Table of contents

We consider the two dimensional Q-random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of . Using a conformal field theory (CFT) approach, we provide the leading topological corrections to the plane limit of this probability. These corrections have universal nature and include, as a special case, the universality class of two-dimensional critical percolation. We compare our predictions to Monte Carlo measurements. Finally, we take Monte Carlo measurements of the torus energy one-point function that we compare to CFT computations.

The thermodynamical properties of the photon-plasma system have been studied using statistical physics approach. Photons develop an effective mass in the medium thus—as a result of the finite chemical potential—a photon Bose–Einstein condensation can be achieved by adjusting one of the relevant parameters (temperature, photon density and plasma density) to criticality. Due to the presence of the plasma, Planck's law of blackbody radiation is also modified with the appearance of a gap below the plasma frequency where a condensation peak of coherent radiation arises for the critical system. This is in accordance with recent optical microcavity experiments which are aiming to develop such photon condensate based coherent light sources. The present study is also expected to have applications in other fields of physics such as astronomy and plasma physics.

We obtain the cumulants of conserved charges in generalized Gibbs ensemble (GGE) by a direct summation of their finite-particle matrix elements. The Gaudin determinant that describes the norm of Bethe states is written as a sum over forests by virtue of the matrix-tree theorem. The aforementioned cumulants are then given by a sum over tree-diagrams whose Feynman rules involve simple thermodynamic Bethe Ansatz (TBA) quantities. The internal vertices of these diagrams have the interpretation of virtual particles that carry anomalous corrections to bare charges. Our derivation follows closely the spirit of recent works Kostov et al (2017 Springer Proc. Math. Stat. 255 77–98) and (2019 Nucl. Phys. B 949 114817) and is valid for all relativistic integrable QFTs with diagonal scattering matrix. We also conjecture that the cumulants of total transport in generalized hydrodynamics (GHD) are given by the same diagrams up to minor modifications. These cumulants play a central role in large deviation theory and were obtained in Myers (2018 (arXiv:1812.02082)) using linear fluctuating hydrodynamics at Euler scale. We match our conjecture with the result of Myers (2018 (arXiv:1812.02082)) up to the fourth cumulant. This highly non-trivial matching provides a strong support for our conjecture.

This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent z  =  2. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large N limit.

We consider the simplest inhomogeneous matrix-product-state for an open chain of N quantum spins that involves only two angles per site and two angles per bond with the following direct physical meanings. The two angles associated to the site k are the two Bloch angles that parametrize the two orthonormal eigenvectors of the reduced density matrix of the spin k alone. The two angles associated to the bond parametrize the entanglement properties of the Schmidt decomposition across the bond . Explicit results are given for the reduced density matrix of two consecutive sites that is needed to evaluate the energy of two-body Hamiltonians, and for the reduced density matrix of two sites at distance r that is needed to evaluate the spin–spin correlations at distance r. The global structure of the MPS manifold as parametrized by these angles is then characterized by its explicit Riemann metric. Finally, the generalizations to any tree-like structure without loops and to the chain with periodic boundary conditions are discussed.

We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the classical case. It is a white noise with a variance proportional to the temperature. The dissipation force is not restricted to be proportional to the velocity and is determined in a way as to guarantee that the stationary state is given by a density operator of the Gibbs canonical type. To this end we derived an equation that gives the time evolution of the density operator, which turns out to be a quantum Fokker–Planck–Kramers equation. The approach is applied to the harmonic oscillator in which case the dissipation force is found to be non Hermitian and proportional to the velocity and position.

We study anomalous transport arising in disordered one-dimensional spin chains, specifically focusing on the subdiffusive transport typically found in a phase preceding the many-body localization transition. Different types of transport can be distinguished by the scaling of the average resistance with system's length. We address the following question: what is the distribution of resistance over different disorder realizations, and how does it differ between transport types? In particular, an often evoked so-called Griffiths picture, that aims to explain slow transport as being due to rare regions of high disorder, would predict that the diverging resistivity is due to fat power-law tails in the resistance distribution. Studying many-particle systems with and without interactions we do not find any clear signs of fat tails. The data is compatible with distributions that decay faster than any power law required by the fat tails scenario. Among the distributions compatible with the data, a simple additivity argument suggests a Gaussian distribution for a fractional power of the resistance.

