly challenging issue to explain how fairness emerges in society. The ultimatum game (UG) and the dictator game (DG) have become prominent paradigms for exploring the emergence of fairness. A great number of mechanisms have been put forward to promote the emergence of fairness in these two games. In this paper, we sort out the recent relevant evolutionary game models regarding fairness and categorize them according to the mechanisms for the emergence of fairness. The main mechanisms consist of network reciprocity, role assignment, spite, empathy, stake size, and indirect reciprocity. Especially for indirect reciprocity, we make a detailed introduction of a theoretical method and some recent works that use this theoretical approach to explore how fairness evolves. Finally, we suggest several potential avenues for future research.

Heavy truck mobility is crucial in serving urban freight supply and demand, but it can also lead to traffic accidents, high energy consumption and pollutant emissions. Exploring the statistical characteristics of heavy truck mobility is highly important for efficiently managing cities and enhancing sustainable urban development. In this paper, we review some scaling laws of urban heavy truck mobility, including the allometry of urban heavy truck mobility and some scaling laws observed in collective mobility networks and individual mobility trajectories of urban heavy trucks. We also introduce models that explain the underlying mechanisms of these scaling laws. We further provide an outlook for future research on urban heavy truck mobility.

Fundamental laws of physics are symmetric under time reversal (T) symmetry, but the T symmetry is strongly broken in the macroscopic world. In this Perspective, I review T symmetry breaking frameworks: second law of thermodynamics, multiscale energy transfer, and open systems. In driven dissipative nonequilibrium systems, including turbulence, the multiscale energy flux from large scales to small scales helps determine the arrow of time. In addition, open systems are often irreversible due to particle and energy exchanges between the system and the environment. Causality is another important factor that breaks the T symmetry.

While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems —from the way legal texts are drafted and connected to the rest of the corpus, up to the level of how judges and courts reach decisions under a variety of conflicting inputs— share several features with standard Complex Adaptive Systems. This review is meant as a gentle introduction to the use of quantitative tools and techniques of complexity science to describe, analyse, and tame the complex web of human interactions that the Law is supposed to regulate. We offer an overview of the main directions of research undertaken so far as well as an outlook for future research, and we argue that statistical physicists and complexity scientists should not ignore the opportunities offered by the cross-fertilisation between legal scholarship and complex-systems modelling.

A unique combination of unusual magnetic properties, such as magnetic bistability associated with ultrafast domain wall propagation or ultrasoft magnetic properties, together with excellent mechanical and corrosion properties can be obtained in amorphous microwires. Such ferromagnetic microwires coated with insulating and flexible glass-coating with diameters ranging from 0.1 to 100 $\mu \textrm {m}$ can be prepared using the Taylor-Ulitovsky method. Magnetic properties of glass-coated microwires are affected by chemical compositions of the metallic nucleus and can be substantially modified by post-processing. We provide an overview of the routes allowing tuning of hysteresis loops and domain wall dynamics in amorphous microwires and new experimental results on the dependence of hysteresis loops on external stimuli, such as applied stress and temperature.

Network percolation is one of the core topics in network science, especially in understanding and optimizing the robustness of real-world networks. As a powerful tool, the message-passing approach shows unique advantages in characterizing network percolation compared with the mean-field approach. This approach simulates the behavioural response when the network is damaged by transmitting and updating messages between network nodes, thereby accurately assessing the robustness of the network. This paper reviews the progress of message-passing approaches in network percolation on simple networks, multilayer networks and higher-order networks in recent years and discusses the application of this approach in other research fields. Finally, we discuss future research directions around this approach.

Fueled by the rapid pace of technological advancements, the convergence of ideas from optics and solid-state physics is yielding valuable insights into the fundamental principles governing interactions between light and matter at the nanoscale, as well as paving the way for future technologies. In this review, we explore a burgeoning avenue that investigates the synergy between plasmonics and optical vortex concepts. The excitation of plasmon modes with phase dislocations, occasionally referred to as plasmonic vortices, has revealed novel facets of physics. One particularly promising expansion of this field pertains to the manipulation of nearby nanostructures. Consequently, we provide commentary on the associated research, which offers innovative solutions to a variety of technological challenges.

The aim of this short review is to summarize the developing theory aimed at describing the effect of plastic events in amorphous solids on its emergent mechanics. Experiments and simulations present anomalous mechanical response of amorphous solids where quadrupolar plastic events collectively induce distributed dipoles that are analogous to dislocations in crystalline solids. The novel theory is described, and a number of pertinent examples are provided, including the comparison of theoretical prediction to simulations or experiments.

Schrödinger's equation is a local differential equation and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a given Hamiltonian may describe several different physically observable phases, each exhibiting its own characteristic global symmetry.

Complex networks can effectively describe interactions within real-world complex systems. In researches of epidemic spreading, scientists constructed various physical contact networks between individuals on the microscopic scale and the metapopulation networks on the macroscopic scale. These different types of network structures significantly impact the propagation dynamics of epidemic in human society. For instance, population flows in global airline networks influence the speed and arrival time of epidemics across large-scale space. In this paper we review the epidemic spreading models on various network structures, including fully mixed networks, three types of lower-order networks, three types of higher-order networks, metapopulation networks, and multiple strains competitive epidemic spreading models. We also provide an overview of the application of complex network theory in the COVID-19 pandemic, covering topics of prediction, prevention, and control of the epidemic. Finally, we discuss the strengths and limitations of these models and propose perspectives for future research.

This paper delves into the frontier of degradation of coral reef ecosystems, a pressing urgent issue to be addressed given the escalating threats faced by the crucial marine environments, and provides a critical assessment of recent advances, emerging trends, and valuable perspective on the studies employing mathematical-dynamical modeling approaches. This study highlights the recent developments in coral bleaching, coral-algal phase shifts, coral disease, and natural enemy bloom, all of which are thoroughly documented and comprehensively expounded. This review study also offers some valuable insights, illuminating ideas, and clear perspective into some current, emerging, and promising research directions for future studies, particularly those based on mathematical and biological modeling. These approaches are anticipated to offer a robust theoretical framework and provide crucial decision-making reference for the protection, restoration, and management of coral reef ecosystems.

In recent years, the interdisciplinary study of complex networks has become increasingly important in fields ranging from biology and physics to sociology and mathematics. This paper focuses on pinning control, an approach essential for achieving coordinated behavior in dynamic networks. We explore recent advancements in pinning control strategies, explaining theoretical frameworks and simulation techniques. Additionally, we discuss the significance of certain structures within networks across different orders. Finally, we conclude with a summary of key insights and propose our outlook on future research.

The discovery of topological semimetals with multifold band crossings has opened up a new and exciting frontier in the field of topological physics. These materials exhibit large Chern numbers, leading to long double Fermi arcs on their surfaces, which are protected by either crystal symmetries or topological order. The impact of these multifold crossings extends beyond surface science, as they are not constrained by the Poincar classification of quasiparticles and only need to respect the crystal symmetry of one of the 1651 magnetic space groups. Consequently, we observe the emergence of free fermionic excitations in solid-state systems that have no high-energy counterparts, protected by non-symmorphic symmetries. In this work, we review the recent theoretical and experimental progress made in the field of multifold topological semimetals. We begin with the theoretical prediction of the so-called multifold fermions and discuss the subsequent discoveries of chiral and magnetic topological semimetals. Several experiments that have realized chiral semimetals in spectroscopic measurements are described, and we discuss the future prospects of this field. These exciting developments have the potential to deepen our understanding of the fundamental properties of quantum matter and inspire new technological applications in the future.

Raman scattering is the inelastic process where photons bounce off molecules, losing energy and becoming red-shifted. This weak effect is unique to each molecular species, making it an essential tool in, e.g., spectroscopy and label-free microscopy. The invention of the laser enabled a regime of stimulated Raman scattering (SRS), where the efficiency is greatly increased by inducing coherent molecular oscillations. However, this phenomenon required high intensities due to the limited interaction volumes, and this limitation was overcome by the emergence of anti-resonant fibres (ARFs) guiding light in a small hollow channel over long distances. Based on their unique properties, this Perspective reviews the transformative impact of ARFs on modern SRS-based applications ranging from development of light sources and convertors for spectroscopy and materials science, to quantum technologies for the future quantum networks, providing insights into future trends and the expanding horizons of the field.

We give an overview exploring the role of kinetics in multicomponent mixtures. Compared to the most commonly studied binary (single species plus solvent) case, multicomponent fluids show a rich interplay between kinetics and thermodynamics due to the possibility of fractionation, interdiffusion of mixture components and collective motion. This leads to a competition between multiple timescales that change depending on the underlying kinetics. At high densities, crowding effects are relevant and non-equilibrium structures can become long-lived. We present the main approaches for the study of kinetic effects in multicomponents mixtures, including the role of crowding, and explore their consequences for equilibrium and non-equilibrium scenarios. We conclude by identifying the main challenges in the field.

Rényi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the Rényi entropy are not widely known. In this paper, we discuss some basic properties of the Rényi entropy relevant to physics, in particular statistical mechanics, and its physical interpretations using free energy, replicas, work, and large deviation.

Network resilience measures complex systems' ability to adjust its activity to retain the basic functionality for systematic errors or failures, which has attracted increasingly attention from various fields. Resilience analyses play an important role for early warning, prediction, and proposing potential strategies or designing optimal resilience systems. This letter reviews the advanced progress of network resilience from three aspects: Resilience measurement, resilience analysis, as well as resilience recovery strategies. We outline the challenges of network resilience which should be investigated in the future.

It is well known that synchronization patterns and coherence have a major role in the functioning of brain networks, both in pathological and in healthy states. In particular, in the perception of sound, one can observe an increase in coherence between the global dynamics in the network and the auditory input. In this perspective article, we show that synchronization scenarios are determined by a fine interplay between network topology, the location of the input, and frequencies of these cortical input signals. To this end, we analyze the influence of an external stimulation in a network of FitzHugh-Nagumo oscillators with empirically measured structural connectivity, and discuss different areas of cortical stimulation, including the auditory cortex.

The ubiquity of labor division within diverse social collectives is a topic well captured by evolutionary game theory. This work offers an integrative review of the evolutionary dynamics underpinning such division of labor from a tripartite standpoint —commencing with a theoretical exposition on numerous archetypes of labor division games. Subsequently, we delineate a suite of control strategies formulated to not only realize but also sustain the phenomenon of division of labor. This is followed by an elucidation of practical implementations pertaining to the allocation of tasks and labor division, grounded in the principles of game theory. We culminate with the proposition of prospective avenues and insightful trajectories for future investigations, cultivating a frontier for the continued exploration within this field.

Recent advances in quantum information science have shed light on the intricate dynamics of quantum many-body systems, for which quantum information scrambling is a perfect example. Motivated by considerations of the thermodynamics of quantum information, this perspective aims at synthesizing key findings from several pivotal studies and exploring various aspects of quantum scrambling. We consider quantifiers such as the out-of-time-ordered correlator (OTOC) and the quantum mutual information, their connections to thermodynamics, and their role in understanding chaotic vs. integrable quantum systems. With a focus on representative examples, we cover a range of topics, including the thermodynamics of quantum information scrambling, and the scrambling dynamics in quantum gravity models such as the Sachdev-Ye-Kitaev (SYK) model. Examining these diverse approaches enables us to highlight the multifaceted nature of quantum information scrambling and its significance in understanding the fundamental aspects of quantum many-body dynamics at the intersection of quantum mechanics and thermodynamics.

In the face of persistent threats posed by infectious diseases, despite remarkable medical advancements, understanding and efficiently controlling their spatial spread through mathematical modeling remain imperative. Networked reaction-diffusion systems offer a promising avenue to effectively delineate population discrete distribution and individual movement heterogeneity. However, the dynamics of spatial diseases within these systems and the formulation of optimal control strategies are currently undergoing vigorous development. In this letter, we illustrate the dynamics of spatial disease spread in networked reaction-diffusion systems through the lens of optimal control, considering various network complexities from pairwise networks to higher-order networks. It then emphasizes their applicability in designing effective spatial disease control strategies across diverse network complexities. Finally, we discuss the existing challenges.

Conventional models of decision-making are predicated upon the notion of rational deliberation. However, empirical evidence has increasingly highlighted the pervasive role of bounded rationality in shaping decisional outcomes. The manifestation of bounded rationality is evident through a spectrum of cognitive biases and heuristics, including but not limited to anchoring, availability, the decoy effect, herd behavior, and the nuanced dynamics of reward and punishment, as well as the implications of weighting and framing effects. This prospective study is dedicated to a comprehensive exploration of such multiple factors together with their impacts to the architecture and functionality of decision-making processes, and their further research potentials as well.

Light is characterized by its electric field, yet quantum optics has revealed the importance of monitoring photon-photon correlations at all orders. We here present a comparative study of two experimental setups, composed of cold and warm rubidium atoms, respectively, which allow us to probe and compare photon correlations. The former operates in the quantum regime where spontaneous emission dominates, whereas the latter exhibits a temperature-limited coherence time. We demonstrate our capability to measure photon correlations up to the fourth order which could be useful to better characterize light scattered by cold atoms beyond the chaotic statistics.

Network science has already been fruitful and confirmed effective on the description of real-world or abstract systems. An increasing number of researches and instances have successfully verified, however, that interactions in systems may occur among three, four, or even more components. The introduction of higher-order perspective brings a revolution on network science, and refreshes researchers' understanding of synchronization. Hence, an overview is presented here in regard of synchronization on higher-order networks. We start from an introduction of how the higher-order networks are represented using algebraic tools. Then a series of landmark researches on synchronization is reviewed under circumstances of whether or not the dynamics contains control. Finally, we summarize our conclusions and propose our outlooks on expectations of future works.

The growth of interfacial instabilities during fluid displacements can be driven by gradients in pressure, viscosity and surface tension, and by applying external fields. Since displacements of non-Newtonian fluids such as polymer solutions, colloidal and granular slurries are ubiquitous in natural and industrial processes, understanding the growth mechanisms and fully developed morphologies of interfacial patterns involving non-Newtonian fluids is extremely important. In this perspective, we focus on displacement experiments, wherein competitions between capillary, viscous, elastic and frictional forces drive the onset and growth of primarily viscous fingering instabilities in confined geometries. We conclude by highlighting several exciting open problems in this research area.

Understanding the dynamics of material objects advected by turbulent flows is a long-standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting finite-sized massive spherical particles advected by a vigorous turbulent flow. We study the fluctuations and temporal correlations of particle accelerations and explore their behaviours with respect to the particle size and the particle mass density by means of fully resolved numerical simulations. We observe that the measured trends cannot be interpreted as the simple multiplicative combination of the two dominant effects: the spatial filtering of fluid accelerations and the added-mass–adjusted fluid-to-particle density ratio. We argue that other hydrodynamical forces or effects, e.g., preferential flow sampling, have still a significant role even at the largest particle sizes, which reach here the integral scale of turbulence.

