We study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run and tumble dynamics. We solve the externally driven non-interacting and zero-range versions of the model exactly and utilise a field theoretic approach to derive the continuum fluctuating hydrodynamics for more general interactions. We make contact with prior approaches to run and tumble dynamics off lattice and determine the steady state and linear stability for a class of crowding interactions, where the jump rate decreases as density increases. In addition to its interest from the perspective of nonequilibrium statistical mechanics, this lattice model constitutes and efficient tool to simulate a class of interacting run and tumble models relevant to bacterial motion, so long as certain conditions (that we derive) are met.
We investigate the nonequilibrium energetics near a critical point of a non-linear driven oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power $\langle\dot{W}\rangle\sim (D_{\rm a}/τ)^{1/4}$ where $D_{\rm a}$ is the effective diffusivity and $τ$ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average stationary power and the variance of the work both below and above the saddle-node bifurcation. Above the bifurcation, the average power attains an opti…
The growth of bacterial flagellar filaments is a self-assembly process where flagellin molecules are transported through the narrow core of the flagellum and are added at the distal end. To model this situation, we generalize a growth process based on the TASEP model by allowing particles to move both forward and backward on the lattice. The bias in the forward and backward jump rates determines the lattice tip speed, which we analyze and also compare to simulations. For positive bias, the system is in a non-equilibrium steady state and exhibits boundary-induced phase transitions. The tip spee…
Despite their inherent non-equilibrium nature, living systems can self-organize in highly ordered collective states that share striking similarities with the thermodynamic equilibrium phases of conventional condensed matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies, microbial suspensions and tissues to the coherent macro-scale dynamics in schools of fish and flocks of birds. Yet, the generic mathematical principles that govern the emergence of structure in such artificial and biological systems are elusive. It is not clear when, or even w…
On one-dimensional two-way infinite lattice system, a property of stationary (space-) translationally invariant states with nonvanishing current expectations are investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show, by applying Goldstone-theorem-like argument,that spectrum of the unitary operators, energy-momentum spectrum with respect to the state, has a singularity at the origin.
We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas. We represent the steady state as $P(η)\propto e^{-H(η)-Ψ(η)}$, and evaluate the lowest order contribution to the nonequilibrium effective interaction $Ψ(η)$. We see that, in dimensions $d\ge2$, all models with nonsingular transition rates have the same $Ψ(η)$, which consists of a three-body effective interaction decaying like $1/r^{2d+1}$. The models with the Metropolis rule show exceptional behavior.
The nonequilibrium reweighting technique, which was recently developed by the present authors, is used for the study of the nonequilibrium steady states. The renewed formulation of the nonequlibrium reweighting enables us to use the very efficient multi-spin coding. We apply the nonequilibrium reweighting to the driven diffusive lattice gas model. Combining with the dynamical finite-size scaling theory, we estimate the critical temperature Tc and the dynamical exponent z. We also argue that this technique has an interesting feature that enables explicit calculation of derivatives of thermodyna…
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation threshold of the lattice is characterized by unconventional activated (exponential) dynamical scaling and strong Griffiths effects. We calculate the critical behavior in two and three space dimensions, and we also relate our results to the recently found infinite-randomness fixed point in the disordered one-dimensional contact process.
A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact expressions for the two-time autocorrelation and response functions on a $d$-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.
We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force. The main result is a phase diagram with three phases: a homogeneous phase, and two distinct ordered phases. Continuous boundaries separate the homogeneous phase from the ordered phases, and a first-order line separates the two ordered phases. The three lines merge in a nonequilibrium bicr…
We present the phase diagram of a far from equilibrium system, mapped by Monte Carlo simulation. The model is a lattice gas of two species of particles and holes. The two species are biased to hop in opposite directions and interact via excluded volume and nearest neighbor attractions. Three phases are found as a function of temperature and charge density.
We study critical hysteresis in the random-field Ising model (RFIM) on a two-dimensional periodic lattice with a variable coordination number $z_{eff}$ in the range $3 \le z_{eff} \le 6$. We find that the model supports critical behavior in the range $4 < z_{eff} \le 6$, but the critical exponents are independent of $z_{eff}$. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.
