Table of contents

Nonlinear stripe patterns in two spatial dimensions break the rotational symmetry and generically show a preferred orientation near domain boundaries, as described by the famous Newell–Whitehead–Segel (NWS) equation. We first demonstrate that, as a consequence, stripes favour rectangular over quadratic domains. We then investigate the effects of patterns 'living' in deformable domains by introducing a model coupling a generalized Swift–Hohenberg model to a generic phase field model describing the domain boundaries. If either the control parameter inside the domain (and therefore the pattern amplitude) or the coupling strength ('anchoring energy' at the boundary) are increased, the stripe pattern self-organizes the domain on which it 'lives' into anisotropic shapes. For smooth phase field variations at the domain boundaries, we simultaneously find a selection of the domain shape and the wave number of the stripe pattern. This selection shows further interesting dynamical behavior for rather steep variations of the phase field across the domain boundaries. The here-discovered feedback between the anisotropy of a pattern and its orientation at boundaries is relevant e.g. for shaken drops or biological pattern formation during development.

Ultra-intense lasers produce and manipulate plasmas, allowing to locally generate extremely high static and electromagnetic fields. This study presents a concept of an ultra-intense optical tweezer, where two counter-propagating circularly polarized intense lasers of different frequencies collide on a nano-foil. Interfering inside the foil, lasers produce a beat wave, which traps and moves plasma electrons as a thin sheet with an optically controlled velocity. The electron displacement creates a plasma micro-capacitor with an extremely strong electrostatic field, that efficiently generates narrow-energy-spread ion beams from the multi-species targets, e.g. protons from the hydrocarbon foils. The proposed ion accelerator concept is explored theoretically and demonstrated numerically with the multi-dimensional particle-in-cell simulations.

A quantum system composed of a molecule and an atomic ensemble, confined in a microscopic cavity, is investigated theoretically. The indirect coupling between atoms and the molecule, realized by their interaction with the cavity radiation mode, leads to a coherent mixing of atomic and molecular states, and at strong enough cavity field strengths hybrid atom–molecule–photon polaritons are formed. It is shown for the Na₂ molecule that by changing the cavity wavelength and the atomic transition frequency, the potential energy landscape of the polaritonic states and the corresponding spectrum could be changed significantly. Moreover, an unforeseen intensity borrowing effect, which can be seen as a strong nonadiabatic fingerprint, is identified in the atomic transition peak, originating from the contamination of the atomic excited state with excited molecular rovibronic states.

Understanding the resilience of infrastructures, such as a transportation network, has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with characteristic link length such as power-grids and the brain. However, although many real-world networks are spatially embedded and their links have characteristics length such as pipelines, power lines or ground transportation lines they are not homogeneous but rather heterogeneous. For example, density of links within cities are significantly higher than between cities. Here we develop and study numerically and analytically a similar realistic heterogeneous spatial modular model using percolation process to better understand the effect of heterogeneity on such networks. The model assumes that inside a city there are many lines connecting different locations, while long lines between the cities are sparse and usually directly connecting only a few nearest neighbours cities in a two dimensional plane. We find that our heterogeneous model experiences two distinct continuous transitions, one when the cities disconnect from each other and the second when each city breaks apart. This is in contrast to the homogeneous model where a single transition is found. Although the critical threshold for site percolation in 2D grid remains an open question we analytically find the critical threshold for site percolation in this model. In addition, it has been found that the homogeneous model experience a single transition having a unique phenomenon called critical stretching where a geometric crossover from random to spatial structure in different scales found to stretch non-linearly with the characteristic length at criticality. In marked contrast, we show here that the heterogeneous model does not experience such a phenomenon indicating that critical stretching strongly depends on the network structure.

Coherent guiding of atoms in two-colour evanescent light fields of two fundamental modes of suspended optical rib waveguides is investigated theoretically. Special attention is paid to waveguides of widths larger than the wavelength of light, which provide better lateral stability of the surface traps and waveguides, and can be used in coherent Bragg beam splitters for matter waves, based on optical gratings formed by interference of evanescent light waves of two crossed optical waveguides. A single-mode regime for evanescent-wave waveguides for atoms is investigated. The general structure and key elements of all-optical atom chips are discussed.

We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.

Capillary attraction at the meniscus between tiny objects plays a crucial role in self-assembly processes. The shape of the meniscus governed by the Laplace equation devotes to a long-range attraction distinct to the DLVO defined forces. Rather than considering trapped particles on ideal smooth surfaces, we use patterned substrates with ordered nano-arrays for theoretical modeling toward the capillary assembly. The vertical elevation of particles is found to change the shape of the meniscus between particles, therefore the interaction energy and capillary force. A minimal model is developed to determine the capillary force between particles and thus the motility of particles, therefore the criterion of the crystallization of colloidal particles. It turns out that the formation of a colloidal crystal or amorphous medium depends on the optimization between the scaled particle separation by its size and the geometrical design of the supporting nano-arrays. Finally, we experimentally confirmed the capillary assembly from colloidal suspensions, by playing the control parameters defined in our theoretical model, with a nice agreement. This model system can mimic the practical applications of nano-structure fabrication on versatile real surfaces for functionality purposes.

We propose the Gaussian continuous-variable quantum key distribution using squeezed states in the composite channels including atmospheric propagation with transmittance fluctuations. We show that adjustments of signal modulation and use of optimal feasible squeezing can be sufficient to significantly overcome the coherent-state protocol and drastically improve the performance of quantum key distribution in atmospheric channels, also in the presence of additional attenuating and noisy channels. Furthermore, we consider examples of atmospheric links of different lengths, and show that optimization of both squeezing and modulation is crucial for reduction of protocol downtime and increase of secure atmospheric channel distance. Our results demonstrate unexpected advantage of fragile squeezed states of light in the free-space quantum key distribution applicable in daylight and stable against atmospheric turbulence.