We study the non-equilibrium dynamics caused by slowly taking a quasiperiodic Hamiltonian across its quantum critical point. The special quasiperiodic Hamiltonian that we study here has two different types of critical lines belonging to two different universality classes, one of them being the well known quantum Ising universality class. In this paper, we verify the Kibble Zurek scaling which predicts a power law scaling of the density of defects generated as a function of the rate of variation of the Hamiltonian. The exponent of this power law is related to the equilibrium critical exponents associated with the critical point crossed. We show that the power-law behavior is indeed obeyed when the two types of critical lines are crossed, with the exponents that are correctly predicted by Kibble Zurek scaling.

In this paper, the matrix elements explicit expressions for the kernel operator in the harmonic oscillator eigenfunctions basis are obtained. The matrix elements are expressed in terms of the two complex variables new polynomials that were constructed in this paper. In the particular case, new polynomials degenerate into Laguerre polynomials. The diagonal elements of the kernel operator matrix are the Wigner functions of the harmonic oscillator, which do not introduce dissipation into the quantum system. The off-diagonal elements contain frequency oscillations responsible for dissipations in the quantum systems.

Using the explicit representation of the kernel operator matrix elements, we construct the distributions of the Wigner function in the phase space for quantum systems.

We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width p  of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general case, corroborated by exact results for three distributions (exponential, uniform, power-law with unit exponent), evidences a very robust dichotomy, irrespective of the window width, between superexponential and subexponential distributions. For superexponential distributions the statistics of records is asymptotically unchanged by taking the moving average, up to interesting distribution-dependent corrections to scaling. For subexponential distributions the probability of record breaking at late times is increased by a universal factor R_p, depending only on the window width.

We study the distribution of first-passage functionals of the type where represents a Brownian motion (with or without drift) with diffusion constant D, starting at x₀  >  0, and t_f is the first-passage time to the origin. In the driftless case, we compute exactly, for all n  >  −2, the probability density . We show that has an essential singular tail as and a power-law tail as . The leading essential singular behavior for small A can be obtained using the optimal fluctuation method (OFM), which also predicts the optimal paths of the conditioned process in this limit. For the case with a drift toward the origin, where no exact solution is known for general n  >  −1, we show that the OFM successfully predicts the tails of the distribution. For it predicts the same essential singular tail as in the driftless case. For it predicts a stretched exponential tail for all n  >  0. In the limit of large Péclet number , where is the drift velocity toward the origin, the OFM predicts an exact large-deviation scaling behavior, valid for all A: , where is the mean value of in this limit. We compute the rate function analytically for all n  >  −1. We show that, while for n  >  0 the rate function is analytic for all z, it has a non-analytic behavior at z  =  1 for  −1  <  n  <  0 which can be interpreted as a dynamical phase transition. The order of this transition is 2 for  −1/2  <  n  <  0, while for  −1  <  n  <  −1/2 the order of transition is ; it changes continuously with n. We also provide an illuminating alternative derivation of the OFM result by using a WKB-type asymptotic perturbation theory for large . Finally, we employ the OFM to study the case of (drift away from the origin). We show that, when the process is conditioned on reaching the origin, the distribution of coincides with the distribution of for with the same .