The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in an internal or external degree of freedom that differs from spatial position, can greatly simplify the simulation of gauge fields and give access to exotic topological states. We review here recent advances in the field and discuss future perspectives.

The growth of interfacial instabilities during fluid displacements can be driven by gradients in pressure, viscosity and surface tension, and by applying external fields. Since displacements of non-Newtonian fluids such as polymer solutions, colloidal and granular slurries are ubiquitous in natural and industrial processes, understanding the growth mechanisms and fully developed morphologies of interfacial patterns involving non-Newtonian fluids is extremely important. In this perspective, we focus on displacement experiments, wherein competitions between capillary, viscous, elastic and frictional forces drive the onset and growth of primarily viscous fingering instabilities in confined geometries. We conclude by highlighting several exciting open problems in this research area.

Ultracold atoms carrying Orbital Angular Momentum (OAM) loaded in lattices constitute a promising platform for engineering topological systems either at the single-particle limit or in the presence of interactions. In this review, we report recent progress on this topic with the focus on bosons with OAM l = 1 in lattices of coplanar ring potentials, which provide an ideal scenario to realise topological non-trivial phases of matter.

Neurological disorders place a significant burden on patients, their families, and society, posing immense scientific challenges in terms of treatment and mechanistic research. Neuromodulation involves the application of invasive or non-invasive technologies to externally manipulate the nervous system of the brain, aiming to provide excitatory or inhibitory modulation that can improve abnormal neural activity. In the previous studies, neurodynamic analysis methods have not only provided novel tools for the study of neuromodulation techniques, but also provided new modulation strategies for the diagnosis and treatment of neurological diseases. In this paper, we present a brief overview of the current state of dynamic modeling and analysis for various neuromodulation techniques, including electrical, optical, magnetical, and ultrasonic approaches, and discuss the future prospects of modeling and analysis developments in neuromodulation.

We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms.

Coupled propagation dynamics based on complex networks have received widespread attention in recent years. This work reviews the research work related to coupling propagation dynamics on single-layer complex networks, multi-layer complex networks and high-order complex networks. We sort out relevant research results from three aspects: competitive propagation, cooperative propagation and asymmetric coupled propagation, finding that different coupling mechanisms focus on different dynamic properties. The dynamic characteristics such as coexistence threshold in competitive propagation, discontinuous phase transition in cooperative propagation, outbreak threshold and propagation prevalence in asymmetric coupling propagation have been extensively discussed. We conclude by giving some valuable future research topics in coupled propagation dynamics.

Individuals often engage in complex, non-isolated interactive environments. The interdependence manifested by strategic interaction environments across multiple dimensions or attributes has advanced the recognition of correlated games. The behavioral choices in one strategic scenario can be influenced by strategic attempts in another. How the correlation between different strategic environments affects the cooperation dynamics has raised much attention recently. In this perspective, we overview the latest progress that accounts for such cross-reciprocity. Firstly, we focus on the cases where individuals consecutively interact in environments with varying payoff structures, the values of which depend on the behaviors present in the previous game. Secondly, we pay attention to how strategic interaction affects the dynamics in multi-issue games in which individuals simultaneously interact in different environments. It holds significant implications for further examining the evolution of behavior from the perspective of correlations between different scenarios. Finally, we come up with some potential directions and points for further research.

We discuss a simple yet powerful control technique called "Linear Augmentation" (LA) for nonlinear dynamical systems. The linear augmentation can be perceived as a type of interaction that may occur naturally in dynamical systems as an environmental effect, or can be explicitly added to a system in order to control its collective dynamical behavior. LA has been known to effectively regulate resulting dynamics of various dynamical systems and can be used as a powerful control strategy in various applications. Examples include targeting attractor(s), regulating multistable dynamics, suppression of extreme events, and controlling chimera states in the nonlinear dynamical systems.

We investigate the way the entropy of a system can be partitioned into the entropies of its constituents in consistency with thermodynamics. This partitioning is described through the concept of an entropy defect, which measures the missing entropy between the sum of entropies of a system's constituents and the entropy of the combined system; this decrease of entropy corresponds to the order induced by the additional long-range correlations developed among the constituents of the combined system. We conclude that the most generalized addition rule is the one characterizing the kappa entropy; when the system resides in stationary states, the kappa entropy becomes the one associated with kappa distributions, while, in general, this entropy applies more broadly, in stationary or nonstationary states. Moreover, we develop the specific algebra of the addition rule with entropy defect. The addition rule forms a mathematical group on the set of any measurable physical-quantity (e.g., entropy). Finally, we use these algebraic properties to restate the generalized zeroth law of thermodynamics so that it is applicable for nonstationary as well as stationary states: If a body C measures the entropies of two other bodies, A and B, then, their combined entropy is measured as the connected A and B entropy, where the entropy defect is involved in all measurements.

The inference of network structure from dynamic data is one of the most challenging scientific problems in network science. To address this issue, researchers have proposed various approaches regarding different types of dynamical data. Since many real evolution processes or social phenomena can be described by discrete state dynamical systems, such as the spreading of epidemic, the evolution of opinions, and the cooperation behaviors, network reconstruction methods driven by discrete state dynamical data were also widely studied. In this letter, we provide a mini-review of recent progresses for reconstructing networks based on discrete state dynamical data. These studies encompass network reconstruction problems where the dynamical processes are known, as well as those where the dynamics are unknown, and extend to the reconstruction of higher-order networks. Finally, we discuss the remaining challenges in this field.

Machine learning is a rapidly growing field with the potential to revolutionize many areas of science, including physics. This review provides a brief overview of machine learning in physics, covering the main concepts of supervised, unsupervised, and reinforcement learning, as well as more specialized topics such as causal inference, symbolic regression, and deep learning. We present some of the principal applications of machine learning in physics and discuss the associated challenges and perspectives.

Our ability to observe the mesoscale topology of complex networks through community detection has significantly advanced in the past decades. This progress has opened up new frontiers in discovering more sophisticated and meaningful community structures that possess fuzzy and higher-order characteristics. This review provides an overview of two emerging research directions, which are fuzzy and higher-order community detection. It includes related concepts and practical scenarios, mathematical descriptions and latest advancements, as well as current challenges and future directions. Therefore, it will facilitate researchers in swiftly grasping the two emerging fields, offering valuable insights for future development of community detection studies.

Committed individuals, who feature steadfast dedication to advocating strong beliefs, values, and preferences, have garnered much attention across statistical physics, social science, and computer science. This survey delves into the profound impact of committed individuals on social dynamics that emerge from coordination games and social dilemma games. Through separate examinations of their influence on coordination, including social conventions and color coordination games, and social dilemma games, including one-shot settings, repeated settings, and vaccination games, this survey reveals the significant role committed individuals play in shaping social dynamics. Their contributions range from accelerating or overturning social conventions to addressing cooperation dilemmas and expediting solutions for color coordination and vaccination issues. Furthermore, the survey outlines three promising directions for future research: conducting human behavior experiments for empirical validation, leveraging advanced large language models as proxies for committed individuals in complex scenarios, and addressing the potential negative impacts of committed individuals.

We review the recent progress of epidemic dynamics in metapopulation networks. Firstly, we give an introduction of the concepts about epidemic models and metapopulation network. Then, the theoretical characterization of epidemics spread in metapopulation networks is summed up. The measures of how to curb the spread of epidemics are summarized. The applications of inferring epidemic pathways based on epidemic data and reconstruction of epidemic transmission by phylogeographic are introduced. Finally, we present the outlooks about further research of epidemic dynamics on metapopulation networks.

We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, along with their potential merits and liabilities, are discussed and commented on.

In this perspective paper, we look into memory effects in out-of-equilibrium systems. To be concrete, we exemplify memory effects with the paradigmatic case of granular fluids, although extensions to other contexts such as molecular fluids with non-linear drag are also considered. The focus is put on two archetypal memory effects: the Kovacs and Mpemba effects. In brief, the first is related to imperfectly reaching a steady state —either equilibrium or non-equilibrium—, whereas the second is related to reaching a steady state faster despite starting further. Connections to optimal control theory thus naturally emerge and are briefly discussed.

We review the recent progress of epidemic dynamics in metapopulation networks. Firstly, we give an introduction of the concepts about epidemic models and metapopulation network. Then, the theoretical characterization of epidemics spread in metapopulation networks is summed up. The measures of how to curb the spread of epidemics are summarized. The applications of inferring epidemic pathways based on epidemic data and reconstruction of epidemic transmission by phylogeographic are introduced. Finally, we present the outlooks about further research of epidemic dynamics on metapopulation networks.

Committed individuals, who feature steadfast dedication to advocating strong beliefs, values, and preferences, have garnered much attention across statistical physics, social science, and computer science. This survey delves into the profound impact of committed individuals on social dynamics that emerge from coordination games and social dilemma games. Through separate examinations of their influence on coordination, including social conventions and color coordination games, and social dilemma games, including one-shot settings, repeated settings, and vaccination games, this survey reveals the significant role committed individuals play in shaping social dynamics. Their contributions range from accelerating or overturning social conventions to addressing cooperation dilemmas and expediting solutions for color coordination and vaccination issues. Furthermore, the survey outlines three promising directions for future research: conducting human behavior experiments for empirical validation, leveraging advanced large language models as proxies for committed individuals in complex scenarios, and addressing the potential negative impacts of committed individuals.

We review the generalization of tunneling time and anomalous behaviour of Faraday and Kerr rotation angles in parity and time $(\mathcal {P}\mathcal {T})\text{-symmetric}$ systems. Similarities of two phenomena are discussed, both exhibit a phase transition-like anomalous behaviour in a certain range of model parameters. Anomalous behaviour of tunneling time and Faraday/Kerr angles in $\mathcal {P}\mathcal {T}\text{-symmetric}$ systems is caused by the motion of poles of scattering amplitudes in the energy/frequency complex plane.

This article contains our comments and views on the status of the current understanding of phase transitions in systems in thermodynamic equilibrium with only hard-core interactions, based on our work in this area. The equation of state for the hard sphere gas in d-dimensions is discussed. The universal repulsive Lee-Yang singularity in the complex activity plane, and its relation to the directed and undirected polymer models are outlined. We also discuss orientationally disordered crystalline mesophases, and some of their models.

In this article, we report some examples of how high-energy electron irradiation can be used as a tool for shaping material properties turning the generation of point-defects into an advantage beyond the presumed degradation of the properties. Such an approach is radically different from what often occurs when irradiation is used as a test for radiation hard materials or devices degradation in harsh environments. We illustrate the potential of this emerging technique by results obtained on two families of materials, namely semiconductors and superconductors.

Being the world's most popular sport, football research has traditionally concentrated on empirical summaries or statistics, with only limited data available in the past. In recent years, social network analysis has been applied to a variety of fields, which also brings new perspectives to the study of football sports. In this paper, we survey the literature related to football networks and discuss the use of network measures to analyze the performance of footballers and teams in different types of football networks. We aim to find out how to construct appropriate football networks based on different perspectives on football research. Various studies on football network analysis, including team performance, player interactions, and club behavior, are reviewed. The findings provide insights into team performance, player roles, and social dynamics within football teams and clubs.

Molecular dynamics (MD) and Monte Carlo (MC) have long coexisted as two main independent branches of molecular simulation. In the late eighties, however, algorithms based on the combination of both were created such as hybrid Monte Carlo which uses large MD steps as MC moves. An entirely different kind of combination emerged a decade later via the transition path sampling (TPS) method in which MD trajectories are not just part of the MC move, but also form the state space being sampled. Algorithms like replica exchange transition interface sampling (RETIS) exploit this idea to compute reaction rates via a series of TPS simulations. RETIS yields results identical to hypothetical long MD runs, but with exponentially reduced computation time. This perspective describes the RETIS method and discusses recent and future advancements that will enable the study of even longer molecular timescales with reasonable computational resources.

We review the physics of coherent elastic neutrino-nucleus scattering and the results and perspectives for the measurements of the radius of the neutron distribution of the nucleus, of the weak mixing angle, and of new neutrino interactions due to physics beyond the Standard Model.

Since their first realization more than a decade ago spin-orbit-coupled Bose-Einstein condensates have been the subject of intense theoretical and experimental investigations. Spin-orbit coupling deeply modifies the equilibrium properties of the condensate, giving rise to novel configurations such as a supersolid stripe phase and a phase-separated plane-wave state. At the level of dynamics, both the frequency and the nature of the collective modes are significantly affected by the coupling with the spin degree of freedom. Here we review some of the most relevant advances in the field and provide our perspective on possible future research directions.

This perspective reviews the subject of synchronization in networks of coupled non-phase oscillators in the presence of parametric mismatches. We first discuss the case of small parametric mismatches, for which the conditions for stability of the synchronous solution are the same as in the case of identical oscillators, but the synchronization error increases with the size of the mismatches. We then analyze the case of larger parameter mismatches and provide an explanation for why parameter mismatches sometimes hinder and sometimes enhance stability of the synchronous solution.

Although the long-term behavior of stochastic evolutionary game dynamics in finite populations has been fully investigated, its evolutionary characteristics in a limited period of time is still unclear. In order to answer this question, we introduce the formulation of the path integral approach for evolutionary game theory. In this framework, the transition probability is the sum of all the evolutionary paths. The path integral formula of the transition probability is expected to be a new mathematical tool to explore the stochastic game evolutionary dynamics. As an example, we derive the transition probability for stochastic evolutionary game dynamics by the path integral in a limited period of time with the updating rule of the Wright-Fisher process.

Classically forbidden regions (CFRs) are common to both non-relativistic quantum mechanics, and to relativistic quantum field theory. It is known since 2001 that CFR contributes roughly sixteen percent of energy to the ground state of a simple harmonic oscillator (Adunas G. Z. et al., Gen. Relativ. Gravit., 33 (2001) 183). Similarly, quantum field theoretic arguments yield a non-zero amplitude for a massive particle to cross the light cone (that is, into the CFR). The signs of these amplitudes are opposite for fermions and antifermions. This has given rise to an erroneous conclusion that amplitude to cross the light cone is identically zero. This is true as long as a measurement does not reveal the considered object to be a particle or antiparticle. However, neutrino oscillation experiments do measure a neutrino ν, or an antineutrino $\bar \nu$. Here we show that in the context of neutrino oscillations these observations have the potential to resolve various short baseline anomalies for a sufficiently light lowest mass eigenstate. In addition, we make a concrete prediction for the upcoming results to be announced later this year by JSNS².

