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We analyze the power spectrum of a regular binary thermal lattice gas in two dimensions and derive a Landau-Placzek formula, describing the power spectrum in the low-wavelength, low frequency domain, for both the full mixture and a single component in the binary mixture. The theoretical results are compared with simul... |
We analyze a nonlinear $q$-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby $q$ (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. |
Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a non-conserved order parameter. |
We study the macroscopic behavior of a stochastic spin ensemble driven by a discrete Markov jump process motivated by the Metropolis-Hastings algorithm where the proposal is made with spatially correlated (colored) noise, and hence fails to be symmetric. However, we demonstrate a scenario where the failure of proposal... |
The large-scale dynamics of quantum integrable systems is often dominated by ballistic modes due to the existence of stable quasi-particles. We here consider as an archetypical example for such a system the spin-$\frac{1}{2}$ XXX Heisenberg chain that features magnons and their bound states. |
We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the system achieves its inert state. |
We compute numerically the distribution of energies W(E,N) for the XY-model with short-range and long-range interactions. We find that in both cases the distribution can be fitted to the functional form: W(E,N) ~ exp(N f(E,N)), with f(E,N) an intensive function of the energy. |
We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. |
The constitutive equations for the heat flux and the Navier tensor are established for a high temperature dilute gas in two spatial dimensions. The Chapman-Enskog procedure to first order in the gradients is applied in order to obtain the dissipative energy and momentum fluxes from the relativistic Boltzmann equation.... |
The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc, and it is shown that the formula actually explains various PDFs ... |
We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T), and their total payoffs come from games with the nearest neighbors... |
We derive exact equations governing the large-scale dynamics of hard rods, including diffusive effects that go beyond ballistic transport. Diffusive corrections are the first-order terms in the hydrodynamic gradient expansion and we obtain them through an explicit microscopic calculation of the dynamics of hard rods. |
Statistics of molecular random walks in a fluid is considered with the help of Bogolyubov equation for generating functional of distribution functions. An invariance group of this equation is found. |
A microscopic model for thermal excitation of vibrational ground state of a molecule interacting with a condensed medium is developed. The master equation for evolution of occupancies of the vibrational levels is derived. |
Population annealing is an easily parallelizable sequential Monte Carlo algorithm that is well-suited for simulating the equilibrium properties of systems with rough free energy landscapes. In this work we seek to understand and improve the performance of population annealing. |
Quantum excitations in lattice systems always propagate at a finite maximum velocity. We probe this mechanism by considering a defect travelling at a constant velocity in the quantum Ising spin chain in transverse field. |
We study the role of quantum statistics in the performance of Otto cycles. First, we show analytically that the work distributions for bosonic and fermionic working fluids are identical for cycles driven by harmonic trapping potentials. |
A simple two-species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the bridge model for which earlier studies have confirmed the existence of symmetry-broken phases, and the ... |
We present the results of systematic numerical computations relating to the extreme value statistics of the characteristic polynomials of random unitary matrices drawn from the Circular Unitary Ensemble (CUE) of Random Matrix Theory. In particular, we investigate a range of recent conjectures and theoretical results i... |
Recently noticed ability of restart to reduce the expected completion time of first-passage processes allows appealing opportunities for performance improvement in a variety of settings. However, complex stochastic processes often exhibit several possible scenarios of completion which are not equally desirable in term... |
Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on the surface is determined completely by geometry. |
A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the pairs of mutual friendships. |
We present a hydrodynamic theoretical model for "Brazil nut" size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. |
We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. |
Frustrated magnets such as spin ice exhibit Coulomb phases, where correlations have power-law forms at long distances. Applied perturbations can cause ordering transitions which cannot be described by the usual Landau paradigm, and are instead naturally viewed as Higgs transitions of an emergent gauge theory. |
We study a one-dimensional model which undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted as to predict the exact location of the critical point and critical exponents in this model. |