We have studied front dynamics for the discrete reaction–diffusion system, which in the continuum is described by the (stochastic) Fisher–Kolmogorov–Petrovsky–Piscunov equation. We have revisited this discrete model in two space dimensions by means of extensive numerical simulations and an improved analysis of the time evolution of the interface separating the stable and unstable phases. In particular, we have measured the full set of scaling exponents which characterize the spatio-temporal fluctuations of such front for different lattice sizes, focusing mainly in the front width and correlation length. These exponents are in very good agreement with those computed in (Moro E 2001 Phys. Rev. Lett. 87 238303) and correspond to those of the Kardar–Parisi–Zhang (KPZ) universality class for one-dimensional interfaces. Furthermore, we have studied the one-point statistics and the covariance of rescaled front fluctuations, which had remained thus far unexplored in the literature and allows for a further stringent test of KPZ universality.

During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the statistical mechanical version of the second law of thermodynamics, and it provides an interpretation of entropy in terms of probabilities. However, we cannot rely on the statistical-mechanical expressions for entropy in systems that are far from equilibrium. In this paper, we compare various extensions of the definition of entropy, which have been proposed for non-equilibrium systems. It has recently been proposed that measures of information density may serve to quantify entropy in both equilibrium and non-equilibrium systems. We propose a new 'bit-wise' method to measure the information density for off-lattice systems. This method does not rely on coarse-graining of the particle coordinates. We then compare different estimates of the system entropy, based on information density and on the structural properties of the system, and check if the various entropies are mutually consistent and, importantly, whether they can detect non-trivial ordering phenomena. We find that, except for simple (one-dimensional) cases, the different methods yield answers that are at best qualitatively similar, and often not even that, although in several cases, the different entropy estimates do detect ordering phenomena qualitatively. Our entropy estimates based on bit-wise data compression contain no adjustable scaling factor, and show large quantitative differences with the thermodynamic entropy obtained from equilibrium simulations. Hence, our results suggest that, at present, there is not yet a single, structure-based entropy definition that has general validity for equilibrium and non-equilibrium systems.

We study a gas of point particles with hard-core repulsion in one dimension where the particles move freely in-between elastic collisions. We prepare the system with a uniform density on the infinite line. The velocities of the particles are chosen independently from a thermal distribution. Using a mapping to the non-interacting gas, we analytically compute the equilibrium spatio-temporal correlations for arbitrary integers . The analytical results are verified with microscopic simulations of the Hamiltonian dynamics. The correlation functions have ballistic scaling, as expected in an integrable model.

The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise to super-diffusivity and transience. Various quantities related to record statistics are calculated exactly, highlighting important differences in behaviour from the simple random walk with independent steps.

The most probable escape path can reveal the optimal fluctuation with overwhelming probability for vanishing noise during escape. However, it fails to offer information for the feature of the nearby paths, while the dispersion of the prehistory distribution does. For gradient systems, the dispersion can be obtained via a relaxation method which takes the advantage of the time reversibility of the fluctuation-dissipation relation. For non-gradient systems, due to the breaking of the time-reversal symmetry, the traditional relaxation method cannot be applied. In this paper, we investigate the dispersion of the exit phenomena in the Maier–Stein system for three sets of parameters. For the gradient case, the traditional relaxation method is extended to the 2D situation. For the non-gradient case, we propose a revised version of the relaxation method which relies on the computation of quasipotential. The results are compared with those of Monte Carlo simulation which shows the efficiency of the algorithms.

In this paper we study equations of fluctuating non-linear hydrodynamics (FNH) for a liquid in which the constituent particles follow Brownian dynamics (BD). Here the microscopic-level dynamics are dissipative as compared to the case of fluids with reversible Newtonian dynamics (ND). The implications of non-linearities in FNH equations for an ND liquid on its long-time dynamics and the possibility of an ideal ergodicity–non-ergodicity (ENE) transition at high density have been widely investigated in literature. It is known that in an ND fluid, dynamics described by FNH equations do not support a sharp ENE transition. In the present paper we demonstrate that, as a consequence of the fluctuation–dissipation constraints, an ideal ENE transition is also not supported from the FNH equations for BD fluid.