In recent years the fluid mechanics community has been intensely focused on pursuing solutions to its long-standing open problems by exploiting the new machine learning (ML) approaches. The exchange between ML and fluid mechanics is bringing important paybacks in both directions. The first is benefiting from new physics-inspired ML methods and a scientific playground to perform quantitative benchmarks, whilst the latter has been open to a large set of new tools inherently well suited to deal with big data, flexible in scope, and capable of revealing unknown correlations. A special case is the problem of modeling missing information of partially observable systems. The aim of this paper is to review some of the ML algorithms that are playing an important role in the current developments in this field, to uncover potential avenues, and to discuss the open challenges for applications to fluid mechanics.

Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. We review the recent progress made on defining amorphous topological phases, their new phenomenology. We discuss the open questions in the field which promise to significantly enlarge the set of materials and synthetic systems benefiting from the robustness of topological matter.

Our ability to observe the network topology and nodes' behaviors of complex systems has significantly advanced in the past decade, giving rise to a new and fast-developing frontier—inferring the underlying dynamical mechanisms of complex systems from the observation data. Here we explain the rationale of data-driven dynamics inference and review the recent progress in this emerging field. Specifically, we classify the existing methods of dynamics inference into three categories, and describe their key ideas, representative applications and limitations. We also discuss the remaining challenges that are worth the future effort.

Spreading dynamics is a common yet sophisticated phenomenon in real life, and percolation theory is widely applied in analysis of this dynamics due to its conciseness and efficiency. With the development of information technology, the quality and quantity of available data are being improved. Although this offers a chance to describe and understand empirical spreading phenomena more comprehensively and accurately, complicated dynamics brought by massive data pose new challenges to the study of social contagion based on percolation theory. In this prospective, we show, by analyzing examples, how the percolation theory is used to describe the information transmission on social networks driven by big data. We also explore the indirect influence mechanism behind the spread of scientific research behavior, and develop a new algorithm to quantify the global influence of nodes from the local topology. Finally, we propose, based on these example studies, several possible new directions of percolation theory in the study of social contagion driven by big data.

Soft Glassy Materials (SGM) consist in dense amorphous assemblies of colloidal particles of multiple shapes, elasticity, and interactions, which confer upon them solid-like properties at rest. They are ubiquitously encountered in modern engineering, including additive manufacturing, semi-solid flow cells, dip coating, adhesive locomotion, where they are subjected to complex mechanical histories. Such processes often include a solid-to-liquid transition induced by large enough shear, which results in complex transient phenomena such as non-monotonic stress responses, i.e., stress overshoot, and spatially heterogeneous flows, e.g., shear banding or brittle failure. In the present article, we propose a pedagogical introduction to a continuum model based on a spatially resolved fluidity approach that we recently introduced to rationalize shear-induced yielding in SGMs. Our model, which relies upon non-local effects, quantitatively captures salient features associated with such complex flows, including the rate dependence of the stress overshoot, as well as transient shear-banded flows together with non-trivial scaling laws for fluidization times. This approach offers a versatile framework to account for subtle effects, such as avalanche-like phenomena, or the impact of boundary conditions, which we illustrate by including in our model the elasto-hydrodynamic slippage of soft particles compressed against solid surfaces.

Multi-terminal Josephson junctions were recently proposed as a versatile and tunable platform to emulate topological Bloch-like Hamiltonians in arbitrary dimensions. In this perspective article, we will give a brief overview of the subject and recognize these mesoscopic devices as realizations of topological flux networks as the ones envisioned by Avron and coworkers in their seminal works on the early days of the quantum Hall effect. We summarize the current state-of-the-art theoretical and experimental research regarding these Josephson devices, highlighting recent developments and giving an outlook on current trends.

The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics. Furthermore, it has provided a natural framework to study basins of attraction in nonlinear dynamics and new criteria for the detection of fractal boundaries. In this article, we describe the concept as well as fundamental applications. In addition, we provide our perspective on the future challenges of applying the basin entropy idea to understanding complex systems.

In this survey, we briefly review some recent advances in the field of indirect reciprocity and reputation mechanism along the routes of theoretical modeling and behavior experiments. Firstly, various game models with reputation evaluation are proposed, and large quantities of numerical simulations demonstrate that introducing the reputation evaluation drastically enhances the level of collective cooperation within the population. In particular, the so-called leading eight rules are found to be evolutionarily stable strategies. Secondly, through extensive human experiments played in the laboratory or via the online labor market, it is validated that providing enough information on the individual strategy or reputation status will help players to select the cooperative partners or perform the rational decision, which eventually facilitates the evolution of cooperation, but some experiments also indicate that allowing the link rewiring may dominate the human cooperation. Finally, several potential and valuable directions are pointed out so as to further explore how the cooperation evolves within the real-world population.

Whispering-gallery mode (WGM) cavities formed by dielectric structures have attracted intensive interest in various fields. The high-quality factor and smaller mode volume associated with the optical modes have inspired experiments in nonlinear optics, nanophotonics, and quantum information science. Moreover, they are also used in optical biosensors and other significant applications. To further reduce the material loss of the resonator, optical gain materials, such as erbium and ytterbium, are doped into the dielectric structure to increase the nonlinear effect and enhance the interaction between light and matter. Here in this review, we outline the most recent advancements in gain-doped optical WGM microcavities. Moreover, we introduce the dynamics of the gain in WGM resonators, the integration of gain media into WGM microcavities with various shapes, and the fabrication and applications of the gain microcavities. Also, the applications of the gain cavity based on the whispering-gallery mode have been introduced, e.g., ultra-sensitive sensors, low-threshold lasers, and high-performance optical systems.

In neural network's literature, Hebbian learning traditionally refers to the procedure by which the Hopfield model and its generalizations store archetypes (i.e., definite patterns that are experienced just once to form the synaptic matrix). However, the term learning in machine learning refers to the ability of the machine to extract features from the supplied dataset (e.g., made of blurred examples of these archetypes), in order to make its own representation of the unavailable archetypes. Here, given a sample of examples, we define a supervised learning protocol based on Hebb's rule and by which the Hopfield network can infer the archetypes. By an analytical inspection, we detect the correct control parameters (including size and quality of the dataset) that tune the system performance and we depict its phase diagram. We also prove that, for structureless datasets, the Hopfield model equipped with this supervised learning rule is equivalent to a restricted Boltzmann machine and this suggests an optimal and interpretable training routine. Finally, this approach is generalized to structured datasets: we highlight an ultrametric-like organization (reminiscent of replica-symmetry-breaking) in the analyzed datasets and, consequently, we introduce an additional broken-replica hidden layer for its (partial) disentanglement, which is shown to improve MNIST classification from $\sim 75\%$ to $\sim 95\%$, and to offer a new perspective on deep architectures.

Like their electronic counterparts, photonic integrated circuits face the challenge of further integration and miniaturization. One of the fundamental limitations comes from waveguide spacing, which leads to serious crosstalk between the neighboring waveguides when it is less than half a wavelength. Here we demonstrate a potential approach to remove this limitation and realize zero-spacing photonic waveguides with extreme compactness. This is achieved by designing pure-dielectric photonic crystal waveguides with shifted spatial dispersion and arranging them with normal dielectric waveguides alternately. Amazingly, the coupling and crosstalk between the two types of waveguides are negligible despite the zero spacing between them. Through proper designs, zero-spacing photonic bending waveguides and circuits can also be realized in practice. Such a finding opens a new avenue for ultra-compact photonic waveguides and circuits with 100% space utilization efficiency.

Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this Perspective, we review a line of works dealing with measurements that reveal structural properties of quantum datasets given in the form of product states. These algorithms are universal, meaning that their performances do not depend on the reference frame in which the dataset is provided. Requiring the universality property implies a characterization of optimal measurements via group representation theory.

Metamaterials have shown potential for next-generation optical materials since they have special electromagnetic responses which cannot be obtained in natural media. Among various metamaterials, hyperbolic metamaterials (HMMs) with highly anisotropic hyperbolic dispersion provide new ways to manipulate electromagnetic waves. Besides, graphene has attracted lots of attention since it possesses excellent optoelectronic properties. Graphene HMMs combine the extraordinary properties of graphene and the strong light modulation capability of HMMs. The experimental fabrication of graphene HMMs recently proved that graphene HMMs are a good platform for terahertz optical devices. The flexible tunability is a hallmark of graphene-based HMMs devices by external gate voltage, electrostatic biasing, or magnetic field, etc. This review provides an overview of up-to-now studies of graphene HMMs and an outlook for the future of this field.

By exploiting the freedom in defining the dual of spinors, we report an unexpected theoretical discovery of a quantum field theory of spin-half bosons. It fulfils Dirac's 1969-70 observation that "there must be boson variables connected with electrons". The theory is local, Lorentz invariant, and has a positive-definite Hamiltonian. We formulate the unitarity-preserving scattering theory to accommodate the new dual and the associated adjoint. A model of Yukawa interaction with spin-half bosons and fermions of equal masses is studied to explicitly show unitarity.

Basic models which give rise to one- and two-dimensional (1D and 2D) solitons, such as the Gross-Pitaevskii (GP) equations for BEC, feature the Galilean invariance, which makes it possible to generate families of moving solitons from quiescent ones. A challenging problem is to find models admitting stable self-accelerating (SA) motion of solitons. SA modes are known in linear systems in the form of Airy waves, but they are poorly localized states. This brief review presents two-component BEC models which make it possible to predict SA solitons. In one system, a pair of interacting 1D solitons with opposite signs of the effective mass is created in a binary BEC trapped in an optical-lattice potential. In that case, opposite interaction forces, acting on the solitons with positive and negative masses, produce equal accelerations, while the total momentum is conserved. The second model is based on a system of GP equations for two atomic components, which are resonantly coupled by a microwave field. The latter model produces an exact transformation to an accelerating references frame, thus predicting 1D and 2D stable SA solitons, including vortex rings.

Over the most recent twenty years, network science has bloomed and impacted different fields such as statistical physics, computer science, sociology, and so on. Studying the percolation behavior of a network system has a very important role in vital nodes identification, ranking, network resilience, and propagation behavior of networks. When a network system undergoes failures, network connectivity is broken. In this perspective, the percolation behavior of the giant connected component and finite-size connected components is explored in depth from the macroscopic and meso-microscopic views, respectively. From a macro perspective, a single network system always shows second-order phase transitions, but for a coupled network system, it shows rich percolation behaviors for various coupling strength, coupling patterns and coupling mechanisms. Although the giant component accounts for a large proportion in the real system, it cannot be neglected that when the network scale is large enough, the scale of finite-size connected components has an important influence on network connectivity. We here systematically analyze the phase transition behaviors of finite-size connected components that are different from the giant component from a meso-microscopic perspective. Studying percolation behaviors from the macro and meso-micro perspectives is helpful for a comprehensive understanding of many fields of network science, such as time-series networks, adaptive networks, and higher-order networks. The intention of this paper is to provide a frontier research progress and promising research direction of network percolation from the two perspectives, as well as the essential theory of percolation transitions on a network system.

I review the role and meaning of the Anthropic Principle, particularly in its relevance to particle physics as that subject evolves. This is neither a technical paper nor a resource letter, but rather an easy introduction.

We studied the canonical structure of 2D F(R) gravity. Its equivalence with Jackiw-Teitelboim gravity is demonstrated when no matter is present. Then, due to AdS₂/CFT₁ correspondence, such F(R) gravity is equivalent to the Sachdev-Ye-Kitaev models. The singular $D\to 2$ limit of F(R) gravity is also studied. It is shown that in such a limit AdS₂/CFT₁ correspondence is not realized.

Swarmalators have emerged as a new paradigm for dynamical collective behavior of multi-agent systems due to the interplay of synchronization and swarming that they inherently incorporate. Their dynamics have been explored with different coupling topologies, interaction functions, external forcing, noise, competitive interactions, and from other important viewpoints. Here we take a systematic approach and review the collective dynamics of swarmalators analytically and/or numerically. Long-term states of position aggregation and phase synchronization are revealed in this perspective with some future problems.

In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in entangled macroscopic superposition states of the radiation.

The solutions of the Dirac equation are given in terms of bispinors, four-component objects which include both spin and chirality as internal degrees of freedom. For massive particles, the Dirac equation couples components of the bispinor with different chiralities, yielding chiral oscillations. This phenomenon can be particularly relevant for recent proposals aimed at measuring non-relativistic cosmic neutrinos, and can find analogies in Dirac-like systems, such as graphene. In this paper, a concise review of chiral oscillations is presented, including their description with the Dirac's equation dynamics and the underlying group structure. Two paradigmatic cases of chiral oscillations in physical systems are shown: the effects on lepton-antineutrino spin quantum correlations, and neutrino flavor oscillations. Finally, extensions of recent theoretical investigations as well as future research developments are discussed.

Usually, in order to compute an anomaly (be it chiral or trace) with a perturbative method, the lowest significant order is sufficient. With the help of gauge or diffeomorphism invariance it uniquely identifies the anomaly. This note is a short review of the ambiguities that arise in the calculation of trace anomalies, and is meant, in particular, to signal cases in which the lowest perturbative order is not enough to unambiguously identify a trace anomaly. This may shed light on some recent contradictory results.

Aqueous dielectrics are ubiquitous in soft- and bio-nano matter systems. The theoretical description of such systems in terms of continuum ("macroscopic") theory remains a serious challenge. In this perspective we first review the existing continuum phenomenological approaches that have been developed in the past decades. In order to describe a path to advance continuum theory beyond these approaches we then take recourse to the Onsager-Dupuis theory of the dielectric behaviour of ice, which, for the case of a solid dielectric, exemplified important conceptual issues we deem relevant for the development of a more fundamental continuum theory of liquid dielectrics. Subsequently, we discuss our recently proposed continuum field theory of structured dielectrics, which provides a generalized approach to the dielectric behavior of such systems.

Active matter is a term encompassing particle-based assemblies with some form of self-propulsion, including certain biological systems as well as synthetic systems such as artificial colloidal swimmers, all of which can exhibit a remarkable variety of new kinds of nonequilibrium phenomena. A wealth of non-active condensed matter systems can be described in terms of a collection of particles coupled to periodic substrates, leading to the emergence of commensurate-incommensurate effects, Mott phases, tribology effects, and pattern formation. It is natural to ask how such phases are modified when the system is active. Here we provide an overview and future directions for studying individual and collectively interacting active matter particles coupled to periodic substrates, where new types of commensuration effects, directional locking, and active phases can occur. Further directions for exploration include directional locking effects, the realization of active solitons or active defects in incommensurate phases, active Mott phases, active artificial spin ice, active doping transitions, active floating phases, active surface physics, active matter time crystals, and active tribology.