The plasmodium of the unicellular slime mould Physarum polycephalum forms an extended vascular network in which protoplasm is transported through the giant cell due to peristaltic pumping. The flow in the veins is always parabolic and it performs shuttle streaming, i.e., the flow reverses its direction periodically. However, particles suspended in the protoplasm are effectively and rapidly distributed within the cell. To elucidate how an effective mixing can be achieved in such a microfluidic system with Poiseuille flow, we performed micro-particle imaging velocimetry experiments and advected virtual tracers in the determined time-dependent flow fields. Two factors were found to be crucial for effective mixing: (i) flow splitting and flow reversals occurring at junctions of veins and (ii) small delays in the reversals of flows in the veins at a junction. These factors enhance the distribution of fluid volumes and hence promote mixing due to chaotic advection. From the residence time distributions of particles at a junction, it is estimated that about 10% of the volume is effectively redistributed at a junction during one period of the shuttle streaming. We presume that the principles of mixing unravelled in P. polycephalum represent a promising approach to achieve efficient mixing in man-made microfluidic devices.

In the mitotic spindle microtubules attach to kinetochores via catch bonds during metaphase, and microtubule depolymerization forces give rise to stochastic chromosome oscillations. We investigate the cooperative stochastic microtubule dynamics in spindle models consisting of ensembles of parallel microtubules, which attach to a kinetochore via elastic linkers. We include the dynamic instability of microtubules and forces on microtubules and kinetochores from elastic linkers. A one-sided model, where an external force acts on the kinetochore is solved analytically employing a mean-field approach based on Fokker–Planck equations. The solution establishes a bistable force–velocity relation of the microtubule ensemble in agreement with stochastic simulations. We derive constraints on linker stiffness and microtubule number for bistability. The bistable force–velocity relation of the one-sided spindle model gives rise to oscillations in the two-sided model, which can explain stochastic chromosome oscillations in metaphase (directional instability). We derive constraints on linker stiffness and microtubule number for metaphase chromosome oscillations. Including poleward microtubule flux into the model we can provide an explanation for the experimentally observed suppression of chromosome oscillations in cells with high poleward flux velocities. Chromosome oscillations persist in the presence of polar ejection forces, however, with a reduced amplitude and a phase shift between sister kinetochores. Moreover, polar ejection forces are necessary to align the chromosomes at the spindle equator and stabilize an alternating oscillation pattern of the two kinetochores. Finally, we modify the model such that microtubules can only exert tensile forces on the kinetochore resulting in a tug-of-war between the two microtubule ensembles. Then, induced microtubule catastrophes after reaching the kinetochore are necessary to stimulate oscillations. The model can reproduce experimental results for kinetochore oscillations in PtK1 cells quantitatively.

We present a theoretic analysis on (azimuthal) spin momentum-dependent orbital motion experienced by particles in a circularly-polarized annular focused field. Unlike vortex phase-relevant (azimuthal) orbital momentum flow whose direction is specified by the sign of topological charge, the direction of (azimuthal) spin momentum flow is determined by the product of the field's polarization ellipticity and radial derivative of field intensity. For an annular focused field with a definite polarization ellipticity, the intensity's radial derivative has opposite signs on two sides of the central ring (intensity maximum), causing the spin momentum flow to reverse its direction when crossing the central ring. When placed in such a spin momentum flow, a probe particle is expected to response to this flow configuration by changing the direction of orbital motion as it traversing from one side to the other. The reversal of the particle's orbital motion is a clear sign that spin momentum flow can affect particles' orbital motion alone even without orbital momentum flow. More interestingly, for dielectric particles the spin momentum-dependent orbital motion tends to be 'negative', i.e., in the opposite direction of the spin momentum flow. This arises mainly because of spin–orbit interaction during the scattering process. For the purpose of experimental observation, we suggest the introduction of an auxiliary radially-polarized illumination to adjust the particle's radial equilibrium position, for the radial gradient force of the circularly-polarized annular focused field tends to constrain the particle at the ring of intensity maximum.

Among the families of transition metal dichalcogenides (TMDs), Pd-based TMDs have been one of the less explored materials. In this study, we investigate the electronic properties of PdX₂ (X = S, Se, or Te) bulk and thin films. The analysis of structural stability shows that the bulk and thin film (1 to 5 layers) structures of PdS₂ exhibit pyrite, while PdTe₂ exhibits 1T. Furthermore, PdSe₂ exhibits pyrite in bulk and thin films down to the bilayer. Most surprisingly, PdSe₂ monolayer transits to 1T phase. For the electronic properties of the stable bulk configurations, pyrite PdS₂ and PdSe₂, and 1T PdTe₂, demonstrate semi-metallic features. For monolayer, on the other hand, the stable pyrite PdS₂ and 1T PdSe₂ monolayers are insulating with band gaps of 1.399 eV and 0.778 eV, respectively, while 1T PdTe₂ monolayer remains to be semi-metallic. The band structures of all the materials demonstrate a decreasing or closing of indirect band gap with increasing thickness. Moreover, the stable monolayer band structures of PdS₂ and PdSe₂ exhibit flat bands and diverging density of states near the Fermi level, indicating the presence of van Hove singularity. Our results show the sensitivity and tunability of the electronic properties of PdX₂ for various potential applications.

Development of acoustic and optoacoustic on-chip technologies calls for new solutions to guiding, storing and interfacing acoustic and optical waves in integrated silicon-on-insulator systems. One of the biggest challenges in this field is to suppress the radiative dissipation of the propagating acoustic waves, while co-localizing the optical and acoustic fields in the same region of an integrated waveguide. Here we address this problem by introducing anti-resonant reflecting acoustic waveguides (ARRAWs)—mechanical analogues of the anti-resonant reflecting optical waveguides. We discuss the principles of anti-resonant guidance and establish guidelines for designing efficient ARRAWs. Finally, we demonstrate examples of the simplest silicon/silica ARRAW platforms that can simultaneously serve as near-IR optical waveguides, and support strong backward Brillouin scattering.