We develop a field-theoretic perturbation method preserving the fluctuation–dissipation relation (FDR) for the dynamics of the density fluctuations of a noninteracting colloidal gas plunged in a quenched Gaussian random field. It is based on an expansion about the Brownian noninteracting gas and can be considered and justified as a low-disorder or high-temperature expansion. The first-order bare theory yields the same memory integral as the mode-coupling theory (MCT) developed for (ideal) fluids in random environments, apart from the bare nature of the correlation functions involved. It predicts an ergodic dynamical behavior for the relaxation of the density fluctuations, in which the memory kernels and correlation functions develop long-time algebraic tails. An FDR-consistent renormalized theory is also constructed from the bare theory. It is shown to display a dynamic ergodic–nonergodic transition similar to the one predicted by the MCT at the level of the density fluctuations, but, at variance with the MCT, the transition does not fully carry over to the self-diffusion, which always reaches normal diffusive behavior at long time, in agreement with known rigorous results.

Supervised deep learning involves the training of neural networks with a large number N of parameters. For large enough N, in the so-called over-parametrized regime, one can essentially fit the training data points. Sparsity-based arguments would suggest that the generalization error increases as N grows past a certain threshold N^*. Instead, empirical studies have shown that in the over-parametrized regime, generalization error keeps decreasing with N. We resolve this paradox through a new framework. We rely on the so-called Neural Tangent Kernel, which connects large neural nets to kernel methods, to show that the initialization causes finite-size random fluctuations of the neural net output function f _N around its expectation . These affect the generalization error for classification: under natural assumptions, it decays to a plateau value in a power-law fashion  ∼N^−1/2. This description breaks down at a so-called jamming transition N  =  N^*. At this threshold, we argue that diverges. This result leads to a plausible explanation for the cusp in test error known to occur at N^*. Our results are confirmed by extensive empirical observations on the MNIST and CIFAR image datasets. Our analysis finally suggests that, given a computational envelope, the smallest generalization error is obtained using several networks of intermediate sizes, just beyond N^*, and averaging their outputs.

Rumors flooding on rapidly-growing online social networks have geared much attention from many fronts. Individuals can transmit rumors via numerous channels since they can be active on multiple platforms. However, no systematic theoretical research of rumors containing dynamics on multiplex networks has been conducted yet. In this study, we propose a family of containing strategies based on the degree product of each user on the multiplex networks. Then, we develop a heterogeneous edge-based compartmental theory to comprehend the containing dynamics. The simulation results demonstrate that strategies with preference to block users with large can significantly reduce the rumor outbreak size and enlarge the threshold. Besides, better performance can be expected on heterogeneous multiplex networks with the increasing of preference intensity and degree heterogeneity. Moreover, take the inter-layer degree correlations r_s into consideration, the strategy performs best on multiplex networks with r_s  =  −1, r_s  =  1 the second, and r_s  =  0 the last. On the contrary, if we prefer to block users with small rather than large , the containing performance will be worse than that of blocking users randomly on most multiplex networks except for uncorrelated multiplex networks with uniform degree distribution. We found that the blocking preferences have no influence on the containing results on uncorrelated multiplex networks with uniform degree distribution. Our theoretical analysis can well predict the rumors containing results and performance differences in all the cases studied. The systematic theoretical research of rumors containing dynamics on multiplex networks in this study will offer inspirations for further investigations on this issue.

In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1D lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here we investigate the general problem of the distribution of edge crossings in random arrangements of the vertices. We generalize the existing formula for the expectation of this number in random linear arrangements of trees to any network and derive an expression for the variance of the number of crossings in an arbitrary layout relying on a novel characterization of the algebraic structure of that variance in an arbitrary space. We provide compact formulae for the expectation and the variance in complete graphs, complete bipartite graphs, cycle graphs, one-regular graphs and various kinds of trees (star trees, quasi-star trees and linear trees). In these networks, the scaling of expectation and variance as a function of network size is asymptotically power-law-like in random linear arrangements. Our work paves the way for further research and applications in one-dimension or investigating the distribution of the number of crossings in lattices of higher dimension or other embeddings.