We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a finite system is, under certain conditions, exactly governed by a universal diffus... |
We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic c... |
We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely t... |
Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-te... |
Based on Sjögren und Sjolander's Mode-Coupling(MC)-Model, we have reformulated and calculated the memory kernel (MK) of the velocity autocorrelation function (VACF)on a Ni$_{0.2}$Zr$_{0.8}$-liquid. Reformulating means here that we have constructed the memory kernel of VACF for our binary system, instead of one for... |
We give meaning to the first and second laws of thermodynamics in case of mesoscopic out-of-equilibrium systems which are driven by diffusion processes. The notion of the entropy production is analyzed. |
The evolution of material points interacting via gravitational force in 3D space was investigated. At initial moment points with masses of 2.48 Sun masses are randomly distributed inside a cube with an edge of 5 light-years. |
I analyze the Nonlocal Conserved Kardar-Parisi-Zhang (NCKPZ) equation with spatially correlated noise. This equation is also known as the Nonlocal Molecular Beam Epitaxy (NMBE) equation andv was originally suggested to study the effect of the long-range nature of interactions coupled with spatially correlated noise on... |
Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. |
By using Newtonian mechanics, we construct a general model of Maxwell's demon, a system in which the engine and the memory interact only through the exchange of information. We show that the Jarzynski relation and the two Sagawa-Ueda relations hold simultaneously, and argue that they are the unique triplet which h... |
We turn the stochastic critical forest-fire model introduced by Drossel and Schwabl (PRL 69, 1629, 1992) into a deterministic threshold model. This new model has many features in common with sandpile and earthquake models of Self-Organized Criticality. |
We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,... |
Deformations of many-body Hamiltonians by certain products of conserved currents, referred to as $T\bar{T}$-deformations, are known to preserve integrability. Generalised $T\bar{T}$-deformations, based on the complete space of pseudolocal currents, were suggested [B. Doyon, J, Durnin, T. Yoshimura, Scipost Physics 13,... |
Recently it was shown that the eigenfunctions for the the asymmetric exclusion problem and several of its generalizations as well as a huge family of quantum chains, like the anisotropic Heisenberg model, Fateev- Zamolodchikov model, Izergin-Korepin model, Sutherland model, t-J model, Hubbard model, etc, can be express... |
A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform of the initial energy distribution is found to play a key role, which is furth... |
Recently van Zon and Cohen [1-3] proposed an extension of the Fluctuation Theorems (FTs) of Evans and Searles [4]. For dissipative nonequilibrium systems, Cohen and van Zon studied the fluctuations of the heat absorbed, over a period of time t, by a surrounding thermostat. |
The overlap, or similarity, between liquid configurations is at the core of the mean-field description of the glass transition, and remains a useful concept when studying three-dimensional glass-forming liquids. In liquids, however, the overlap involves a tolerance, typically of a fraction $a/\sigma$ of the inter-part... |
The properties of the interface between solid and melt are key to solidification and melting, as the interfacial free energy introduces a kinetic barrier to phase transitions. This makes solidification happen below the melting temperature, in out-of-equilibrium conditions at which the interfacial free energy is ill-de... |
The dynamics of the forward vortex cascade in 2D turbulence in a superfluid film is investigated using analytic techniques. The cascade is formed by injecting pairs with the same initial separation (the stirring scale) at a constant rate. |
Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be... |
Synthetic antiferromagnets with strong perpendicular anisotropy can be modeled by layered Ising antiferromagnets. Accounting for the fact that in the experimental systems the ferromagnetic layers, coupled antiferromagnetically via spacers, are multilayers, we propose a description through Ising films where ferromagnet... |
We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. |
We demonstrate occurrence of bimodality and dynamical hysteresis in a system describing an overdamped quartic oscillator perturbed by additive white and asymmetric Lévy noise. Investigated estimators of the stationary probability density profiles display not only a turnover from unimodal to bimodal character but also ... |
We use molecular dynamics computer simulations to calculate the frequency dependence of the specific heat of a SiO_2 melt. The ions interact with the BKS potential and the simulations are done in the NVE ensemble. |
We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the q... |
The interplay between competing short-range (SR) and long-range (LR) interactions can cause nontrivial structures in phase diagrams. Recently, horn-shaped unusual structures were found by Monte Carlo simulations in the phase diagram of the Ising antiferromagnet (IA) with infinite-range ferromagnetic-like (F) interacti... |