It is hard to overstate the importance that the concept of symmetry has had in every field of physics, a fact alluded to by the Nobel Prize winner P. W. Anderson, who once wrote that "physics is the study of symmetry". Whereas the idea of symmetry is widely used in science in general, very few (if not almost no) applications have found its way into the field of finance. Still, the phenomenon appears relevant in terms of for example the symmetry of strategies that can happen in the decision making to buy or sell financial shares. Game theory is therefore one obvious avenue where to look for symmetry but, as will be argued, also technical analysis and long-term economic growth could be phenomena which show the hallmark of a symmetry.

Evolutionary game theory is a powerful tool for studying the frequency-dependent selection, where the success of one strategy depends on the frequency of all strategies. The classic theoretical approach is the replicator equation, where the strategy evolution is deterministic for infinitely large populations. However for the stochastic evolutionary systems of finite populations, one of the most difficult obstacles lies in making qualitative or quantitative analytical deductions about evolutionary outcomes. In this paper, we present a brief yet important report about quantitative analytical methods for finite-size evolutionary game systems, from the two perspectives of how to calculate fixation probabilities and stationary frequencies. Importantly, we not only review some crucial developments about theoretical approaches which were achieved in this field but also put forward two remarkable prospects for further research.

Ten years ago, the new era of time crystals began. Time crystals are systems that behave in the time dimension like ordinary space crystals do in space dimensions. We present a brief history of a decade of research on time crystals, describe current research directions, indicate challenges, and discuss some future perspectives for condensed matter physics in the time domain.

The coupling between a moving ground-state atom and the quantum electromagnetic field is at the origin of several intriguing phenomena ranging from the dynamical Casimir emission of photons to Sagnac-like geometric phase shifts in atom interferometers. Recent progress in this emerging field reveals unprecedented connections between non-trivial aspects of modern physics such as electrodynamic retardation, non-unitary evolution in open quantum systems, geometric phases, non-locality and inertia.

The introduction of spin degree of freedom has not only made the electronic transport properties colorful, but also highly attracted people's attention to the spin-related quantum heat transport, with the rapid progress of spin caloritronics in recent year. Against this background, the modeling and tuning of quantum heat transport in magnetic nanostructures has become an emerging and attractive topic. In particular, the spin-phonon interaction has played a crucial role in the novel transport behaviors of heat and spin. In this perspective article, we give an insight into the current theoretical and experimental progresses and discuss the further research perspectives of spin-phonon interaction-related heat transfer.

In 2002, in a seminal article, Bandt and Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as ordinal patters) which are defined in terms of the temporal ordering of data points in a time series, and whose probabilities are known as ordinal probabilities. With the ordinal probabilities the Shannon entropy can be calculated, which is the permutation entropy. Since it was proposed, the ordinal method has found applications in fields as diverse as biomedicine and climatology. However, some properties of ordinal probabilities are still not fully understood, and how to combine the ordinal approach of feature extraction with machine learning techniques for model identification, time series classification or forecasting, remains a challenge. The objective of this perspective article is to present some recent advances and to discuss some open problems.

Cancer is a collection of related genetic diseases exhibiting uncontrolled cell growth that interferes with normal functioning of human organisms. It results from accumulation of unfavorable mutations in tissues. While the biochemical picture of how cancer appears is known, the molecular mechanisms of tumor formation remain not fully understood despite tremendous efforts of researchers in multiple fields. New approaches for investigating cancer are constantly sought. In this paper, we discuss a powerful method of clarifying better a more microscopic picture of cancer by analyzing the dynamics of tumor formation. Using physics- and chemistry-inspired discrete-state stochastic description of cancer initiation, it is shown how the mechanisms of tumor formation can be uncovered. This approach is suggested as a powerful new physical-chemical tool for a better understanding of complex processes associated with cancer.

We consider the Dirac cones and higher-order topological phases in quasi-continuous media of classical waves (e.g., photonic and sonic crystals). Using sonic crystals as prototype examples, we revisit some of the known systems in the study of topological acoustics. We show the emergence of various Dirac cones and higher-order topological band gaps in the same framework by tuning the geometry of the system. We provide a pedagogical review of the underlying physics and methodology via the bulk-edge-corner correspondence, symmetry-based indicators, Wannier representations, filling anomaly, and fractional corner charges. In particular, the theory of the Dirac cones and the higher-order topology are put in the same framework. These examples and the underlying physics principles can be inspiring and useful in the future study of higher-order topological metamaterials.

A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed at framing dark energy and dark matter in a comprehensive geometric view. Considering the concept of perfect scalars, we show that the field equations of such theories naturally contain perfect fluid terms. Specific examples are developed for the Friedman-Lemaître-Roberson-Walker metric.

We discuss the possibility that the complexity of biological systems may lie beyond the predictive capabilities of theoretical physics: in Stuart Kauffman's words, there is a World Beyond Physics (WBP). It is argued that, in view of modern developments of statistical mechanics, the WBP is smaller than one might anticipate from the standpoint of fundamental physical theories.

The response of dissipative systems to multi-chromatic fields exhibits generic properties which follow from the discrete time-translation symmetry of each driving component. We derive these properties and illustrate them with paradigmatic examples of classical and quantum dissipative systems. In addition, some computational aspects, in particular a matrix continued-fraction method, are discussed. Moreover, we propose possible implementations with quantum optical settings.

How to explain why cooperation can emerge in the real society is one of the most challenging scientific problems. In the past few years, in order to solve the evolutionary puzzle of cooperation, researchers have put forward a variety of solutions and accordingly proposed some mechanisms for the evolution of cooperation. Among them, the implementation of prosocial incentive strategy can increase the benefits of cooperators or reduce the benefits of defectors, which has been regarded as an effective measure to solve the cooperation problem. In this perspective, we provide a mini yet profound review of recent research efforts that explore the roles of incentive strategies in the evolution of cooperation and how to design the optimal incentive protocols to promote the evolution of cooperation more efficiently. Importantly, we show some crucial developments about incentive strategies which have been made in the field and meanwhile come up with some significant routes of further research.

Cooperation is ubiquitous in human as well as animals societies, however, the study of the driving forces behind cooperation is still an open question. Thus, exploring the hidden order related to cooperation has become a hot issue recently. Fortunately, evolutionary game theory and network science provide some new research perspectives for the cooperative behavior. In this letter, we focus on the present study of cooperation mechanism, and further put forward some feasible research prospects from the perspective of evolutionary game by arranging and researching the thread of history. Specifically, we first summarize the cooperation research status from the aspects of network topology and individuals' strategy updating rules etc., and we then discuss the hidden order behind the emergence and maintenance of cooperation, the development trends are presented in the last.

We study the evolution of pulses propagating through focusing nonlinear media. A small disturbance of a smooth initial non-uniform pulse amplitude leads to formation of a region of strong nonlinear oscillations. We develop here an asymptotic method for finding the law of motion of the front of this region. The method is based on the conjecture that instability fronts propagate with the minimal group velocity of linear waves. To support this conjecture, at first we review several physical situations where this statement was obtained as a result of direct calculations. Then we generalize it to situations with a non-uniform flow and apply it to the focusing nonlinear Schrödinger equation for the particular cases of Talanov and Akhmanov-Sukhorukov-Khokhlov initial distributions. The approximate analytical results agree very well with the exact numerical solutions for these two problems.

Controlling the spontaneous emission of atoms or molecules is an interesting research topic in the field of quantum optics. Here we provide a perspective on modulating the interaction between two quantum emitters through a sandwich structure composed of graphene and hexagonal boron nitride (hBN). The dependence of interaction between quantum emitters on the thickness of hBN and chemical potential of graphene is investigated in detail. When the transition frequency of quantum emitter is located in the hyperbolic band of type I supported by hBN, the radiative state can be easily modulated by adjusting the chemical potential of graphene. So it is easy to switch the interaction of quantum emitters from superradiant state to subradiant state by external electric field. When the transition frequency of quantum emitter is located in hyperbolic band of type II, the system can be always in the superradiant state. We predict the further research perspectives of spontaneous emission and superradiance with the help of metasurfaces based on two-dimensional materials.

In the recent years, the emergence of metal-free surface-enhanced Raman scattering (SERS) substrates has provided promising alternatives for reliable, high-sensitivity Raman spectroscopy due to their potential to realize highly tuneable, biocompatible, and reproducible Raman enhancement. In this perspective article, we discuss recent developments and anticipate new opportunities for metal-free SERS. Specifically, we review the theory of metal-free SERS, including electromagnetic enhancement and chemical enhancement, and introduce promising substrates developed recently, including MXenes, transition metal dichalcogenides, and carbon-based substrates. Moreover, we clarify challenges, provide potential solutions, and discuss unexploited applications. This perspective provides not only a broad and detailed view of metal-free SERS at the current stage, but also a roadmap for its future advancement.

Liquid crystals subjected to modulated surface alignment assemble into metasurface-type structures capable of various flat-optical functionalities, including light diffraction and focusing, deflection and splitting. Remaining in a fluid phase, they are susceptible to external stimuli, and, in particular, can be efficiently controled by low voltages. We overview the existing approaches to the design and fabrication of liquid-crystal metasurfaces, highlight their realized optical functions and discuss the applied potential in emerging photonic devices.

Recent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery".

Partial synchronization patterns play an important role in the functioning of neuronal networks, both in pathological and in healthy states. They include chimera states, which consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics, and other complex patterns. In this perspective article we show that partial synchronization scenarios are governed by a delicate interplay of local dynamics and network topology. Our focus is in particular on applications of brain dynamics like unihemispheric sleep and epileptic seizure.

The distribution of quantum entanglement is essential for quantum communication. Contrary to classical communication, the signal in quantum communication is impossible to copy due to the basic principles of quantum mechanics, i.e., quantum state collapse and no-cloning theorem. However, the communication range is limited by inevitable photon loss. To counteract this issue, one can insert several repeater stations between two remote end nodes to divide the full distance into several shorter segments and successively operate entanglement swapping between adjacent repeater stations to enable long-distance quantum communication. Up to now, one can classify quantum repeaters (QRs) into three generations based on the methods of reducing errors resulted from photon loss and imperfect operations. In this paper, we will briefly review advances for each generation of QRs and discuss the advantages and challenges of each generation. Moreover, we also discuss some efficient proposals of building blocks to overcome the bottlenecks for QRs.

We generalize Planck's law for black-bodies, classically described by Maxwell-Boltzmann distributions, to include space and astrophysical plasmas described by kappa distributions. This provides the spectral intensity of electromagnetic radiation emitted by black bodies in thermal equilibrium with the surrounding and interacting plasmas. According to the generalized concept of thermal equilibrium, systems with correlations among their particles' velocities/energies reside in stationary states described by kappa distributions associated with the thermodynamic parameters of temperature and kappa index. Using these distributions, we derive the generalized expressions of the i) mean energy of photon ensemble, ii) spectral intensity with respect to frequency and wavelength, and iii) Stefan-Boltzmann law, characterized by the well-known fourth power of temperature, but now multiplied by a new kappa-dependent factor. Finally, we discuss the implications of these new developments for space and astrophysical plasmas.

Experimental tests of Lorentz violation are important to our understanding of fundamental physics, and interest in them has picked up a great deal in the twenty-first century. For some of the most natural forms of Lorentz violation involving electrons and positrons, there are competing bounds coming from high-energy astrophysical observations and laboratory tests with optical atomic clocks. I discuss the advantages and limitations of both these approaches and how they may evolve in the future.

In solids, electronic Bloch states are formed by atomic orbitals. While it is natural to expect that orbital composition and information about Bloch states can be manipulated and transported, in analogy to the spin degree of freedom extensively studied in past decades, it has been assumed that orbital quenching by the crystal field prevents significant dynamics of orbital degrees of freedom. However, recent studies reveal that an orbital current, given by the flow of electrons with a finite orbital angular momentum, can be electrically generated and transported in wide classes of materials despite the effect of orbital quenching in the ground state. Orbital currents also play a fundamental role in the mechanisms of other transport phenomena such as spin Hall effect and valley Hall effect. Most importantly, it has been proposed that orbital currents can be used to induce magnetization dynamics, which is one of the most pivotal and explored aspects of magnetism. Here, we give an overview of recent progress and the current status of research on orbital currents. We review proposed physical mechanisms for generating orbital currents and discuss candidate materials where orbital currents are manifest. We review recent experiments on orbital current generation and transport and discuss various experimental methods to quantify this elusive object at the heart of orbitronics —an area which exploits the orbital degree of freedom as an information carrier in solid-state devices.

In the last two decades, a large number of exotic hadron states have been observed in experiments, which arouses great attention in the hadron physics community. In this short review, we briefly summarize progresses of our group on several exotic hadron states. Two approaches, quenched and unquenched quark models, are adopted in the calculation. The channel coupling effects, the multiquark states couple to open channels and the quark-antiquark states couple to meson-meson states, are emphasized. X(3872) is showed to be a mixture state of $c\bar{c}$ and $D\bar{D}^*$ in the unquenched quark model. X(2900) can be explained as a resonance state $\bar{D}^{*}K^{*}$ with the quantum numbers $IJ^{P}=00^{+}$ in both the quark delocalization color screening model and the chiral quark model. The reported state X(6900) can be explained as a compact resonance state with $IJ^{P}=00^{+}$ in both two quark models, and several fully heavy tetraquark states are predicated. The possible hidden-charm pentaquarks are systematically investigated in QDCSM, and seven resonance states are obtained in the corresponding baryon-meson scattering process, among which the $\Sigma_{c}D$ with $J^{P}=\frac{1}{2}^{-}$, $\Sigma_{c}D^{*}$ with $J^{P}=\frac{3}{2}^{-}$ and $J^{P}=\frac{1}{2}^{-}$ are consistent with the experimental report of P_c(4312), P_c(4440), and P_c(4457), respectively. More experimental data on exotic hadron states are vital for understanding exotic hadron states in quark models.

Thermocell, as a novel thermoelectric conversion device based on redox reaction or ion diffusion, has exhibited great advantages like high thermopower coefficient, cost effectiveness and good scalability for low-grade heat harvesting. Compared to the liquid-based thermocell, the gel-based version has garnered more and more attention because of its merits in leakage prevention, flexibility and integration, and significant achievements have been made in recent years. In this perspective, we briefly summarize the state-of-the-art progress on the gel-based thermocells. The basic working principle of thermocells is firstly introduced, followed by the discussion on the nuts and bolts for further system optimization. The emerging strategies on the performance improvement are highlighted as well as the underlying physics. Finally, the challenges and future directions in this field are prospected.