This paper reports on a series of evacuation experiments exploring the impact of different obstacles on crowd dynamics. The experiments include three scenarios: evacuation without any obstacle (NO), evacuation with a bar-type obstacle in which the participants can choose to pass by or step over (CO), and evacuation with a bar-type obstacle in which the participants can only pass by (PO). The height of the obstacle and the distance between the obstacle and the exit in the CO cases are also taken into account. The evacuation times in the CO cases are basically longer than those in the PO cases. But a low CO obstacle very close to the exit can enhance the evacuation efficiency, compared to that of a PO obstacle. As the height of the CO obstacle increases, the pedestrian cluster around the exit separates into two clusters around the obstacle corners. In addition, the longer the distance between the CO obstacle and the exit, the fewer pedestrians prefer to step over the obstacle.

Although bidirectional motion on stairs can be commonly observed for external stairs and in some transportation facilities, a study that aims to investigate pedestrians' walking characteristics under such conditions has never been conducted. In this paper, we perform a controlled experiment to study the bidirectional stair motion with varying flow ratios. It is found that on average, ascending pedestrians walk slower than those descending independent of the flow ratio. At the same density, the average velocity is the smallest for the full bidirectional flow when compared with those in the descending and ascending ones, indicating that the full bidirectional flow is not a simple combination of unidirectional pedestrians. According to the individual time to collision, congestion level and crowd danger, the run when the flow ratio is 0.5 can be considered to be the most critical with a large number of fierce conflicts. Thus, a balanced ascending and descending flow situation should be intentionally avoided for stairs where the bidirectional motion may occur.

Movement is fundamental to the animal ecology, determining how, when, and where an individual interacts with the environment. The animal dynamics is usually inferred from trajectory data described as a combination of moves and turns, which are generally influenced by the vast range of complex stochastic stimuli received by the individual as it moves. Here we consider a statistical physics approach to study the probability distribution of animal move lengths based on stochastic differential Langevin equations and the superstatistics formalism. We address the stochastic influence on the move lengths as a Wiener process. Two main cases are considered: one in which the statistical properties of the noise do not change along the animal's path and another with heterogeneous noise statistics. The latter is treated in a compounding statistics framework and may be related to heterogeneous landscapes. We study Langevin dynamics processes with different types of nonlinearity in the deterministic component of movement and both linear and nonlinear multiplicative stochastic processes. The move length distributions derived here comprise the possibility of movement multiscales, diffusive and superdiffusive (Lévy-like) dynamics, and include most of the distributions currently considered in the literature of animal movement, as well as some new proposals.

Among the several approaches that have been attempted at studying opinion dynamics, the Sznajd model provides some particularly interesting features, such as its simplicity and ability to represent some of the mechanisms believed to be involved in real-world opinion dynamics. The standard Sznajd model at zero temperature is characterized by converging to one stable state, implying null diversity of opinions. In the present work, we develop an approach—namely the adaptive Sznajd model—in which changes of opinion by an individual (i.e. a network node) implies in possible alterations in the network topology. This is accomplished by allowing agents to change their connections preferentially to other neighbors with the same state. The diversity of opinions along time is quantified in terms of the exponential of the entropy of the opinions density. Several interesting results are reported, including the possible formation of echo chambers or social bubbles. Additionally, depending on the parameters configuration, the dynamics may converge to different equilibrium states for the same parameter setting, which suggests that this phenomenon can be a phase transition. The average degree of the network strongly influences the resultant opinion distribution, which means that echo chambers are easily formed in systems with low link density.