Recurrence time quantifies the duration required for a physical system to return to its initial state, playing a pivotal role in understanding the predictability of complex systems. In quantum systems with subspace measurements, recurrence times are governed by Anandan-Aharonov phases, yielding fractionally quantized ... |
We study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at criticality, the constraint can induce new finite-size corrections with exponent y_{can}=2y_t-d both in energy-like and magneti... |
By using simple mode coupling equations, we investigate the depolarized light scattering spectra of two so-called "fragile" glassforming liquids, salol (phenylsalicylate) and CKN (Ca_{0.4}K_{0.6}(NO_3)_{1.4}), measured by Cummins and coworkers. Nonlinear integrodifferential equations for the time evolution of ... |
Recently we have proposed (J. Chem. |
We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe |
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the result of the balance between the dissipation and the random forces which ... |
Nonreciprocal interactions that violate Newton's law 'actio=reactio' are ubiquitous in nature and are currently intensively investigated in active matter, chemical reaction networks, population dynamics, and many other fields. An outstanding challenge is the thermodynamically consistent formulation of the ... |
This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), <a href="http://goo.gl/pZWA6X" rel="external noopener nofollow" class="link-external link-http">this http URL</a>. |
It is of great current interest to establish toy models of ergodicity breaking transitions in quantum many-body systems. Here we study a model that is expected to exhibit an ergodic to nonergodic transition in the thermodynamic limit upon tuning the coupling between an ergodic quantum dot and distant particles with sp... |
We discuss some general properties of the symmetry-resolved von-Neumann entanglement entropy in systems with particle number conservation and describe how to obtain the entanglement components from correlation functions for Gaussian systems. We introduce majorization as an important tool to derive entanglement bounds.... |
A simple Ising spin model which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. |
We study the finite temperature properties of the extended Bose-Hubbard model on a cubic lattice. This model exhibits the so-called supersolid state. |
We introduce a family of rotationally invariant random matrix ensembles characterized by a parameter $\lambda$. While $\lambda=1$ corresponds to well-known critical ensembles, we show that $\lambda \ne 1$ describes "Lévy like" ensembles, characterized by power law eigenvalue densities. |
Correlated classical and quantum many-particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging both, conceptionally and with respect to computational resources. |
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by giving an explanation for the, at the first sight unreasonable, effectiveness of th... |
The spontaneously oscillating hair bundle of sensory cells in the inner ear is an example of a stochastic, nonlinear oscillator driven by internal active processes. Moreover, this internal activity is adaptive -- its power input depends on the current state of the system. |
We study the heartbeat activity of healthy individuals at rest and during exercise. We focus on correlation properties of the intervals formed by successive peaks in the pulse wave and find significant scaling differences between rest and exercise. |
We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable ... |
The mean compositions of individual components can be tuned to control phase behavior in number-conserving passive mixtures. In this work, we investigate the role of variable average density in a system of infinitely many non-reciprocally interacting scalar densities, within the framework of the multi-species non-reci... |
We consider the possibilities for prediction of liquids' density under pressure basing on the inverse reduced fluctuations parameter, which is directly connected with the isothermal compressibility. This quantity can be determined basing on the thermodynamical properties of saturated liquid and it consists of only... |
In this paper, we introduce a new stochastic process of $N$ interacting particles on the line that evolve via Dyson Brownian motion (DBM) with Dyson's index $\beta > 0$ and undergo simultaneous resetting to their initial positions at a constant rate $r$. We call this process the resetting Dyson Brownian motion ... |
We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the Renormalization Group as a tool to improve perturbative calculations, and c... |
We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators, with time dependent kernels, which act on the functions and their spatial derivati... |
Catalytically active macromolecules are envisioned as key building blocks in development of artificial nanomotors. However, theory and experiments report conflicting findings regarding their dynamics. |
We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry including conservation of magnetization by renormalization group (RG) theory within the minimal subtraction scheme in two loop order. Within the stability region of the Heisenberg fixed point and the biconical f... |