As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett.89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The second is that small fluctuations of the parameters of optical elements do not affect the first conclusion. This implies that the method is robust against the certain type of errors as we considered. Last but not least, we present an example of implementation of the simulation on a photonic chip as well as an optimized scheme. By such examples, we show a reduction of the costs compared to its classical counterpart and the potential for further improvement, which promotes a more general application.

We study the phase diagram and transport properties of arbitrarily doped quantum wires functionalized by magnetic adatoms. The appropriate theoretical model for these systems is a dense one-dimensional Kondo lattice (KL) which consists of itinerant electrons interacting with localized quantum magnetic moments. We discover the novel phase of the locally helical metal where transport is protected from a destructive influence of material imperfections. Paradoxically, such a protection emerges without a need of the global helicity, which is inherent in all previously studied helical systems and requires breaking the spin-rotation symmetry. We explain the physics of this protection of the new type, find conditions, under which it emerges, and discuss possible experimental tests. Our results pave the way to the straightforward realization of the protected ballistic transport in quantum wires made of various materials.

We present a detailed analysis about the changes of the orbital electron-correlation effects in one quantum-dot circuit, by considering finite couplings between the quantum dots and Majorana zero modes (MZMs). It is found that the dot-MZM couplings complicate the orbital-Kondo effect, because the orbital correlation occurs between the localized states in the quantum dots and the continuum hybridized states induced by the indirect metal-MZM couplings. When two of such correlation exist in pair, they have an opportunity to induce a long-range RKKY correlation, which is related to the MZMs. Further investigation shows that this RKKY interaction leads to the anomalous fractional Josephson effect. Our work can be helpful in clarifying the influence of MZM on the orbital electron correlation effects.

We construct an artificial neural network to study the pairing symmetries in disordered superconductors. For Hamiltonians on square lattice with s-wave, d-wave, and nematic pairing potentials, we use the spin-polarized local density of states near a magnetic impurity in the clean system to train the neural network. We find that, when the depth of the artificial neural network is sufficient large, it will have the power to predict the pairing symmetries in disordered superconductors. In a large parameter regime of the potential disorder, the artificial neural network predicts the correct pairing symmetries with relatively high confidences.

This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D₀), as well as a low (D_m) and a high (D_d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D_d will redistribute particles near the channel wall, while the diffusivity D_m will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D_d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D_m, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.

A key element of optical spectroscopy is the link between observable selection rules and the underlying symmetries of an investigated physical system. Typically, selection rules directly relate to the sample properties probed by light, yielding information on crystalline structure or chirality, for example. Considering light-matter coupling more broadly may extend the scope of detectable symmetries, to also include those directly arising from the interaction. In this letter, we experimentally demonstrate an emerging class of symmetries in the electromagnetic field emitted by a strongly driven atomic system. Specifically, generating high-harmonic radiation with attosecond-controlled two-color fields, we find different sets of allowed and forbidden harmonic orders. Generalizing symmetry considerations of circularly polarized high-harmonic generation, we interpret these selection rules as a complete triad of dynamical symmetries. We expect such emergent symmetries also for multi-atomic and condensed-matter systems, encoded in the spectral and spatial features of the radiation field. Notably, the observed phenomenon gives robust access to chiral processes with few-attosecond time precision.

We report on the observation of strain- and magneto-electric coupling in a system consisting of a thin film of ferromagnetic La_(1−x)Sr_xMnO₃ (LSMO, x = 0.5 and 0.3) on a ferroelectric BaTiO₃ (BTO) substrate. Pronounced magnetization steps occur at the BTO structural phase transitions. We associate these steps with a strain induced change of the magnetic anisotropy. Temperature dependent magneto-electric coupling could be evidenced by the magnetic response to an applied AC electric field in all ferroelectric phases of the BTO substrate. In a DC electric field, the magnetization changes are asymmetric with respect to the polarity. Polarized neutron reflectometry hints to oxygen migration as possible mechanism for this asymmetry. It also reveals strain-induced magnetization changes throughout most of the thickness of 252 Å (x = 0.5) and 360 Å (x = 0.3), respectively, of the LSMO layer. We conclude that the change of the magnetization depth profile at the interface as previously proposed by ab initio calculations is not the relevant mechanism. Instead strain, oxygen vacancies and frustration at interfacial steps dominate the magnetic response to an applied electric field.

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin–orbit coupled Bose–Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play an important role in the experiments of BEC with artificial gauge fields. Beams created by FWM processes are an important source of correlated particles and can be used in the experiments testing quantum properties of atomic ensembles.

Plasma sheaths characterized by electrons with relativistic energies and far from thermodynamic equilibrium are governed by a rich and largely unexplored physics. A reliable kinetic description of relativistic non-equilibrium plasma sheaths—besides its interest from a fundamental point of view—is crucial to many application, from controlled nuclear fusion to laser-driven particle acceleration. Sheath models proposed in the literature adopt either relativistic equilibrium distribution functions or non-relativistic non-equilibrium distribution functions, making it impossible to properly capture the physics involved when both relativistic and non-equilibrium effects are important. Here we tackle this issue by solving the electrostatic Vlasov–Poisson equations with a new class of fully-relativistic distribution functions that can describe non-equilibrium features via a real scalar parameter. After having discussed the general properties of the distribution functions and the resulting plasma sheath model, we establish an approach to investigate the effect of non-equilibrium solely. Then, we apply our approach to describe laser–plasma ion acceleration in the target normal sheath acceleration scheme. Results show how different degrees of non-equilibrium lead to the formation of sheaths with significantly different features, thereby having a relevant impact on the ion acceleration process. We believe that this approach can offer a deeper understanding of relativistic plasma sheaths, opening new perspectives in view of their applications.