Spin-orbit (SO) coupling combined with space inversion symmetry breaking is at the origin of the lifting of the spin degeneracy in the band structure of many materials. The momentum-dependent energy splitting and the degree of spin polarization are indicative of the strength and symmetry of the SO interaction, and enter in the figure of merit of essentially all conceptual designs aiming to control the electron spin degree of freedom in solids. Here we briefly review the role played by spin-and-angle–resolved photoemission (spin ARPES or SARPES) in revealing the spin polarization specifically in the topological states of 3-dimensional (3D) topological insulators (TIs), and we discuss how the progress in the technique can assist the rise of several active fields like spintronics, spin-orbitronics or the generation of spin-polarized beams.

We propose to measure the six motional frequencies of an unbalanced two-ion crystal in a Penning trap using a scheme that has been demonstrated in a quantum-metrology experiment with a single ion in a linear Paul trap. To study the feasibility, we derive the quantum Hamiltonian for the unbalanced crystal formed by a target and a sensor ion (⁴⁰Ca$^+)$, and deduce characteristic coordinates $\xi_{c'}^\pm, \xi_z^\pm$, and $\xi_m^\pm$, associated to the amplitudes of the displacement operator $\alpha_{c'}^\pm, \alpha_z^\pm$, and $\alpha_m^\pm$, respectively, when a dipolar time-varying field is applied. The final state after excitation is read out using rapid adiabatic passage. We also present the status of the 7 tesla open-ring Penning trap where first experiments on the ²³²Th$^+{\text{--}}^{40}$Ca$^+$ crystal, cooled to the ground state, are foreseen in the short-term future. Finally, we underline possible experiments with this unique platform.

In this perspective we discuss recent theoretical and experimental concepts giving a route to a better understanding of conventional and unconventional pairing mechanisms between opposite-spin fermions arising in one-dimensional mesoscopic systems. With special attention, we focus on the problem of experimental detectability of correlations between particles. We argue that state-of-the-art experiments with few ultracold fermions may finally break an impasse and give pioneering and unquestionable verification of the existence of correlated pairs with non-zero center-of-mass momentum.

Nuclear magnetic resonance (NMR) schemes can be applied to micron-, and nanometer-sized samples by the aid of quantum sensors such as nitrogen vacancy (NV) color centers in diamond. These minute devices allow for magnetometry of nuclear spin ensembles with high spatial and frequency resolution at ambient conditions, thus having a clear impact in different areas such as chemistry, biology, medicine, and material sciences. In practice, NV quantum sensors are driven by microwave (MW) control fields with a twofold objective: On the one hand, MW fields bridge the energy gap between NV and nearby nuclei which enables a coherent and selective coupling among them while, on the other hand, MW fields remove environmental noise on the NV leading to enhanced interrogation time. In this work we review distinct MW radiation patterns, or dynamical decoupling techniques, for nanoscale NMR applications.

We review methods to shuttle quantum particles fast and robustly. Ideal robustness amounts to the invariance of the desired transport results with respect to deviations, noisy or otherwise, from the nominal driving protocol for the control parameters; this can include environmental perturbations. "Fast" is defined with respect to adiabatic transport times. Special attention is paid to shortcut-to-adiabaticity protocols that achieve, in faster-than-adiabatic times, the same results of slow adiabatic driving.

The cosmological term, Λ, was introduced 104 years ago by Einstein in his gravitational field equations. Whether Λ is a rigid quantity or a dynamical variable in cosmology has been a matter of debate for many years, especially after the introduction of the general notion of dark energy (DE). Λ is associated to the vacuum energy density, $\rho_{\mathrm{vac}}$, and one may expect that it evolves slowly with the cosmological expansion. Herein we present a devoted study testing this possibility using the promising class of running vacuum models (RVMs). We use a large string SNIa+BAO+H(z)+LSS+CMB of modern cosmological data, in which for the first time the CMB part involves the full Planck 2018 likelihood for these models. We test the dependence of the results on the threshold redshift ${z_{*}}$ at which the vacuum dynamics is activated in the recent past and find positive signals up to $\sim4.0\sigma$ for ${z_{*}}\simeq 1$. The RVMs prove very competitive against the standard ΛCDM model and give a handle for solving the $\sigma_8$ tension and alleviating the H₀ one.

Attempts at generalizing Shannon entropy and Kullback-Leibler divergence (relative entropy) led to a plenthora of deformation models in theoretical physics, including q-model, κ-model, etc. Naudts and Zhang (Inf. Geom., 1 (2018) 79) established that these models can be unified under two notions: deformed ϕ-exponential family (Naudts, J., J. Inequal. Pure Appl. Math., 5 (2004) 102) and conjugate $(\rho, \tau)$-embedding (Zhang J., Neural Comput., 16 (2004) 159) of probability functions. Conjugate $(\rho, \tau)$-embedding has a gauge freedom which, upon its fixing, subsumes the U-model of Eguchi (Sugaku Expositions, 19 (2006) 197) proposed in a statistical machine learning context. The generalization by $(\rho, \tau)$-entropy, $(\rho, \tau)$-cross-entropy, $(\rho, \tau)$-divergence, when applied to the ϕ-exponential family, yields either a Hessian structure or a conformal Hessian structure under different gauge selections —this "splitting" is the hallmark when deforming the exponential family with its dually flat (Hessian) geometry. This letter provides a unified information geometric perspective of deformation of the exponential model, with calculations for Tsallis q-model.

Recently room temperature superconductivity with $T_C=15$ degrees Celsius has been discovered in a pressurized complex ternary hydride, CSH_x, which is a carbon- and hydrogen-doped H₃S alloy. The nanoscale structure of H₃S is a particular realization of the 1993 patent claim of superlattice of quantum wires for room temperature superconductors and the maximum T_C occurs at the top of a superconducting dome. Here we focus on the electronic structure of materials showing nanoscale heterostructures at the atomic limit made of a superlattice of quantum wires like hole-doped cuprate perovskites, and organics focusing on A15 intermetallics and pressurized hydrides. We provide a perspective of the theory of room temperature multigap superconductivity in heterogeneous materials tuned at a shape resonance or Fano resonance in the superconducting gaps near a Lifshitz transition focusing on H₃S where the maximum T_C occurs where the multiband metal is tuned by pressure near a Lifshitz transition. Here the superconductivity dome of T_C vs. pressure is driven by both electron-phonon coupling and contact exchange interaction. We show that the T_C amplification up to room temperature is driven by the Fano resonance between a superconducting gap in the anti-adiabatic regime and other gaps in the adiabatic regime. In these cases the T_C amplification via contact exchange interaction is the missing term in conventional multiband BCS and anisotropic Migdal-Eliashberg theories including only Cooper pairing.

The wave turbulence theory predicts that a conservative system of nonlinear waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution of classical waves. Considering light propagation in a multimode fiber, we show that light condensation is driven by an energy flow toward the higher-order modes, and a bi-directional redistribution of the wave-action (or power) to the fundamental mode and to higher-order modes. The analysis of the near-field intensity distribution provides experimental evidence of this mechanism. The kinetic equation also shows that the wave-action and energy flows can be inverted through a thermalization toward a negative temperature equilibrium state, in which the high-order modes are more populated than low-order modes. In addition, a Bogoliubov stability analysis reveals that the condensate state is stable.

The study of thermal heat engines was pivotal to establishing the principles of equilibrium thermodynamics, with implications far wider than only engine optimization. For nonequilibrium systems, which by definition dissipate energy even at rest, how to best convert such dissipation into useful work is still largely an outstanding question, with similar potential to illuminate general physical principles. We review recent theoretical progress in studying the performances of engines operating with active matter, where particles are driven by individual self-propulsion. We distinguish two main classes, either autonomous engines exploiting a particle current, or cyclic engines applying periodic transformation to the system, and present the strategies put forward so far for optimization. We delineate the limitations of previous studies, and propose some future perspectives, with a view to building a consistent thermodynamic framework far from equilibrium.

Neural networks are computing models that have been leading progress in Machine Learning (ML) and Artificial Intelligence (AI) applications. In parallel, the first small-scale quantum computing devices have become available in recent years, paving the way for the development of a new paradigm in information processing. Here we give an overview of the most recent proposals aimed at bringing together these ongoing revolutions, and particularly at implementing the key functionalities of artificial neural networks on quantum architectures. We highlight the exciting perspectives in this context, and discuss the potential role of near-term quantum hardware in the quest for quantum machine learning advantage.

All quantum systems are subject to noise and imperfections due to stray fields, inhomogeneities or drifting experimental controls. An understanding of the effects of noise and decoherence is critical to the progress towards fully functional quantum devices. In this perspective, we focus on noise in quantum systems which are modelled by a dynamic stochastic parameter in the Hamiltonian. We will outline exact evolution equations describing the ensemble average dynamics for a variety of common noise types and their connections. We will also highlight an approximate evolution equation valid in the weak noise limit for an arbitrary classical stochastic field. This framework should serve as a starting point for identifying signatures of differing noise types and optimisation of robust control protocols.

Scales are a path breaking evolutionary adaptation that accompanied vertebrate evolution for the past 500 million years. Inherently lightweight with diverse shapes, sizes, materials, and distribution, they provide remarkable architecture-material enhancement, typical of metamaterials. Here we provide a perspective on mechanical behavior of fish scale inspired structures and explain the origins of some of their striking mechanical properties that include directional nonlinearity, interlocking behavior, and multiple penetration modes. We outline and explain the progress in understanding the complexities of these structures in global and local deformation modes and conclude by offering future perspectives and challenges.

A recent 3-XORSAT challenge required to minimize a very complex and rough energy function, typical of glassy models with a random first-order transition and a golf-course–like energy landscape. We present the ideas beyond the quasi-greedy algorithm and its very efficient implementation on GPUs that are allowing us to rank first in such a competition. We suggest a better protocol to compare algorithmic performances and we also provide analytical predictions about the exponential growth of the times to find the solution in terms of free-energy barriers.

Despite half a century of research, there is still no general agreement about the optimal approach to build a robust multi-period portfolio. We address this question by proposing the detrended cluster entropy approach to estimate the weights of a portfolio of high-frequency market indices. The information measure gathered from the markets produces reliable estimates of the weights at varying temporal horizons. The portfolio exhibits a high level of diversity, robustness and stability as not affected by the drawbacks of traditional mean-variance approaches.

Model systems of self-propelled particles reproduce many phenomena observed in laboratory active matter systems that defy our thermal equilibrium-based intuition. In particular, in stationary states of self-propelled systems, it is recognized that velocities of different particles exhibit non-trivial equal-time correlations. Such correlations are absent in equivalent equilibrium systems. Recently, researchers found that the range of the velocity correlations increases with increasing persistence time of the self-propulsion and can extend over many particle diameters. Here we review the initial studies of long-ranged velocity correlations in solid-like systems of self-propelled particles. Then, we demonstrate that the long-ranged velocity correlations are also present in dense fluid-like systems. We show that the range of velocity correlations in dense systems of self-propelled particles is determined by the combination of the self-propulsion and the virial bulk modulus that originates from repulsive interparticle interactions.

Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the dynamics and thermodynamics of quantum systems. Significant effort has been invested in developing various methods for tackling this issue and in this Perspective paper we focus on one such technique, namely collision models, which have emerged as a remarkably flexible approach. We discuss their application to understanding non-Markovian dynamics and to studying the thermodynamics of quantum systems, two areas in which collision models have proven to be particularly insightful. Their simple structure endows them with extremely broad applicability which has spurred their recent experimental demonstrations. By focusing on these areas, our aim is to provide a succinct entry point to this remarkable framework.

The status of our basic understanding of the physics and structure of glasses is presented in the light of recent developments in the experimental, phenomenological, and numerical approach to the description of real systems. Spontaneous and induced dynamic heterogeneities appear in the supercooled state of liquids and become frozen intact below the glass transition point. In most cases, mesoscopic heterogeneities due to partial microphase separation are frozen in glasses. Thus, glasses can be described as dynamically arrested heterogeneous supercooled liquids with more solid-like and liquid-like nanoscale regions. The critical issue is that, depending on material type and temperature, the heterogeneities exhibit different size distributions with the solid-like regions probably displaying a degree of hidden quasi-order. This scenario naturally explains some of the important physical properties of real glasses.

The aim of this focus article is to present a comprehensive classification of the main entropic forms introduced in the last fifty years in the framework of statistical physics and information theory. Most of them can be grouped into three families, characterized by two-deformation parameters, introduced respectively by Sharma, Taneja, and Mittal (entropies of degree $(\alpha,\,\beta$)), by Sharma and Mittal (entropies of order $(\alpha,\,\beta)$), and by Hanel and Thurner (entropies of class $(c,\,d)$). Many entropic forms examined will be characterized systematically by means of important concepts such as their axiomatic foundations à la Shannon-Khinchin and the consequent composability rule for statistically independent systems. Other critical aspects related to the Lesche stability of information measures and their consistency with the Shore-Johnson axioms will be briefly discussed on a general ground.

We derive the self-consistent harmonic approximation for the 2D XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our analysis is then specialized to power-law couplings decaying with the distance r as $\propto 1/r^{2+\sigma}$ in order to investigate the robustness, at finite σ, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit $\sigma \to \infty$. We propose an ansatz for the functional form of the variational couplings and show that for any $\sigma>2$ the BKT mechanism occurs. The present investigation provides an upper bound $\sigma^\ast=2$ for the critical threshold $\sigma^\ast$ above which the traditional BKT transition persists in spite of the non-local nature of the couplings.

The development of "fault-tolerant" quantum computers, unaffected by noise and decoherence, is one of the fundamental challenges in quantum technology. One of the approaches currently followed is the realization of "topologically protected" qubits which make use of quantum systems characterized by a degenerate ground state of composite particles, known as "non-Abelian anyons", able to encode and manipulate quantum information in a non-local manner. In this paper, we discuss the potential of quasi-two-dimensional electron gas (q2DEG) at the interface between band insulating oxides, like LaAlO₃ and SrTiO₃, as an innovative technological platform for the realization of topological quantum systems. Being characterized by a unique combination of unconventional spin-orbit coupling, magnetism, and 2D-superconductivity, these systems naturally possess most of the fundamental characteristics needed for the realization of a topological superconductor. These properties can be widely tuned by electric field effect acting on the orbital splitting and occupation of the non-degenerate 3d_xy and 3d_{xz, yz} bands. The topological state in oxide q2DEGs quasi-one-dimensional nanochannels could be therefore suitably controlled, leading to conceptual new methods for the realization of a topological quantum electronics based on the tuning of the orbital degrees of freedom.