Chaperone-assisted translocation through a nanopore embedded in membrane holds a prominent role in the transport of biopolymers. Inspired by classical Brownian ratchet, we develop a theoretical framework characterizing such a translocation process through a master equation approach. In this framework, the polymer chain, provided with reversible binding of chaperones, undergoes forward/backward diffusion, which is rectified by chaperones. We drop the assumption of timescale separation and keep the length of a polymer chain finite, both of which happen to be key points in most of the previous studies. Our framework makes it accessible to derive analytical expressions for mean translocation velocity and an effective diffusion constant in a stationary state, which is the basis of a comprehensive understanding of the dynamics of such a process. Generally, the translocation of polymer chains across a membrane consist of three subprocesses: initiation, termination, and translocation of the main body part of a polymer chain, where the translocation of the main body part depends on both the binding/unbinding kinetics of chaperones and the diffusion of the biopolymer chain. This is the main concern of this study. Our results show that the increase of the forward/backward diffusion rate of a polymer chain and the binding/unbinding ratio of chaperones both raise the mean translocation velocity of a polymer chain, and the mean velocity finally reaches a saturation amount with an extremely rapid diffusion or extremely high binding/unbinding ratio. Roughly speaking, the dependence of effective diffusion constant on these two major processes achieves similar behavior. Besides, longer polymer chains employ higher velocity when the diffusion rate and binding/unbinding ratio are both large and similar results hold for polymer chains that are not too long in terms of the effects on the effective diffusion constant.

We investigate a system of interacting bosons with random intersite tunnelling amplitudes. We describe these by introducing Gaussian-distributed hopping integrals into the standard Bose–Hubbard model. This system has been recently shown to exhibit a quantum phase transition to a glassy state. The latter is characterized by a quenched disorder of boson wave-function phases. In this aspect, the system resembles quantum spin-glass systems that attracted much attention. By exploiting this analogy, we employ the well-established methodology originated by Sherrington and Kirkpatrick, which bases on the replica trick and the Trotter–Suzuki expansion. This treatment transforms the original quantum problem into an effective classical one with an additional time-like dimension. Here, we focus on autocorrelation functions of canonical variables of the effective system in the time-like domain. Deep in the disordered phase, we find a highly dynamical nature of correlations in agreement with the expected short memory of the system. This behaviour weakens while approaching and passing the phase boundary, where in the glassy phase asymptotically non-vanishing correlations are encountered. Thus, the state features infinite memory, which is consistent with the quenched nature of glassy disorder with random but frozen boson phases.

We investigate, through a kinetic-exchange model, the impact that an external field, like advertising and propaganda, has on opinion dynamics. We address the situations where two opposite alternatives can be selected but the possibility of indecision also exists. In this model, individuals influence each other through pairwise interactions, which can be of agreement or disagreement, and there are also external fields that can skew decision making. Two parameters are used to model the external interactions: one measures the sensitivity of the individuals to be influenced, another quantifies in which direction. We study this model in a fully connected social network scenario, by means of numerical simulations of the kinetic exchange dynamics and analytical results derived from the mean-field rate equations. We show how the external bias gives rise to imperfect bifurcations, and cusp catastrophes, allowing abrupt changes and hysteresis depending on the level of disagreement in interpersonal interactions and on the strength of the external influence.

We propose a stochastic model for a memristive system by generalizing known approaches and experimental results. We validate our theoretical model by experiments carried out on a memristive device based on multilayer structure. In the framework of the proposed model we obtain the exact analytic expressions for stationary and nonstationary solutions. We analyze the equilibrium and non-equilibrium steady-state distributions of the internal state variable of the memristive system and study the influence of fluctuations on the resistive switching, including the relaxation time to the steady-state. The relaxation time shows a nonmonotonic dependence, with a minimum, on the intensity of the fluctuations. This paves the way for using the intensity of fluctuations as a control parameter for switching dynamics in memristive devices.

We study memory dependent binary-state dynamics, focusing on the noisy-voter model. This is a non-Markovian process if we consider the set of binary states of the population as the description variables, or Markovian if we incorporate 'age', related to the time spent holding the same state, as a part of the description. We show that, in some cases, the model can be reduced to an effective Markovian process, where the age distribution of the population rapidly equilibrates to a quasi-steady state, while the global state of the system is out of equilibrium. This effective Markovian process shares the same phenomenology of the non-linear noisy-voter model and we establish a clear parallelism between these two extensions of the noisy-voter model.