Scattering effects are ubiquitous in practical wireless optical links. Here a transmission model with complete consideration of scattered light and beam wandering effects for underwater link is developed, with the aim to completely characterize the received quantum state of light through dense scattering medium. Based on this model, we show the influence of scattered photons on the improvement of the entanglement after transmission through turbid water may vary for different copropagation scenarios, i.e., the contribution of scattered light on entanglement transmission may be turned from positive to negative, with increase of the strength of underwater beam wandering. And the attenuation coefficient and aperture size are found to be the dominant factors affecting the entanglement through underwater link. While for the counterpropagation scenario, the scattered photons will severely deteriorate the entanglement transmission especially for the high-loss scattering links. These findings may shed light on quantum entanglement transmission and help to develop its applications through dense scattering medium.

A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understand the power of neural networks, and show that image classification problems can be efficiently solved must obey the area law.

The accelerated progress in manufacturing noisy, intermediate-scale quantum (NISQ) computing hardware has opened the possibility of exploring its application in transforming approaches to solving computationally challenging problems. The important limitations common among all NISQ computing technologies are the absence of error correction and the short coherence time, which limit the computational power of these systems. Shortening the required time of a single run of a quantum algorithm is essential for reducing environment-induced errors and for the efficiency of the computation. We have investigated the ability of a variational version of adiabatic state preparation (ASP) to generate an accurate state more efficiently compared to existing adiabatic methods. The standard ASP method uses a time-dependent Hamiltonian, connecting the initial Hamiltonian with the final Hamiltonian. In the current approach, a navigator Hamiltonian is introduced which has a non-zero amplitude only in the middle of the annealing process. Both the initial and navigator Hamiltonians are determined using variational methods. A Hermitian cluster operator, inspired by coupled-cluster theory and truncated to single and double excitations/de-excitations, is used as a navigator Hamiltonian. A comparative study of our variational algorithm (VanQver) with that of standard ASP, starting with a Hartree–Fock Hamiltonian, is presented. The results indicate that the introduction of the navigator Hamiltonian significantly improves the annealing time required to achieve chemical accuracy by two to three orders of magnitude. The efficiency of the method is demonstrated in the ground-state energy estimation of molecular systems, namely, H₂, P4, and LiH.

To date, individual addressing of ion qubits has relied primarily on local Rabi or transition frequency differences between ions created via electromagnetic field spatial gradients or via ion transport operations. Alternatively, it is possible to synthesize arbitrary local one-qubit gates by leveraging local phase differences in a global driving field. Here we report individual addressing of ⁴⁰Ca⁺ ions in a two-ion crystal using axial potential modulation in a global gate laser field. We characterize the resulting gate performance via one-qubit randomized benchmarking, applying different random sequences to each co-trapped ion. We identify the primary error sources and compare the results with single-ion experiments to better understand our experimental limitations. These experiments form a foundation for the universal control of two ions, confined in the same potential well, with a single gate laser beam.

We examine skyrmions under a dc drive interacting with a square array of obstacles for varied obstacle size and damping. When the drive is applied in a fixed direction, we find that the skyrmions are initially guided in the drive direction but also move transverse to the drive due to the Magnus force. The skyrmion Hall angle, which indicates the difference between the skyrmion direction of motion and the drive direction, increases with drive in a series of quantized steps as a result of the locking of the skyrmion motion to specific symmetry directions of the obstacle array. On these steps, the skyrmions collide with an integer number of obstacles to create a periodic motion. The transitions between the different locking steps are associated with jumps or dips in the velocity–force curves. In some regimes, the skyrmion Hall angle is actually higher than the intrinsic skyrmion Hall angle that would appear in the absence of obstacles. In the limit of zero damping, the skyrmion Hall angle is 90°, and we find that it decreases as the damping increases. For multiple interacting skyrmion species in the collective regime, we find jammed behavior at low drives where the different skyrmion species are strongly coupled and move in the same direction. As the drive increases, the species decouple and each can lock to a different symmetry direction of the obstacle lattice, making it possible to perform topological sorting in analogy to the particle sorting methods used to fractionate different species of colloidal particles moving over two-dimensional obstacle arrays.

Although the Cu doped Bi₂Se₃ topological insulator was discovered and intensively studied for almost a decade, its electrical and magnetic properties in normal state, and the mechanism of 'high-T_c' superconductivity regarding the relatively low-carrier density are still not addressed yet. In this work, we report a systematic investigation of magnetic susceptibility, critical fields, and electrical transport on the nominal Cu_0.20Bi₂Se₃ single crystals with ${T}_{\mathrm{c}}^{\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{t}}$ = 4.18 K, the highest so far. The composition analysis yields the Cu stoichiometry of x = 0.09(1). The magnetic susceptibility shows considerable anisotropy and an obvious kink at around 96 K was observed in the magnetic susceptibility for H∥c, which indicates a charge density anomaly. The electrical transport measurements indicate the two-dimensional (2D) Fermi liquid behavior at low temperatures with a high Kadowaki–Woods ratio, A/γ² = 30.3a₀. The lower critical field at 0 K limit was extracted to be 6.0 Oe for H∥ab. In the clean limit, the ratio of energy gap to T_c was determined to be Δ₀/k_BT_c = 2.029 ± 0.124 exceeding the standard BCS value 1.764, suggesting Cu_0.09Bi₂Se₃ is a strong-coupling superconductor. The in-plane penetration depth at 0 K was calculated to be 1541.57 nm, resulting in an unprecedented high ratio of T_c/λ⁻²(0) ≅ 9.86. Moreover, the ratio of T_c to Fermi temperature is estimated to be ${T}_{\mathrm{c}}/{T}_{\mathrm{F}}^{2\mathrm{D}}$ = 0.034. Both ratios fall into the region of unconventional superconductivity according to Uemura's regime, supporting the unconventional superconducting mechanism in Cu_xBi₂Se₃. Finally, the enhanced T_c value higher than 4 K is proposed to arise from the increased density of states at Fermi energy and strong electron–phonon interaction induced by the charge density instability.