Over the last two decades, it has been argued that the Lorentz transformation mechanism, which imposes the generalization of Newton's classical mechanics into Einstein's special relativity, implies a generalization, or deformation, of the ordinary statistical mechanics. The exponential function, which defines the Boltzmann factor, emerges properly deformed within this formalism. Starting from this, the so-called κ-deformed exponential function, we introduce new classes of statistical distributions emerging as the κ-deformed versions of already known distribution as the Generalized Gamma, Weibull, Logistic ones which can be adopted in the analysis of statistical data that exhibit power-law tails.

In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a simple response to study certain processes in solids and fluids. However, in many situations we are not talking about a FDT, but about the noise intensity. For example, noise has enormous importance in diffusion and growth phenomena. Although we have an explicit FDT for diffusion phenomena, we do not have one for growth processes where we have a noise intensity. We show that there is a hidden FDT for the growth phenomenon, similar to the diffusive one. Moreover, we show that growth with correlated noise presents as well a similar form of FDT. We also call attention to the hierarchy within the theorems of statistical mechanics and how this explains the violation of the FDT in some phenomena.

This letter focuses on open challenges in the fields of environmental data analysis and ecological complex systems. It highlights relations between research problems in stochastic population dynamics, machine learning and big data research, and statistical physics. Recent and current developments in statistical modeling of spatiotemporal data and in population dynamics are briefly reviewed. The presentation emphasizes stochastic fluctuations, including their statistical representation, data-based estimation, prediction, and impact on the physics of the underlying systems. Guided by the common thread of stochasticity, a deeper and improved understanding of environmental processes and ecosystems can be achieved by forging stronger interdisciplinary connections between statistical physics, spatiotemporal data modeling, and ecology.

We explore the quench dynamics of a two-dimensional, weakly interacting disordered Bose gas for various relative strengths of interactions and disorder. This allows us to identify two well distinct out-of-equilibrium regimes. When interactions are smaller than the disorder, the gas experiences multiple scattering and exhibits a short-range spatial coherence. At short time this coherence is only smoothly affected by interactions, via a diffusion process of the particles' energies. When interactions are larger than the disorder, scattering ceases and the gas behaves more and more like a fluid, ultimately like a superfluid at low energy. In the superfluid regime, the gas exhibits a long-range algebraic coherence, characteristic of a pre-thermal regime in disorder.

Recent studies of networks representing complex systems from the brain to social graphs have revealed their higher-order architecture, which can be described by aggregates of simplexes (triangles, tetrahedrons, and higher cliques). Current research aims at quantifying these hidden geometries by the algebraic topology methods and deep graph theory and understanding the dynamic processes on simplicial complexes. Here, we use the recently introduced model for geometrical self-assembly of cliques to grow nano-networks of triangles and study the field-driven spin reversal processes on them. With the antiferromagnetic interactions between the Ising spins attached to the nodes, this assembly ideally supports the geometric frustration, which is recognized as the origin of some new phenomena in condensed matter physics. In the dynamical model, a gradual switching from the pairwise to triangle-based interactions is controlled by a parameter. Thus, the spin frustration effects on each triangle give way to the mesoscopic ordering conditioned by a complex arrangement of triangles. We show how the balance between these interactions changes the shape of the hysteresis loop. Meanwhile, the fluctuations in the accompanying Barkhausen noise exhibit robust indicators of self-organized criticality, which is induced by the network geometry alone without any magnetic disorder.

Here we will give a perspective on new possible interplays between machine learning and quantum physics, including also practical cases and applications. We will explore the ways in which machine learning could benefit from new quantum technologies and algorithms to find new ways to speed up their computations by breakthroughs in physical hardware, as well as to improve existing models or devise new learning schemes in the quantum domain. Moreover, there are lots of experiments in quantum physics that do generate incredible amounts of data and machine learning would be a great tool to analyze those and make predictions, or even control the experiment itself. On top of that, data visualization techniques and other schemes borrowed from machine learning can be of great use to theoreticians to have better intuition on the structure of complex manifolds or to make predictions on theoretical models. This new research field, named as quantum machine learning, is very rapidly growing since it is expected to provide huge advantages over its classical counterpart and deeper investigations are timely needed since they can be already tested on the already commercially available quantum machines.

In this perspective we discuss three emerging fields of condensed matter physics which in recent years have attracted considerable attention. In particular, we consider the recent challenging topics on time-dependent phase transitions, topological phenomena, and unconventional superconductivity, with the aim to foster the community towards new applications and technological advancements. As for the time-dependent phase transitions, in recent years the experiments have shown light-induced phase transitions and new fields of application are emerging, including material design. Regarding topological materials, new challenges have arisen to detect the Majorana origin of quantized conductance in superconducting hybrid structures, as well as the effect of interaction on edge channels. Finally, concerning superconductivity, non-conventional pairing and correlation effects dominate the physics of a vast class of two-dimensional materials and novel devices were recently conceived. This work offers a comprehensive overview on these topics for promoting new ideas in these fertile fields of research.

Quantum control methods, like rapid adiabatic passage, stimulated Raman adiabatic passage, shortcuts to adiabaticity and optimal control, have become an integral part of modern quantum technologies, for example quantum computation and sensing, where they are exploited in order to find the optimal pulse sequences which drive quantum systems to the desired target state in minimum time or with maximum fidelity, overcoming decoherence and dissipation. In this perspective, we use the basic example of adiabatic population inversion in a two-level system in order to present these methods and review the latest developments in the field, while we touch upon the emerging method of reinforcement learning.

Spintronics, since its inception, has mainly focused on ferromagnetic materials for manipulating the spin degree of freedom in addition to the charge degree of freedom, whereas much less attention has been paid to antiferromagnetic materials. Thanks to the advances of micro-nano-fabrication techniques and the electrical control of the Néel order parameter, antiferromagnetic spintronics is booming as a result of abundant room temperature materials, robustness against external fields and dipolar coupling, and rapid dynamics in the terahertz regime. For the purpose of applications of antiferromagnets, it is essential to have a comprehensive understanding of the antiferromagnetic dynamics at the microscopic level. Here, we first review the general form of equations that govern both antiferromagnetic and ferrimagnetic dynamics. This general form unifies the previous theories in the literature. We also provide a survey for the recent progress related to antiferromagnetic dynamics, including the motion of antiferromagnetic domain walls and skyrmions, the spin pumping and quantum antiferromagnetic spintronics. In particular, open problems in several topics are outlined. Furthermore, we discuss the development of antiferromagnetic quantum magnonics and its potential integration with modern information science and technology.

After the Bak-Tang-Wisenfeld seminal work on self-organized criticality (SOC), the following claim appeared by other workers in the 1990s: Earthquakes (EQs) cannot be predicted, since the Earth is in a state of SOC and hence any small earthquake has some probability of cascading into a large event. Here, we discuss that such claims do not stand in the light of natural time analysis, which was shown at the beginning of the 2000s to extract the maximum information possible from complex systems time series. A useful quantity to identify the approach of a dynamical system to criticality is the variance $\kappa_1(\equiv \langle \chi^2 \rangle - \langle \chi \rangle^2)$ of natural time χ, which becomes equal to 0.070 at the critical state for a variety of dynamical systems. This also holds for experimental results of critical phenomena such as growth of ricepiles, seismic electric signals activities, and the subsequent seismicity before the associated main shock. Another useful quantity is the change $\Delta S$ of the dynamic entropy $S (=\langle \chi \ln \chi \rangle - \langle \chi \rangle \ln \langle \chi \rangle)$ under time reversal, which is minimized before a large avalanche upon analyzing the Olami-Feder-Christensen model for EQs in natural time. Such a minimum actually occurred on 22 December 2010, well before the M9 Tohoku EQ in Japan on 11 March 2011, being accompanied by increases of both the complexity measure of the $\Delta S$ fluctuations and the variability of the order parameter of seismicity (which was minimized two weeks later). These increases conform to the seminal work on phase transitions by Lifshitz and Slyozov and independently by Wagner as well as to more recent work by Penrose et al. In addition, the evolution of the complexity measure of the $\Delta S$ fluctuations reveals a reliable estimation of the occurrence time of this M9 EQ.

This paper provides a brief review of the interesting physics that arises from the use of detrending methods for time series analysis for the study of phenomena related to problems of adaptation to climate change. It presents illustrative examples of some of the newly developed or already existent methodological solutions that can be used to study climate phenomena, and of three sectors —public health, infrastructure and cultural heritage— where statistical physics tools can be utilized. In the context of adaptation to climate change statistical physics can offer data-led understandings that are of wider value to the scientific community and applicable local-scale insights.

Topological properties play an increasingly important role in future research and technology. This also applies to the field of topological magnetic excitations which has recently become a very active and broad field. In this Perspective article, we give an insight into the current theoretical and experimental investigations and try an outlook on future lines of research.

Light-matter interactions are an established field that is experiencing a renaissance in recent years due to the introduction of exotic coupling regimes. These include the ultrastrong and deep-strong coupling regimes, where the coupling constant is smaller and of the order of the frequency of the light mode, or larger than this frequency, respectively. In the past few years, quantum simulations of light-matter interactions in all possible coupling regimes have been proposed and experimentally realized, in quantum platforms such as trapped ions, superconducting circuits, cold atoms, and quantum photonics. We review this fledgling field, illustrating the benefits and challenges of the quantum simulations of light-matter interactions with quantum technologies.

Emerging collective behavior in complex dynamical networks depends on both coupling function and underlying coupling topology. Through this Perspective, we provide a brief yet profound excerpt of recent research efforts that explore how the synergy of attractive and repulsive interactions influence the destiny of ensembles of interacting dynamical systems. We review the incarnation of collective states ranging from chimera or solitary states to extreme events and oscillation quenching arising as a result of different network arrangements. Though the existing literature demonstrates that many of the crucial developments have been made, nonetheless, we come up with significant routes of further research in this field of study.

Critical slowing down is considered to be an important indicator for predicting critical transitions in dynamical systems. Researchers have used it prolifically in the fields of ecology, biology, sociology, and finance. When a system approaches a critical transition or a tipping point, it returns more slowly to its stable attractor under small perturbations. The return time to the stable state can thus be used as an index, which shows whether a critical change is near or not. Based on this phenomenon, many methods have been proposed to determine tipping points, especially in biological and social systems, for example, related to epidemic spreading, cardiac arrhythmias, or even population collapse. In this perspective, we briefly review past research dedicated to critical slowing down indicators and associated tipping points, and we outline promising directions for future research.

Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interest in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological systems and psychological-economic systems, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective paper, we overview the latest progress of evolutionary game theory in this direction. We describe both mathematical methods and interdisciplinary applications across different fields. The ideas worthy of further consideration are discussed in prospects, with the central role of promoting cooperations in a changing world.

Lotka's seminal work (Lotka A. J., Proc. Natl. Acad. Sci. U.S.A., 6 (1920) 410) "on certain rhythmic relations" is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant than ever. It is because non-transitive interactions have a paramount role on maintaining biodiversity and adequate human intervention into ecological systems requires a deeper understanding of the related dynamical processes. In this Perspective we overview different aspects of biodiversity, with focus on how it can be maintained based on mathematical modeling of the last years. We also briefly discuss the potential links to evolutionary game models of social systems, and finally, give an overview about potential prospects for future research.

Quantum secure direct communication (QSDC) enables direct message transmission over quantum channels. Loopholes involved in practical apparatus, particularly nonideal measurement devices, provide a potential interface for attacking practical quantum communication. Measurement-device–independent (MDI) QSDC protocols deal with all side-channel attacks on practical measurement devices and directly transmit secret messages over classical channels with both integrity and eavesdropper detection and prevention. We review the recent development of MDI QSDC protocols using both single photons and entangled photon pairs. These two types of MDI QSDC protocols are useful for their respective distinct characters and can be generalized to perform more interesting communication networks.

Intriguing mechanical properties of two-dimensional (2D) atomically thin materials make them well suit for a new class of resonant NEMS. Resonant 2D NEMS show high fundamental frequencies, outstanding tenability and broad dynamic range due to the ultrahigh strength, ultralow mass density and ultrahigh strain stretchability. Recent work toward exploring fabrication and transduction techniques, device performances and the nonlinear dynamic characteristics of 2D NEMS are summed up. Nonlinear dynamic behaviors including nonlinear mode coupling, nonlinear damping and nonlinear pull-in instability are reported in 2D NEMS.

Rydberg antiblockade (RAB) allows more than one Rydberg atom to be excited in the presence of Rydberg-Rydberg interaction (RRI) and has many potential applications in quantum optics, many-body physics and quantum information. In this paper, we would review the conditions and possible applications of different types of RAB regimes under weak, intermediate and strong RRIs, respectively. Both van der Waals (vdW) and dipole-dipole (DD) interactions are considered for each interaction strength. This work displays the layout of RAB and provides a reference for further study of RAB-regime-based quantum optics and quantum information processing tasks.

The place and role of an Observer in quantum mechanics has been a subject of an ongoing debate since the theory's inception. Wigner brought this question to the fore in a celebrated scenario in which a super-Observer observes a Friend making a measurement. Here we briefly review why this "Wigner Friend scenario" has been taken to require the introduction of the Observer's consciousness, or alternatively to show the inconsistency of quantum measurement theory. We will argue that quantum theory can consistently leave observers outside its narrative, by making only minimal assumptions about how the information about the observed results is stored in material records.

Tremendous research efforts have been invested in exploring and designing so-called shortcuts to adiabaticity. These are finite-time processes that produce the same final states that would result from infinitely slow driving. Most of these techniques rely on auxiliary fields and quantum control, which makes them rather costly to implement. In this Perspective we outline an alternative paradigm for optimal control that has proven powerful in a wide variety of situations ranging from heat engines over chemical reactions to quantum dynamics —thermodynamic control. Focusing on only a few, selected milestones we seek to provide a pedagogical entry point into this powerful and versatile framework.

Among intermetallic compounds between 3d transition metals and pnictogens, compounds containing chromium and arsenide ions are of special interest due to their rich variety of electronic, magnetic and superconducting properties. The monopnictide CrAs compound, although known since over fifty years ago, was observed to exhibit pressure-induced superconductivity in the vicinity of an antiferromagnetic quantum critical point, making it the first superconductor among Cr-based compounds. After this discovery, seeking for ambient pressure superconductivity in Cr-based compounds, bulk superconductivity was discovered in the pnictide K₂Cr₃As₃. These discoveries boost the search and the investigation of the several interesting phenomena exhibited by these materials that actually need to be properly addressed. Here, we try to give a comprehensive overview on these materials showing that they may provide a tunable platform for emphasising the role played by the quantum criticality, the low dimensionality, the magnetic fluctuations and the topology.