We study the probability distribution of residence time, $T$, of the sand grains in the one dimensional abelian sandpile model on a lattice of $L$ sites, for $T<<L^2$ and $T>>L^2$. The distribution function decays as $\exp(-\frac{K_LT}{L^2})$. |
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those degrees of freedom that mostly determine the behaviour of the system and separate... |
We show that the two complementary parts of the dynamics associated to the Feigenbaum attractor, inside and towards the attractor, form together a q -deformed statistical-mechanical structure. A time-dependent partition function produced by summing distances between neighboring positions of the attractor leads to a q-... |
We present a nonlinear stochastic model of the human gait control system in a variety of gait regimes. The stride interval time series in normal human gait is characterized by slightly multifractal fluctuations. |
We investigate roughening transitions in the context of transverse-field Ising models. As a modification of the transverse Ising model with short range interactions, which has been shown to exhibit domain wall roughening, we have looked into the possibility of a roughening transition for the case of long-range interac... |
We derive and study the Bloch and Bogoliubov spectrum of a Bose-Einstein condensate (BEC) confined in a one-dimensional optical superlattice (created by interference between a primary optical lattice and a secondary optical lattice of small strength), using the Bogoliubov approximation and the hydrodynamic theory with ... |
We study the domain growth of the one-dimensional kinetic Ising model under the competing influence of Glauber dynamics at temperature T and Kawasaki dynamics with a configuration-independent rate. The scaling of the structure factor is shown to have the form for nonconserved dynamics with the corrections arising from... |
The connection between the out of equilibrium linear response function and static properties established by Franz, Mezard, Parisi and Peliti for slowly relaxing systems is analyzed in the context of phase ordering processes. Separating the response in the bulk of domains from interface response, we find that in order ... |
Eigenstate Thermalization Hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically. |
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a genuinely new class of stochastic processes--relativistic Lévy processes. |
We ask whether the Eigenstate Thermalization Hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, {\it every} eigenstate is thermal. We examine expectation values of few-body operators in highly-excited many-body eigenstates and search for `outliers', the eigenstates that deviate the mo... |
This work presents an approach to evaluate the exact value of the fractal dimension of the cutting path $d^{CP}_f$ on hierarchical structures with finite order of ramification. This represents the first renormalization group treatment of the universality class of watersheds. |
The random intensity of noise approach to one-dimensional Laval-Dubrulle-Nazarenko type model having deductive support from the three-dimensional Navier-Stokes equation is used to describe Lagrangian acceleration statistics of a fluid particle in developed turbulent flows. Intensity of additive noise and cross correla... |
We study analytically the role of initial conditions in nonequilibrium quantum dynamics considering the one-dimensional ferromagnets in the regime of spontaneously broken symmetry. We analyze the expectation value of local operators for the infinite-dimensional space of initial conditions of domain wall type, generall... |
A strongly non-integrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the observable is an order parameter for a spontaneously broken symmetry, which ha... |
Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase ... |
Here we have simulated the random-bond type quenched disorder in 3D Heisenberg <a href="http://magnet.Here" rel="external noopener nofollow" class="link-external link-http">this http URL</a> we have used classical Monte-Carlo simulation with Heisenberg spin and use 3D simple cubic lattice for this <a href="http://simul... |
We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length $\sigma$, where the particles are confined between two parallel walls and only nearest neighbor interactions occur. As in our previous work (PRE, 94, 050603 (2016)), the transfer operator method is used, but here we impose... |
In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles (SP) on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavel... |
In this Letter, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a parameter Kd (or a nondimensional parameter K) such that if Kd>0, th... |
We predict the existence of an anomalous crossover between thermal and shot noise in macroscopic diffusive conductors. We first show that, besides thermal noise, these systems may also exhibit shot noise due to fluctuations of the total number of carriers in the system. |
Brownian particles placed sequentially in contact with distinct thermal reservoirs and subjected to external driving forces are promising candidates for the construction of reliable thermal engines. In this contribution, we address the role of driving forces for enhancing the machine performance. |
It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Lévy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. |
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