We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor Q_i. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure Q_i as function of frequency, power and temperature. We observe a linear increase of Q_i with frequency, as predicted by the simulations for a constant electromechanical coupling. Additionally, Q_i shows a weak power dependence and a negligible temperature dependence around 10 mK, excluding two level systems and non-equilibrium quasiparticles as the main source of losses at that temperature.

Coherent, broadband pulses of extreme ultraviolet light provide a new and exciting tool for exploring attosecond electron dynamics. Using photoelectron streaking, interferometric spectrograms can be generated that contain a wealth of information about the phase properties of the photoionization process. If properly retrieved, this phase information reveals attosecond dynamics during photoelectron emission such as multielectron dynamics and resonance processes. However, until now, the full retrieval of the continuous electron wavepacket phase from isolated attosecond pulses has remained challenging. Here, after elucidating key approximations and limitations that hinder one from extracting the coherent electron wavepacket dynamics using available retrieval algorithms, we present a new method called absolute complex dipole transition matrix element reconstruction (ACDC). We apply the ACDC method to experimental spectrograms to resolve the phase and group delay difference between photoelectrons emitted from Ne and Ar. Our results reveal subtle dynamics in this group delay difference of photoelectrons emitted form Ar. These group delay dynamics were not resolvable with prior methods that were only able to extract phase information at discrete energy levels, emphasizing the importance of a complete and continuous phase retrieval technique such as ACDC. Here we also make this new ACDC retrieval algorithm available with appropriate citation in return.

Spin pumping is a widely recognized method to generate the spin current in the spintronics, which can be found in varieties of magnetic materials and is acknowledged as a fundamentally dynamic process equivalent to the spin-transfer torque. In this work, we theoretically verified the oscillating spin current mixed by AC and DC components can be pumped from the microwave-motivated breathing skyrmion. The spin current can be pumped within a relatively low-frequency microwave compared with the in-plane ferromagnetic resonance (FMR). Although the amplitude of spin current density for a single confined skyrmion is several times lower than the FMR spin pumping, the pumped current would be improved to be the same order as the FMR through a tight skyrmion lattice. Based on the spin pumping of breathing skyrmion, we designed a high reading-speed racetrack memory model whose reading speed is much higher than the SOT (spin–orbit torque)/STT (spin-transfer torque) skyrmion racetrack. Our work focuses on the spin pumping phenomenon inside the breathing skyrmion, and it may contribute to the applications of the skyrmion-based device.

In this article we report on a novel way to incorporate complex network structure into the analysis of interacting particle systems. More precisely, it is well-known that in well-mixed/homogeneous/all-to-all-coupled systems, one may derive mean-field limit equations such as Vlasov–Fokker–Planck equations (VFPEs). A mesoscopic VFPE describes the probability of finding a single vertex/particle in a certain state, forming a bridge between microscopic statistical physics and macroscopic fluid-type approximations. One major obstacle in this framework is to incorporate complex network structures into limiting equations. In many cases, only heuristic approximations exist, or the limits rely on particular classes of integral operators. In this paper, we notice that there is a much more elegant, and profoundly more general, way available due to recent progress in the theory of graph limits. In particular, we show how one may easily enter complex network dynamics via graphops (graph operators) into VFPEs.

The electric dipole moment of the electron (eEDM) can be measured with high precision using heavy polar molecules. In this paper, we report on a series of new techniques that have improved the statistical sensitivity of the YbF eEDM experiment. We increase the number of molecules participating in the experiment by an order of magnitude using a carefully designed optical pumping scheme. We also increase the detection efficiency of these molecules by another order of magnitude using an optical cycling scheme. In addition, we show how to destabilise dark states and reduce backgrounds that otherwise limit the efficiency of these techniques. Together, these improvements allow us to demonstrate a statistical sensitivity of 1.8 × 10⁻²⁸ e cm after one day of measurement, which is 1.2 times the shot-noise limit. The techniques presented here are applicable to other high-precision measurements using molecules.

As it has been demonstrated that trapped ion systems have unmatched long-lived quantum-bit (qubit) coherence and can support high-fidelity quantum manipulations, how to scale up the system size becomes an inevitable task for practical purposes. In this work, we theoretically analyse the physical limitation of scalability with a trapped ion array, and propose a feasible scheme of architecture that in principle allows an arbitrary number of ion qubits, for which the overhead only scales linearly with the system size. This scheme relies on the combined ideas of a trap architecture of tunable size, stabilisation of an ion crystal by optical tweezers, and continuous sympathetic cooling without touching the stored information. We demonstrate that illumination of optical tweezers modifies the motional spectrum by effectively pinning the ions, lifting the frequencies of the motional ground modes. By doing so, we make the structure of the array less vulnerable from thermal excitations, and suppress the position fluctuations to insure faithful gate operations. Finally, we also explore the local behaviour of cooling when a sub-array is isolated by optical tweezers from other parts of the crystal.

We use a variety of experimental techniques to characterize Cu clusters on bulk MoS₂ formed via physical vapor deposition of Cu in ultrahigh vacuum, at temperatures ranging from 300 K to 900 K. We find that large facetted clusters grow at elevated temperatures, using high Cu exposures. The cluster size distribution is bimodal, and under some conditions, large clusters are surrounded by a denuded zone. We propose that defect-mediated nucleation, and coarsening during deposition, are both operative in this system. At 780 K, a surprising type of facetted cluster emerges, and at 900 K this type predominates: pyramidal clusters with a triangular base, exposing (311) planes as side facets. This is a growth shape, rather than an equilibrium shape.