We review a strategy to use an ion-based analog quantum simulator to study the many-body electron-electron Coulomb interaction of an electron gas. This is made possible by an exact unitary dilatation mapping, which allows an experimentally challenging system to be replaced by an alternative one that may be experimentally more accessible. We show the feasibility of this simulation strategy mathematically. As a bonus, the dilatation transformation does not even need to be physically implemented when only the system spectrum is needed, in which case the simulation induces no experimental complexity overhead. This proposal is dimension-agnostic, and could be generalized as a simulation strategy between systems involving terms with different position or momentum dependence.

We provide a compact review on recent developments on axion F(R) gravity. The axion field is a string-theory–originated theoretical particle that is a perfect candidate for low-mass particle dark matter. In this review we present how a viable inflationary phenomenology and a viable late-time evolution can be described by an axion F(R) gravity theory, in which the F(R) gravity part can drive in a geometric way the inflationary and the late-time era, and the axion field behaves as dark matter, with its energy density $\rho_a$ behaving as a function of the scale factor as $\rho_a\sim a^{-3}$. We also briefly discuss the effect of a non-trivial axion Chern-Simons coupling on the inflationary phenomenology of the R² model. Finally, we briefly discuss the effects of a non-minimal coupling of the axion field with the curvature on neutron stars, and also the propagation of gravity waves in Chern-Simons axion gravity.

We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are possible, provided a sequence includes at least two such observations. Complex valued probability amplitudes, each defined for an entire sequence of outcomes, are attributed to Observer's reasoning, and the problem of wave function's collapse is dismissed as a purely semantic one. Our examples include quantum "weak values", and a simplified version of the "delayed quantum eraser".

Topological phase transitions occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and driving, and hence require a variety of techniques and concepts to describe their topological properties. For instance, topology may be accessed from single-particle Bloch wave functions, Green's functions, or many-body wave functions. We demonstrate that despite this diversity, all topological phase transitions display a universal feature: namely, a divergence of the curvature function that composes the topological invariant at the critical point. This feature can be exploited via a renormalization-group–like methodology to describe topological phase transitions. This approach serves to extend notions of correlation function, critical exponents, scaling laws and universality classes used in Landau theory to characterize topological phase transitions in a unified manner.

Recent developments in practical quantum engineering and control techniques have allowed significant developments for experimental studies of open quantum systems and decoherence engineering. Indeed, it has become possible to test experimentally various theoretical, mathematical, and physical concepts related to non-Markovian quantum dynamics. This includes experimental characterization and quantification of non-Markovian memory effects and proof-of-principle demonstrations how to use them for certain quantum communication and information tasks. We describe here recent experimental advances for open system studies, focussing in particular to non-Markovian dynamics including the applications of memory effects, and discuss the possibilities for ultimate control of decoherence and open system dynamics.

We consider two atoms trapped in a one-dimensional harmonic-oscillator potential interacting through a contact interaction. We study the response of the system against a monopolar perturbation during the transition from the non-interacting to the strongly interacting Tonks-Girardeau regime, as the interaction is varied from zero to infinitely large repulsive values. The response of the system is then characterized by the moments of the dynamic structure function which are explicitly calculated from the dynamic structure function and by means of sum rules.

During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse sets of research communities. This interest has arisen due to fundamental problematics as to how to define and quantify memory effects in the quantum domain, how to exploit and develop applications based on them, and also due to the following question: what are the ultimate limits for controlling open system dynamics? We give here a simple theoretical introduction to the basic approaches to define and quantify quantum non-Markovianity —also highlighting their connections and differences. In addition to the importance of the development for open quantum systems studies, we also discuss the implications of the progress for other fields including, e.g., formal studies of stochastic processes and quantum information science, and conclude with possible future directions the recent developments open.

In recent years, the concept of shortcuts to adiabaticity (STA), originally developed for speeding up slow adiabatic state evolution in quantum systems, has found numerous applications in guided-wave optics. Optical waveguides, enabled by the advanced fabrication technologies, provide an ideal platform to implement the STA protocols in terms of geometry variations; moreoever, STA has enabled the development of short and robust waveguide components, with applications in beam couplers, beam splitters, mode converters, mode (de)multiplexers, and polarization manipulation devices. Concepts such as counterdiabatic driving, invariant-based inverse engineering, fast-forward approach, or fast quasiadiabatic dynamics, have been shown to provide shortcuts to adiabatic mode evolution in optical waveguides, resulting in compact functional devices with large bandwidth and fabrication tolerance. Novel devices have recently been fabricated following years of theoretical efforts, showing that STA have emerged as a new paradigm in optical waveguides. In this work, we discuss the major STA protocols for applications in optical waveguides and illustrate the shortcuts with device examples.

To know how particles move in small cavities, micro-channels and in general in crowded media currently constitutes a challenge for the understanding of basic mechanisms governing the behaviour of small-scale soft-matter and biological systems. The presence of obstacles, constrictions and irregularities in the shape of these structures significantly alters their trajectories thus modifying their transport properties. An analysis of these properties based on the use of diffusion and stochastic equations faces the problem of solving these equations for very complex boundaries which may constitute a formidable task. Recent studies on transport through confined media have shown that this problem can be considerably simplified if one assimilates spatial restrictions to the entropic barriers which particles must surmount in order to proceed. A wide variety of situations can be studied in this way, including many that were thought to be beyond the reach of classical transport theories, such as diffusion through deformable channels, motion of ions at very small length scales and behaviour of confined active matter.

In the past decade, the advent of time-resolved spectroscopic tools has provided a new ground to explore fundamental interactions in solids and to disentangle degrees of freedom whose coupling leads to broad structures in the frequency domain. Time- and angle-resolved photoemission spectroscopy (tr-ARPES) has been utilized to directly study the relaxation dynamics of a metal in the presence of electron-phonon coupling. The effect of photo-excitations on the real and imaginary part of the self-energy as well as the time scale associated with different recombination processes are discussed. In contrast with a theoretical model, the phonon energy does not set a clear scale governing quasiparticle dynamics, which is also different from the results observed in a superconducting material. These results point to the need for a more complete theoretical framework to understand electron-phonon interaction in a photo-excited state.

Terahertz pulses are very popular because of their numerous applications, for example in security. Located between microwaves and optical waves in the electromagnetic spectrum, their spectral domain can now be exploited for molecular spectroscopy using terahertz emission from plasmas formed by femtosecond laser pulses ionizing gases such as air. Downconversion of broadband optical spectra in a plasma produces intense radiation suitable for the detection of suspect materials remotely. The different physical mechanisms involved to create terahertz radiation by laser-matter interaction are reviewed. The new potentialities offered by intense ultrafast lasers allow the acquisition of unique spectral signatures characterizing various materials.

Inferring causal relations from empirical data is a central task in any scientific inquiry. To that aim, a mathematical theory of causality has been developed, not only stating under which conditions such inference becomes possible but also offering a formal framework to reason about cause and effect within quantum theory. This perspective article provides an overview of the latest results in the growing field of quantum causality, with a special focus on experimental implementations and concepts that only recently have entered in the quantum information dictionary. Ideas like bilocality, instrumental variables and interventions will be discussed from both a fundamental and an experimental perspective.

Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to quantum states with novel properties of genuine nonequilibrium nature. In turn, for the theoretical description it is in general not sufficient to understand nonequilibrium dynamics on the basis of the properties of the involved Hamiltonians. Instead it becomes important to characterize time-evolution operators, which adds time as an additional scale to the problem. In this perspective article we summarize recent progress in the field of dynamical quantum phase transitions, which are phase transitions in time with temporal nonanalyticities in matrix elements of the time-evolution operator. These transitions are not driven by an external control parameter, but rather occur due to sharp internal changes generated solely by unitary real-time dynamics. We discuss the obtained insights on general properties of dynamical quantum phase transitions, their physical interpretation, potential future research directions, as well as recent experimental observations.

We provide an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the connection between the asymptotic states of memristors and the Ising model, and the relation to the dynamics and statics of disordered systems.

We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e., classical time-dependent fluctuations affecting the tunneling amplitudes of the walker. In order to illustrate the general features of the model, we review recent results on two paradigmatic examples: the dynamics of quantum walks on the line and the effects of noise on the performances of quantum spatial search on the complete and the star graph. We also discuss future perspectives, including extension to many-particle quantum walk, to noise model for on-site energies and to the analysis of different noise spectra. Finally, we address the use of quantum walks as a quantum probe to characterize defects and perturbations occurring in complex, classical and quantum, networks.

Noise is an inherent part of neuronal dynamics, and thus of the brain. It can be observed in neuronal activity at different spatiotemporal scales, including in neuronal membrane potentials, local field potentials, electroencephalography, and magnetoencephalography. A central research topic in contemporary neuroscience is to elucidate the functional role of noise in neuronal information processing. Experimental studies have shown that a suitable level of noise may enhance the detection of weak neuronal signals by means of stochastic resonance. In response, theoretical research, based on the theory of stochastic processes, nonlinear dynamics, and statistical physics, has made great strides in elucidating the mechanism and the many benefits of stochastic resonance in neuronal systems. In this perspective, we review recent research dedicated to neuronal stochastic resonance in biophysical mathematical models. We also explore the regulation of neuronal stochastic resonance, and we outline important open questions and directions for future research. A deeper understanding of neuronal stochastic resonance may afford us new insights into the highly impressive information processing in the brain.

Kappa distributions describe particle velocities and energies in collisionless particle systems such as space and astrophysical plasmas. While we understand the possible mechanisms that may generate these distributions in these plasmas, the thermodynamic origin of these distributions remains a challenge: Particle systems at thermal equilibrium are known to be described by the Maxwell-Boltzmann distribution, but it is unknown whether this distribution is unique or other distribution functions consistent with thermodynamics may exist. This paper resolves the thermodynamic origin of kappa distributions. For particle systems eventually reaching thermal equilibrium, we show: i) the existence of two thermodynamic integrals characterizing thermal equilibrium, corresponding to two independent intensive thermodynamic quantities, temperature and kappa index (parameter labelling kappa distributions); ii) the adaptation of Sackur-Tetrode entropy for kappa distributions with applications in solar wind plasma; iii) the pseudo-additivity rule of entropy; iv) that the most general, physically meaningful, distribution function that particle systems are stabilized into when reaching thermal equilibrium is the kappa distribution.

This mini-review collects results predicting the creation of matter-wave solitons by the spinor system of Gross-Pitaevskii equations (GPEs) with the self-attractive cubic nonlinearity and linear first-order-derivative terms accounting for the spin-orbit coupling (SOC). In 1D, the so-predicted bright solitons are similar to usual ones, supported by the GPE in the absence of SOC. Essentially new results were recently obtained for 2D and 3D systems: SOC suppresses the collapse instability in the multidimensional GPE, creating 2D ground-state solitons and metastable 3D ones of two types: semi-vortices (SVs), with vorticities m = 1 in one component and m = 0 in the other, and mixed modes (MMs), with m = 0 and $m=\pm 1$ present in both components. With the Galilean invariance broken by SOC, moving solitons exist up to a certain critical velocity. The latest result predicts stable 2D "quantum droplets" of the MM type in the presence of the Lee-Huang-Yang corrections to the GPE system, induced by quantum fluctuations, in the case when the inter-component attraction dominates over the self-repulsion in each component.

Like ordinary molecules are composed of atoms, colloidal molecules consist of several species of colloidal particles tightly bound together. If one of these components is self-propelled or swimming, novel "active colloidal molecules" emerge. Active colloidal molecules exist on various levels such as "homonuclear", "heteronuclear" and "polymeric" and possess a dynamical function moving as propellers, spinners or rotors. Self-assembly of such active complexes has been studied a lot recently and this perspective article summarizes recent progress and gives an outlook to future developments in the rapidly expanding field of active colloidal molecules.

In the past decade, the concept of parity-time $(\mathcal{PT})$ symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying, observing, and utilizing some of the peculiar aspects of $\mathcal{PT}$ symmetry in optics. Together with related concepts of non-Hermitian physics of open quantum systems, such as non-Hermitian degeneracies (exceptional points) and spectral singularities, $\mathcal{PT}$ symmetry represents one among the most fruitful ideas introduced in optics in the past few years. Judicious tailoring of optical gain and loss in integrated photonic structures has emerged as a new paradigm in shaping the flow of light in unprecedented ways, with major applications encompassing laser science and technology, optical sensing, and optical material engineering. In this perspective, I review some of the main achievements and emerging areas of $\mathcal{PT}$-symmetric and non-Hermtian photonics, and provide an outline of challenges and directions for future research in one of the fastest growing research area of photonics.

Recent experiments have reported the emergence of high-temperature superconductivity with critical temperature T_c between 43 K and 123 K in a potassium-doped aromatic hydrocarbon para-Terphenyl or p-Terphenyl. This achievement provides the record for the highest T_c in an organic superconductor overcoming the previous record of T_c = 38 K in Cs₃C₆₀ fulleride. Here we propose that the driving mechanism is the quantum resonance between superconducting gaps near a Lifshitz transition which belongs to the class of Fano resonances called shape resonances. For the case of p-Terphenyl our numerical solutions of the multigap equation shows that high T_c is driven by tuning the chemical potential by K doping and it appears only in a narrow energy range near a Lifshitz transition. At the maximum critical temperature, T_c = 123 K, the condensate in the appearing new small Fermi surface pocket is in the BCS-BEC crossover while the T_c drops below 0.3 K where it is in the BEC regime. Finally, we predict the experimental results which can support or falsify our proposed mechanism: a) the variation of the isotope coefficient as a function of the critical temperature and b) the variation of the gaps and their ratios 2Δ/T_c as a function of T_c.

The symbolic dynamics technique is well known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Our main example is the investigation of share price returns in a coarse-grained way. A nontrivial spectrum of Rényi entropies is found. We study how the spectrum depends on the time scale of returns, the sector of stocks considered, as well as the number of symbols used for the symbolic description. Overall our analysis confirms that in the symbol space transition probabilities of observed share price returns depend on the entire history of previous symbols, thus emphasizing the need for a modelling based on non-Markovian stochastic processes. Our method allows for quantitative comparisons of entirely different complex systems, for example the statistics of symbol sequences generated by share price returns using 4 symbols can be compared with that of genomic sequences.

Collective behavior among coupled dynamical units can emerge in various forms as a result of different coupling topologies as well as different types of coupling functions. Chimera states have recently received ample attention as a fascinating manifestation of collective behavior, in particular describing a symmetry breaking spatiotemporal pattern where synchronized and desynchronized states coexist in a network of coupled oscillators. In this perspective, we review the emergence of different chimera states, focusing on the effects of different coupling topologies that describe the interaction network connecting the oscillators. We cover chimera states that emerge in local, nonlocal and global coupling topologies, as well as in modular, temporal and multilayer networks. We also provide an outline of challenges and directions for future research.