We report on the results of the experimental investigations of the local resistive switching (RS) in the contact of a conductive atomic force microscope (CAFM) probe to a nanometer-thick yttria stabilized zirconia (YSZ) film on a conductive substrate under a Gaussian noise voltage applied between the probe and the substrate. The virtual memristor was found to switch randomly between the low resistance state and the high resistance state as a random telegraph signal (RTS). The potential profile of the virtual memristor calculated from its response to the Gaussian white noise shows two local minima, which is peculiar of a bistable nonlinear system.

Human mobility plays a key role on the transformation of local disease outbreaks into global pandemics. Indeed, the inclusion of population movement into epidemic models has become mandatory for understanding current epidemic episodes as well as designing efficient prevention policies. Following this challenge, here we develop a Markovian framework that enables us to address the impact of recurrent mobility patterns on epidemic onset at different temporal scales. The formalism is validated by comparing its predictions with results from mechanistic simulations. The fair agreement between theory and numerical simulations, enables us to derive an analytical expression for the epidemic threshold, capturing the critical conditions triggering epidemic outbreaks. Finally, by performing an exhaustive analysis of this epidemic threshold, we reveal that the impact of tuning human mobility on the emergence of diseases is strongly affected by the temporal scales associated to both epidemiological and mobility processes.

We rejuvenate well-aged quasi-2D binary colloidal glasses by thermal cycling, and systematically measure both the statistical responses and particle-level structural evolutions during rejuvenation. While the elastic moduli and boson peak are continuously rejuvenated with the increasing number of cycles, the mean square displacement (MSD) fluctuates significantly between the different groups of thermal cycles. The decoupling between the thermo-dynamical and dynamical evolutions suggests different microscopic origins for the different bulk properties of glasses. We find that a small fraction of structural rearrangements triggered by thermal cycling can alter the whole elastic continuum and lead to the significant thermodynamic rejuvenation, while localized defects can be activated and deactivated at the positions close to the rearrangements with significantly high mobility change and hence result in the fluctuated dynamics even with only about 10% of the particles as fast regions. Our results offer a comprehensive picture for the microscopic mechanisms underlying bulk glass rejuvenation, which can be readily used to refine glass properties or to formulate further statistical theories in glassy systems.

We consider a finite-size periodically driven quantum system of coupled kicked rotors which exhibits two distinct regimes in parameter space: a dynamically-localized one with kinetic-energy saturation in time and a chaotic one with unbounded energy absorption (dynamical delocalization). We provide numerical evidence that the kinetic energy grows subdiffusively in time in a parameter region close to the boundary of the chaotic dynamically-delocalized regime. We map the different regimes of the model via a spectral analysis of the Floquet operator and investigate the properties of the Floquet states in the subdiffusive regime. We observe an anomalous scaling of the average inverse participation ratio (IPR) analogous to the one observed at the critical point of the Anderson transition in a disordered system. We interpret the behavior of the IPR and the behavior of the asymptotic-time energy as a mark of the breaking of the eigenstate thermalization in the subdiffusive regime. Then we study the distribution of the kinetic-energy-operator off-diagonal matrix elements. We find that in presence of energy subdiffusion they are not Gaussian and we propose an anomalous random matrix model to describe them.

Motivated by the time behavior of the functional arising in the variational approach to the KPZ equation, we have adapted a path-integral scheme to deal with unstable systems. In a simple mesoscopic model and under two scenarios, we define a suitable mean value of (the exponential of) the entropy production between arbitrary initial and final states. This definition leads naturally to an integral fluctuation theorem (FT)—and on the way, to detailed and Crooks' FT. We also find the general form of a large-deviation function, as well as its particular form for a particle submitted to a constant force.