Topological edge states have crucial applications in nano spintronics and valleytronics devices, while topological inner-edge states have seldom been extensively researched in this field. Based on the inner-edge states of the hybridized zigzag silicene-like nanoribbons, we investigate their transport properties. We propose two types of spin–valley filters. The first type can generate two different spin–valley polarized currents in output leads, respectively. The second type outputs the specific spin–valley polarized current in only one of the output leads. All these inner-edge states have the spin–valley-momentum locking property. These types of filters can switch the output spin–valley polarizations by modulating the external fields. Besides, we also find that the device size plays a crucial role in designing these spin–valley filters. Moreover, the local current distributions are calculated to visualize the detailed transport process and understand the mechanism. The mechanism lies that the spin–valley polarized current can nearly freely pass through the system with the same momentum, spin and valley degrees of freedom. The small reflection of the current results from the inter-valley scattering. In particular, we also consider the realistic (disorder) effects on the performance of these filters to ensure the robustness of our systems. We believe these spin–valley current filtering effects have potential applications in the future spintronics and valleytronics device designs.

The nonsymmetrized current noise is crucial for the analysis of light emission in nanojunctions. The latter represent non-classical photon emitters whose description requires a full quantum approach. It was found experimentally that light emission can occur with a photon energy exceeding the applied dc voltage, which intuitively should be forbidden due to the Pauli principle. This overbias light emission cannot be described by the single-electron physics, but can be explained by two-electron or even three-electron processes, correlated by a local resonant mode in analogy to the well-known dynamical Coulomb blockade (DCB). Here, we obtain the nonsymmetrized noise for junctions driven by an arbitrarily shaped periodic voltage. We find that when the junction is driven, the overbias light emission exhibits intriguingly different features compared to the dc case. In addition to kinks at multiples of the bias voltage, side kinks appear at integer multiples of the ac driving frequency. Our work generalizes the DCB theory of light emission to driven tunnel junctions and opens the avenue for engineered quantum light sources, which can be tuned purely by applied voltages.

The effective Hamiltonian method has recently received considerable attention due to its power to deal with finite-temperature problems and large-scale systems. In this work, we put forward a machine learning (ML) approach to generate realistic effective Hamiltonians. In order to find out the important interactions among many possible terms, we propose some new techniques. In particular, we suggest a new criterion to select models with less parameters using a penalty factor instead of the commonly-adopted additional penalty term, and we improve the efficiency of variable selection algorithms by estimating the importance of each possible parameter by its relative uncertainty and the error induced in the parameter reduction. We also employ a testing set and optionally a validation set to help prevent over-fitting problems. To verify the reliability and usefulness of our approach, we take two-dimensional MnO and three-dimensional TbMnO₃ as examples. In the case of TbMnO₃, our approach not only reproduces the known results that the Heisenberg, biquadratic, and ring exchange interactions are the major spin interactions, but also finds out that the next most important spin interactions are three-body fourth-order interactions. In both cases, we obtain effective spin Hamiltonians with high fitting accuracy. These tests suggest that our ML approach is powerful for identifying the effective spin Hamiltonians. Our ML approach is general so that it can be adopted to construct other effective Hamiltonians.

Unconventional superconductivity often emerges in close proximity to a magnetic instability. Upon suppressing the magnetic transition down to zero temperature by tuning the carrier concentration, pressure, or disorder, the superconducting transition temperature T_c acquires its maximum value. A major challenge is the elucidation of the relationship between the superconducting phase and the strong quantum fluctuations expected near a quantum phase transition (QPT) that is either second order (i.e. a quantum critical point) or weakly first order. While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use sensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the T = 0 penetration depth in the electron-doped iron-based superconductor Ba(Fe_1−xCo_x)₂As₂. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe₂(As_1−xP_x)₂ compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic–magnetic transition, the former is a charge-doped and significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transitions. Thus, our observation of a sharp peak in λ(x) near optimal doping, combined with the theoretical result that a QPT alone does not mandate the appearance of such peak, unveils a puzzling and seemingly universal manifestation of magnetic quantum fluctuations in iron-based superconductors and unusually robust quantum phase transition under the dome of superconductivity.

Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of noise is a challenging task. In this paper, we provide two different prescriptions to characterize noisy stabilizer states, including the surface and the color codes, in terms of localizable entanglement over a subset of qubits. In one approach, we exploit appropriately constructed entanglement witness operators to estimate a witness-based lower bound of localizable entanglement, which is directly accessible in experiments. In the other recipe, we use graph states that are local unitary equivalent to the stabilizer state to determine a computable measurement-based lower bound of localizable entanglement. If used experimentally, this translates to a lower bound of localizable entanglement obtained from single-qubit measurements in specific bases to be performed on the qubits outside the subsystem of interest. Towards computing these lower bounds, we discuss in detail the methodology of obtaining a local unitary equivalent graph state from a stabilizer state, which includes a new and scalable geometric recipe as well as an algebraic method that applies to general stabilizer states of arbitrary size. Moreover, as a crucial step of the latter recipe, we develop a scalable graph-transformation algorithm that creates a link between two specific nodes in a graph using a sequence of local complementation operations. We develop open-source Python packages for these transformations, and illustrate the methodology by applying it to a noisy topological color code, and study how the witness and measurement-based lower bounds of localizable entanglement varies with the distance between the chosen qubits.

A terahertz multifunction modulator composed of upper-layer double graphene ribbons and lower-layer a graphene strip, which can generate a Fano resonance produced by hybrid between a broad mode and a narrow mode, is proposed to realize electro-optical switch and filtering function. The electric field distribution, hybrid theory, and quantum level theory are all employed to explain the Fano resonance, whose transmission spectra are fitted by coupled mode theory. In comparison to other graphene-based terahertz modulators, the amplitude modulation degree can reach 99.57%, meaning an excellent electro-optical switch can be realized. Moreover, the extinction ratio of Fano resonance can reach 99.70%, demonstrating an unparalleled electro-optical filter is implemented. Finally, variations in the lateral and longitudinal lengths of the lower-layer a graphene strip enable excellent dual-band, triple-band filters. Thus, this work provides a new way to implement terahertz multi-function modulators.