Extreme Light Infrastructure-Nuclear Physics (ELI-NP), to become operational in 2019, is a new Research Center built in Romania that will use extreme electromagnetic fields for nuclear physics research. The ELI-NP facility will combine two large equipments with state-of-the-art parameters, namely a 2 × 10 PW high-power laser system and a very brilliant gamma-beam system delivering beams with energies up to 19.5 MeV. The laser and gamma-beam systems under construction and typical proposed first-phase experiments are described.

Revealing complicated behaviors from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. The past decade has witnessed a rapid development of complex network studies, which allow to characterize many types of systems in nature and technology that contain a large number of components interacting with each other in a complicated manner. Recently, the complex network theory has been incorporated into the analysis of time series and fruitful achievements have been obtained. Complex network analysis of time series opens up new venues to address interdisciplinary challenges in climate dynamics, multiphase flow, brain functions, ECG dynamics, economics and traffic systems.

The motion control of relativistic electrons with lasers allows for an efficient and elegant way to map the space with ultra-intense electric-field components, which, in turn, permits a unique improvement of the electron beam parameters. This perspective addresses the recent laser plasma accelerator experiments related to the phase space engineering of electron beams in a plasma medium performed at LOA.

We report on a systematic analysis of the frequency spectrum of a system often considered for quantum computing purposes, metadevice applications, and high-sensitivity sensors, namely a superconducting loop interrupted by Josephson junctions, the core of an rf-SQUID. We analyze both the cases in which a single junction closes the superconducting loop and the one in which the single junction is replaced by a superconducting interferometer. Perturbation analysis is employed to display the variety of the solutions of the system and the implications of the results for the present interest in fundamental and applied research are analyzed.

Techniques in time- and angle-resolved photoemission spectroscopy have facilitated a number of recent advances in the study of quantum materials. We review developments in this field related to the study of incoherent nonequilibrium electron dynamics, the analysis of interactions between electrons and collective excitations, the exploration of dressed-state physics, and the illumination of unoccupied band structure. Future prospects are also discussed.

This perspective addresses the study of "extreme" states of matter created by laser pulses. We define "warm dense states" and "high energy density", their importance in physics, how to produce and diagnose them, either using isochoric heating with short-pulse lasers or laser-driven shock waves.

Extremely compliant elastic materials, such as thin membranes or soft gels, can be deformed when wetted by a liquid drop. It is commonly assumed that the solid capillarity in "soft wetting" can be treated in the same manner as liquid surface tension. However, the physical chemistry of a solid interface is itself affected by any distortion with respect to the elastic reference state. This gives rise to phenomena that have no counterpart in liquids: the mechanical surface stress is different from the excess free energy in surface. Here we point out some striking consequences of this "Shuttleworth effect" in the context of wetting on deformable substrates, such as the appearance of elastic singularities and unconventional capillary forces. We provide a synthesis between different viewpoints on soft wetting (microscopic and macroscopic, mechanics and thermodynamics), and point out key open issues in the field.

Prototype nitride quantum light sources, particularly single-photon emitters, have been successfully demonstrated, despite the challenges inherent in this complex materials system. The large band offsets available between different nitride alloys have allowed device operation at easily accessible temperatures. A wide range of approaches has been explored: not only self-assembled quantum dot growth but also lithographic methods for site-controlled nanostructure formation. All these approaches face common challenges, particularly strong background signals which contaminate the single-photon stream and excessive spectral diffusion of the quantum dot emission wavelength. If these challenges can be successfully overcome, then ongoing rapid progress in the conventional III-V semiconductors provides a roadmap for future progress in the nitrides.

We propose to use optical tweezers to probe the Casimir interaction between microspheres inside a liquid medium for geometric aspect ratios far beyond the validity of the widely employed proximity force approximation. This setup has the potential for revealing unprecedented features associated to the non-trivial role of the spherical curvatures. For a proof of concept, we measure femtonewton double-layer forces between polystyrene microspheres at distances above 400 nm by employing very soft optical tweezers, with stiffness of the order of fractions of a fN/nm. As a future application, we propose to tune the Casimir interaction between a metallic and a polystyrene microsphere in saline solution from attraction to repulsion by varying the salt concentration. With those materials, the screened Casimir interaction may have a larger magnitude than the unscreened one. This line of investigation has the potential for bringing together different fields including classical and quantum optics, statistical physics and colloid science, while paving the way for novel quantitative applications of optical tweezers in cell and molecular biology.

A recent experiment has shown a macroscopic quantum coherent condensate at 203 K, about 19 degrees above the coldest temperature recorded on the Earth surface, 184 K $(-89.2\ ^\circ \text{C}, -128.6\ ^\circ \text{F})$ in pressurized sulfur hydride. This discovery is relevant not only in material science and condensed matter but also in other fields ranging from quantum computing to quantum physics of living matter. It has given the start to a gold rush looking for other macroscopic quantum coherent condensates in hydrides at the temperature range of living matter $200<T_c <400\ \text{K}$. We present here a review of the experimental results and the theoretical works and we discuss the Fermiology of $\text{H}_{3}\text{S}$ focusing on Lifshitz transitions as a function of pressure. We discuss the possible role of the shape resonance near a neck disrupting Lifshitz transition, in the Bianconi-Perali-Valletta (BPV) theory, for rising the critical temperature in a multigap superconductor, as the Feshbach resonance rises the critical temperature in Fermionic ultracold gases.

The progress in the generation of ultrashort pulses has continuously triggered the introduction of new spectroscopic and measurement techniques which offer the opportunity to investigate unexplored research areas with unprecedented time resolution. Few-optical cycle pulses tunable from near-infrared to visible-UV allow to shed light on ultrafast electronic relaxation processes and to achieve real-time detection of molecular vibrations and structural dynamics. High-energy few-optical cycle pulses allow the efficient production of high-order harmonics up to XUV spectral region, leading to the generation of attosecond pulses shedding light on electron wave packet dynamics in complex molecules.

The dynamical mean-field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important step in this method involves the calculation of response functions of a multiorbital impurity problem which is related to the original model. Recently there has been considerable progress in the development of techniques based on the density matrix renormalization group (DMRG) and related matrix product states (MPS) implying a substantial improvement to previous methods. In this paper we review some of the standard algorithms and compare them to the newly developed techniques, showing examples for the particular case of the half-filled two-band Hubbard model.

Graphene has been an intensely studied material, owing to its unique band structure and concomitant outstanding electronic properties. In the past decades, ultrafast terahertz (THz) spectroscopy has developed into a powerful tool to characterize ultrafast charge carrier dynamics in a wide range of materials and material structures. In this Perspective we review recent experimental work exploring the ultrafast electron dynamics in graphene in the THz spectral range, and present a simple thermodynamic picture describing the THz linear, nonlinear, and photo-induced conductivity of this remarkable material.

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.

I give a view of Cosmic Microwave Background research, briefly describing its evolution and summarizing recent observations that include the Planck satellite and ground-based experiments. I describe some of the cosmological properties that the community has been able to extract from its rich information, and look to future goals for upcoming observations.

We investigate in detail the Casimir torque induced by quantum vacuum fluctuations between two nanostructured plates. Our calculations are based on the scattering approach and take into account the coupling between different modes induced by the shape of the surface which are neglected in any sort of proximity approximation or effective medium approach. We then present an experimental setup aiming at measuring this torque.

In the last few years a multi-disciplinary approach has been launched to investigate the brain using new techniques, which are capable of probing neuronal function across the entire length scales of the brain. Here, we discuss optical tools and spatial light patterning techniques to investigate brain function from the perspective of individual neurons and neuronal circuits. We discuss both biochemical and genetic tools to stimulate neurons, as well as techniques to record neuronal activity. We discuss optical projection and imaging tricks that can be dynamically customized to a particular neuron morphology and neuronal circuit layout facilitating a systematic study of their input/output transfer functions. These optical techniques will play a major role towards understanding the operation of a brain.

Single-photon emitters (SPEs) are at the basis of many applications for quantum information management. Semiconductor-based SPEs are best suited for practical implementations because of high design flexibility, scalability and integration potential in practical devices. Single-photon emission from ordered arrays of InGaN nano-disks embedded in GaN nanowires is reported. Intense and narrow optical emission lines from quantum dot-like recombination centers are observed in the blue-green spectral range. Characterization by electron microscopy, cathodoluminescence and micro-photoluminescence indicate that single photons are emitted from regions of high In concentration in the nano-disks due to alloy composition fluctuations. Single-photon emission is determined by photon correlation measurements showing deep anti-bunching minima in the second-order correlation function. The present results are a promising step towards the realization of on-site/on-demand single-photon sources in the blue-green spectral range operating in the GHz frequency range at high temperatures.

Besides being a source of energy, light can also cool gases of atoms down to the lowest temperatures ever measured, where atomic motion almost stops. The research field of cold atoms has emerged as a multidisciplinary one, highly relevant, e.g., for precision measurements, quantum gases, simulations of many-body physics, and atom optics. In this focus article, we present the field as seen in 2015, and emphasise the fundamental role in its development that has been played by mastering light.

Light allows to time travel: light from the Universe offers the possibility to look back to its ancestral epochs, at the very first moments. Nowadays light is also a carrier that allows time to travel, bringing atomic clocks references with the most advanced precision. The frontier of timekeeping and time transfer using light paves the way to unprecedented applications in science and metrology. Light is fundamental in the present effort to redefine the unit of time, to improve our knowledge of fundamental physics laws, geodesy, radioastronomy. Light could be also a new mean to investigate dark matter in the known Universe and possibly to detect gravitational waves.

Matter-field interaction finds its simplest implementation in Cavity Quantum Electrodynamics (CQED). A single two-level atom is coupled to a few photons stored in a single mode of a high-quality resonator. In the strong-coupling regime, the coherent atom-field interaction overwhelms dissipative processes. This situation illustrates the basic quantum postulates. It is also ideal for the exploration of the quantum-classical boundary and for the realization of quantum information protocols. We briefly describe the general frame of CQED. We illustrate its fundamental interest by discussing two recent experiments, performed with circular Rydberg atoms and superconducting millimeter-wave cavities.

Nanophotonics is a multidisciplinary frontier of science that merges nanoscience and nanotechnology with conventional optics and photonics. We focus on two principal issues of nanophotonics: manipulation of optical field and light-matter interaction via various optical nanostructures. These two issues are behind all the efforts to explore, design, and build nanophotonic devices to accomplish the fundamental cause of large-scale optical integration for information processing, interconnection, and computing. We discuss various mechanisms of light-matter interaction enhancement to realize bright fluorescence, Raman, and nonlinear optical radiation, and explore methodologies and various devices for highly sensitive optical sensing and detecting, ultrahigh spatial resolution imaging, and high-efficiency energy conversion between light and electricity, heat, and other forms. All these concepts, insights, methodologies, and technologies in nanophotonics will set a solid platform to explore and achieve better future information and energy technologies that use light as powerful information and energy carriers and as prominent media to probe and manipulate the intrinsic properties of matters via light-matter interaction.

This paper provides an overview of the present questions, goals, and challenges in the field of experimental nuclear astrophysics. A number of different stellar environments and the associated conditions for nuclear-reactions–driven nucleosynthesis events and patterns are discussed. Experimental goals are presented and specific activities and initiatives are summarized for each of these burning environments. New facilities are under development and will help to provide a sound experimental base for understanding the evolution of the elements in our Universe.

Here it is shown that the chemical and physical properties of a collection of nanocrystals either isolated or self-assembled in 3D superlattices called supracrystals markedly depend on the crystalline structure of the nanocrystal.

Based on the past twenty-five years of lattice Boltzmann research, we venture into a far-flung prediction for the next twenty-five, with past and future privileged over the present state of affairs.

The status of laser-driven inertial confinement fusion research is briefly reviewed. The recent major achievement of fusion energy release exceeding the energy delivered by the laser to the fuel (Hurricane O. et al., Nature, 506 (2014) 343), and the efforts towards ignition demonstration using indirect-drive are discussed. Physics model reliability is addressed. The potentials of alternative schemes, in particular direct-drive shock ignition, are also illustrated.

In the hole-doped, high-temperature superconducting cuprates, an intrinsic heterogeneity is found, from the early observations to recent data. Below optimum doping, the heterogeneity consists of dynamic metallic and, at low temperatures, superconducting regions in the form of clusters or stripes, which develop and decay as a function of time and location in the antiferromagnetic lattice. This behaviour is underlined by the interesting linear relation between the oxygen isotope shifts of the magnetic penetration depth and the critical temperature with a slope that is a factor 2 larger than expected for the homogeneous distribution of superfluid density. Allusion is also made to the Bose-Einstein condensation reported in structurally heterogeneous, polycrystalline polymer platelets as well as especially to the heterogeneous distribution of visible and dark matter in the Universe, which point to a change of paradigm in modern physics.

Based on the invention and operation of the transistor, the alloy diode laser, the quantum-well diode laser and the high-speed heterojunction bipolar transistor (HBT), we have invented and realized now a transistor laser (TL). The transistor laser is a three-terminal technology providing coupling and the coherent light emission in the transistor. The quantum-well (QW) heterojunction bipolar transistor laser, inherently a fast switching device, operates by transporting a small minority base charge density ${\sim}10^{16}\ \text{cm}^{-3}$ over a nanoscale base thickness $(<900\ \text{A})$ in picoseconds. The TL, owing to its fast recombination speed, its unique three-terminal configuration, and complementary nature of its optical and electrical collector output signals, enables resonance-free base current and collector voltage modulation. It is a compact source of electro-optical applications such as nonlinear signal mixing, frequency multiplication, negative feedback, and optoelectronics logic gates.

Following a historical introduction on the nature of light and its interaction with matter, a survey is given of the development of lasers capable of delivering short pulses of very intense radiation. The peak intensities of these laser pulses are so high that the corresponding laser fields can compete with, or even dominate, the Coulomb field in governing the dynamics of atomic systems. As a result, new phenomena, known as multiphoton processes, can occur. An outline is given of the basic properties found in the study of three important multiphoton processes. Firstly, the multiphoton ionization of atoms and the phenomenon of "above-threshold ionization". Secondly, the emission by atoms of high-order harmonics of the frequency of the driving laser and their use to generate laser pulses having durations in the attosecond range. Thirdly, laser-assisted electron-atom collisions. A review is then given of the main non-perturbative methods which have been used to perform theoretical studies of multiphoton processes.

The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.