An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits (Yurke B and Denker J S 1984 Phys. Rev. A29 1419, Reiter F and Sørensen A S 2012 Phys. Rev. A85 032111 and Amin M H et al 2012 Phys. Rev. A86 052314), the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method. This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer–Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians.

We describe quantum limits to field sensing that relate noise, geometry and measurement duration to fundamental constants, with no reference to particle number. We cast the Tesche and Clarke (TC) bound on dc-SQUID sensitivity as such a limit, and find analogous limits for volumetric spin-precession magnetometers. We describe how randomly-arrayed spins, coupled to an external magnetic field of interest and to each other by the magnetic dipole–dipole interaction, execute a spin dynamics that depolarizes the spin ensemble even in the absence of coupling to an external reservoir. We show the resulting spin dynamics are scale invariant, with a depolarization rate proportional to spin number density and thus a number-independent quantum limit on the energy resolution per bandwidth E_R. Numerically, we find E_R ⩾ αℏ, α ∼ 1, in agreement with the TC limit, for paradigmatic spin-based measurements of static and oscillating magnetic fields.

In this article we present a full description of the quantum Kerr Ising model—a linear optical network of parametrically pumped Kerr nonlinearities. We consider the non-dissipative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally, we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities.

A comprehensive analysis of the exact unitary dynamics of two-component mass-imbalanced fermions in a one-dimensional double-well potential is accomplished by considering the total number of particles maximum up to six. The simultaneous effect of mass imbalance between the flavors and their mutual interactions on the dynamics is scrutinized through the exact diagonalization. In particular, we investigate the occupation dynamics of such systems being initially prepared in experimentally accessible states in which opposite components occupy opposite wells. Moreover, to capture the role of interactions, we also inspect situations in which initial states contain an opposite-spin pair localized in a chosen well. Finally, to assess the amount of quantum correlations produced during the evolution, we analyze the behavior of the von Neumann entanglement entropy between components.

The coupling of laser energy to electrons is fundamental to almost all topics in intense laser–plasma interactions, including laser-driven particle and radiation generation, relativistic optics, inertial confinement fusion and laboratory astrophysics. We report measurements of total energy absorption in foil targets ranging in thickness from 20 μm, for which the target remains opaque and surface interactions dominate, to 40 nm, for which expansion enables relativistic-induced transparency and volumetric interactions. We measure a total peak absorption of ∼80% at an optimum thickness of ∼380 nm. For thinner targets, for which some degree of transparency occurs, although the total absorption decreases, the number of energetic electrons escaping the target increases. 2D particle-in-cell simulations indicate that this results from direct laser acceleration of electrons as the intense laser pulse propagates within the target volume. The results point to a trade-off between total energy coupling to electrons and efficient acceleration to higher energies.

In the first experimental realization of dilute Bose–Bose liquid drops using two hyperfine states of ³⁹K some discrepancies between theory and experiment were observed. The standard analysis of the data using the Lee–Huang–Yang beyond mean-field theory predicted critical numbers which were significantly off the experimental measurements. Also, the radial size of the drops in the experiment proved to be larger than expected from this theory. Using a new functional, which is based on quantum Monte Carlo results of the bulk phase incorporating finite-range effects, we can explain the origin of the discrepancies in the critical number. This result proves the necessity of including finite-range corrections to deal with the observed properties in this setup. The controversy on the radial size is reasoned in terms of the departure from the optimal concentration ratio between the two species of the mixture.

We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called thermodynamic uncertainty relations (TURs). We not only strengthen the bounds but extend their realm of applicability and in many cases prove their optimality, without resorting to large deviation theory or information-theoretic techniques. In particular, we find the best TUR based on entropy production alone. We also derive a periodic uncertainty principle of which previous known bounds for periodic or stationary Markov chains known in the literature appear as limit cases. From it a novel bound for stationary Markov processes is derived, which surpasses previous known bounds. Our results exploit the non-invariance of the system under a symmetry which can be other than time reversal and thus open a wide new spectrum of applications.

During the past decades, pattern formulation with reaction–diffusion systems has attracted great research interest. Complex networks, from single-layer networks to more complicated multiplex networks, have made great contribution to the development of this area, especially with emergence of Turing patterns. While among vast majority of existing works on multiplex networks, they only take into account the simple case with ordinary diffusion, which is termed as self-diffusion. However, cross-diffusion, as a significant phenomenon, reveals the direction of species' movement, and is widely found in chemical, biological and physical systems. Therefore, we study the pattern formulation on multiplex networks with the presence of both self-diffusion and cross-diffusion. Of particular interest, heterogeneous patterns with abundant characteristics are generated, which cannot arise in other systems. Through linear analysis, we theoretically derive the Turing instabilities region. Besides, our numerical experiments also generate diverse patterns, which verify the theoretical prediction in our work and show the impact of cross-diffusion on pattern formulation on multiplex networks.

Odd-parity error rejection (OPER), in particular the method of actively odd parity pairing (AOPP), can drastically improve the asymptotic key rate of sending-or-not-sending twin-field (SNS-TF) quantum key distribution (QKD). However, in practice, the finite-key effects have to be considered for the security. Here, we propose a zigzag approach to verify the phase-flip error of the survived bits after OPER or AOPP. Based on this, we can take all the finite-key effects efficiently in calculating the non-asymptotic key rate. Numerical simulation shows that our approach here produces the highest key rate over all distances among all existing methods, improving the key rate by more than 100% to 3000% in comparison with different prior art methods with typical experimental setting. These verify the advantages of the AOPP method with finite data size. Also, with our zigzag approach here, the non-asymptotic key rate of SNS-TF QKD can by far break the absolute bound of repeater-less key rate with whatever detection efficiency. We can even reach a non-asymptotic key rate more than 40 times of the practical bound and 13 times of the absolute bound with 10¹² pulses.

The van der Waals dispersion interaction between two chiral molecules in the presence of arbitrary magnetoelectric media is derived using perturbation theory. To be general, the molecular polarisabilities are assumed to be of electric, paramagnetic and diamagnetic natures, and the material environment is considered to possess a chiral electromagnetic response. The derived expressions of electric dipole polarisable–chiral, magnetic dipole susceptible–chiral, and diamagnetic susceptible–chiral, and chiral–chiral interaction potentials when added to the previously obtained contributions in the literature, form a complete set of dispersion interaction formulas. We present them in a unified form making use of electric–magnetic duality. As an application, the case of two anisotropic molecules embedded in a bulk magnetoelectric medium is considered, where we derive the retarded and non-retarded limits with respect to intermolecular distance.

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic spinor representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.

Microswimmers are encountered in a wide variety of biophysical settings. When interacting with flow fields, they show interesting dynamical features such as hydrodynamic trapping, clustering, and preferential orientation. One important step towards the understanding of such features is to clarify the interplay of hydrodynamic flows with microswimmer motility and shape. Here, we study the dynamics of ellipsoidal microswimmers in a two-dimensional axisymmetric vortex flow. Despite this simple setting, we find surprisingly rich dynamics, which can be comprehensively characterized in the framework of dynamical systems theory. By classifying the fixed-point structure of the underlying phase space as a function of motility and microswimmer shape, we uncover the topology of the phase space and determine the conditions under which microswimmers are trapped in the vortex. For spherical microswimmers, we identify Hamiltonian dynamics, which are broken for microswimmers of a different shape. We find that prolate ellipsoidal microswimmers tend to align parallel to the velocity field, while oblate microswimmers tend to remain perpendicular to it. Additionally, we find that rotational noise allows microswimmers to escape the vortex with an enhanced escape rate close to the system's saddle point. Our results clarify the role of shape and motility on the occurrence of preferential concentration and clustering and provide a starting point to understand the dynamics in more complex flows.

We study statistical properties of the process Y(t) of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion X(t) with the Hurst index H ∈ (0,1). We show that the disorder-averaged mean-squared displacement of the passive advection grows in the large time t limit in proportion to ${t}^{2-H}$, which defines a family of anomalous super-diffusions. We evaluate the disorder-averaged Wigner–Ville spectrum of the advection process Y(t) and demonstrate that it has a rather unusual power-law form $1/{f}^{3-H}$ with a characteristic exponent which exceed the value 2. Our results also suggest that sample-to-sample fluctuations of the spectrum can be very important.

Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system, including the implied level of systemic risk, requires detailed information about the structure of the underlying network of dependencies. However, since data about financial linkages are typically subject to confidentiality, network reconstruction techniques become necessary to infer both the presence of connections and their intensity. Recently, several 'horse races' have been conducted to compare the performance of the available financial network reconstruction methods. These comparisons were based on arbitrarily chosen metrics of similarity between the real network and its reconstructed versions. Here we establish a generalized maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization uses the maximization of a certain conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved and, therefore, cannot enter directly, as sufficient statistics, in the likelihood function. The resulting approach admits as input any reconstruction method for the purely binary topology and, conditionally on the latter, exploits the available partial information to infer link weights. We find that the most reliable method is obtained by 'dressing' the best-performing binary method with an exponential distribution of link weights having a properly density-corrected and link-specific mean value and propose two safe (i.e. unbiased in the sense of maximum conditional entropy) variants of it. While the one named CReM_A is perfectly general (as a particular case, it can place optimal weights on a network if the bare topology is known), the one named CReM_B is recommended both in case of full uncertainty about the network topology and if the existence of some links is certain. In these cases, the CReM_B is faster and reproduces empirical networks with highest generalized likelihood among the considered competing models.

Machine learning applications in materials science are often hampered by shortage of experimental data. Integration with external datasets from past experiments is a viable way to solve the problem. But complex calibration is often necessary to use the data obtained under different conditions. In this paper, we present a novel calibration-free strategy to enhance the performance of Bayesian optimization with preference learning. The entire learning process is solely based on pairwise comparison of quantities (i.e., higher or lower) in the same dataset, and experimental design can be done without comparing quantities in different datasets. We demonstrate that Bayesian optimization is significantly enhanced via data integration for organic molecules and inorganic solid-state materials. Our method increases the chance that public datasets are reused and may encourage data sharing in various fields of physics.

The 'in silico' exploration of chemical, physical and biological systems requires accurate and efficient energy functions to follow their nuclear dynamics at a molecular and atomistic level. Recently, machine learning tools have gained a lot of attention in the field of molecular sciences and simulations and are increasingly used to investigate the dynamics of such systems. Among the various approaches, artificial neural networks (NNs) are one promising tool to learn a representation of potential energy surfaces. This is done by formulating the problem as a mapping from a set of atomic positions x and nuclear charges Z_i to a potential energy V(x). Here, a fully-dimensional, reactive neural network representation for malonaldehyde (MA), acetoacetaldehyde (AAA) and acetylacetone (AcAc) is learned. It is used to run finite-temperature molecular dynamics simulations, and to determine the infrared spectra and the hydrogen transfer rates for the three molecules. The finite-temperature infrared spectrum for MA based on the NN learned on MP2 reference data provides a realistic representation of the low-frequency modes and the H-transfer band whereas the CH vibrations are somewhat too high in frequency. For AAA it is demonstrated that the IR spectroscopy is sensitive to the position of the transferring hydrogen at either the OCH- or OCCH₃ end of the molecule. For the hydrogen transfer rates it is demonstrated that the O–O vibration (at ∼250 cm⁻¹) is a gating mode and largely determines the rate at which the hydrogen is transferred between the donor and acceptor. Finally, possibilities to further improve such NN-based potential energy surfaces are explored. They include the transferability of an NN-learned energy function across chemical species (here methylation) and transfer learning from a lower level of reference data (MP2) to a higher level of theory (pair natural orbital-LCCSD(T)).