We explore driven lattice gases for the existence of an intensive thermodynamic variable which could determine "equilibration" between two nonequilibrium steady-state systems kept in weak contact. In simulations, we find that these systems satisfy surprisingly simple thermodynamic laws, such as the zero-th law and the fluctuation-response relation between the particle-number fluctuation and the corresponding susceptibility remarkably well. However at higher densities, small but observable deviations from these laws occur due to nontrivial contact dynamics and the presence of long-range spatial…
We study the nonequilibrium critical point of the zero temperature random field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random field Ising model belong to the same universality class. The physics of this curious…
We consider dislocations in a vortex lattice that is driven in a two-dimensional superconductor with random impurities. The structure and dynamics of dislocations is studied in this genuine nonequilibrium situation on the basis of a coarse-grained equation of motion for the displacement field. The presence of dislocations leads to a characteristic anisotropic distortion of the vortex density that is controlled by a Kardar-Parisi-Zhang nonlinearity in the coarse-grained equation of motion. This nonlinearity also implies a screening of the interaction between dislocations and thereby an instabil…
We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites $L^d$. We compute the distribution of the eigenvalues of the time averaged state over a time window $[t_0,t_0+t]$ in the limit of large $L$. This allows us to infer the size of a subspace that captures time evolution in $[t_0,t_0+t]$ with an accuracy $1-ε$. We estimate the size to be $ \frac{\sqrt{2\mathfrak{e}_2}}π\mathrm{erf}^{-1}(1-ε) L^{\frac{d}{2}}t$, where $\mathfrak{e}_2$ is the energy variance per site, and $\mathrm{erf}^{-1}$ is the inverse…
We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity - nonequilibrium entropy. There are two families of limiters: (i) based on restriction of nonequilibrium entropy (entropy "trimm…
The critical behavior of driven lattice gas models has been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in the universality classes to which they belong. This is of paramount importance as it implies the question of whether or not a microscopic model and its mesoscopic field theory may possess different symmetries in nonequilibrium critical phenomena in contrast to their equilibrium counterparts. Here, we heat with finite rates two generic models of driven lattice gases across their resp…
We propose a new model suitable for a nonequilibrium molecular dynamics (MD) simulation of electrical conductors. The model consists of classical electrons and atoms. The atoms compose a lattice vibration system. The electrons are scattered by electron-electron and electron-atom interactions. Since the scattering cross section is physically more important than the functional form of a scattering potential, we propose to devise the electron-atom interaction potential in such a way that its scattering cross section agrees with that of quantum-mechanical one. To demonstrate advantages of the prop…
We study a nonequilibrium Ising model that stochastically evolves under the simultaneous operation of several spin-flip mechanisms. In other words, the local magnetic fields change sign randomly with time due to competing kinetics. This dynamics models a fast and random diffusion of disorder that takes place in dilute metallic alloys when magnetic ions diffuse. We performe Monte Carlo simulations on cubic lattices up to L=60. The system exhibits ferromagnetic and paramagnetic steady states. Our results predict first-order transitions at low temperatures and large disorder strengths, which corr…
The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the familiar spin--flip dynamics at temperature T with completely--random flips; one may interpret these as ideally simulating some (dynamic) impurities. We find evidence that, in the present case, the nonequilibrium mechanism adds to the basic thermal one resulting on a renormalization of microscopic parameters such as the probability of interfacial broken bond…
We study a symmetry property of momentum distribution functions in the steady state of heat conduction. When the equation of motion is symmetric under change of signs for all dynamical variables, the distribution function is also symmetric. This symmetry can be broken by introduction of an asymmetric term in the interaction potential or the on-site potential, or employing the thermal walls as heat reservoirs. We numerically find differences of behavior of the models with and without the on-site potential.
We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that the large-deviations function describing the repartition of mass between the two systems is additive, in the sense of being a sum of contributions from each system. We show that this additivity property is satisfied on condition that a macroscopic detailed balance condition holds at contact, and that the coarse-grained contact dynamics satisfies a factoriza…
Mixtures of active and passive particles are predicted to exhibit a variety of nonequilibrium phases. Here we report a dynamic clustering phase in mixtures of colloids and motile bacteria. We show that colloidal clustering results from a balance between bond breaking due to persistent active motion and bond stabilization due to torques that align active particle velocity tangentially to the passive particle surface. Furthermore, dynamic clustering spans a broad regime between diffusivity-based and motility-induced phase separation that subsumes typical bacterial motility parameters.
This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynam…
Symmetric Mass Generation Transition and its Nonequilibrium Critical Dynamics in a Bilayer Honeycomb Lattice Model
School of Physics, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University（中山大学物理学院磁电物理与器件广东省重点实验室）；Beijing National Laboratory for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家研究中心）；University of Chinese Academy of Sciences（中国科学院大学）
Effect of exchange anisotropy on the relaxation time of spin and vector chirality is studied for the antiferromagnetic classical Heisenberg model on the triangular lattice by using the nonequilibrium relaxation Monte Carlo method. We identify the Berezinskii-Kosterlitz-Thouless (BKT) transition and the chiral transition in a wide range of the anisotropy, even for very small anisotropy of $\sim$ 0.01%. As the anisotropy decreases, both the critical temperatures steeply decrease, while the BKT critical region becomes divergently wide. We elucidate a sharp "V shape" of the phase diagram around th…
This Chapter contains an overview of the effects of nonlinear interactions in selected problems of non-equilibrium statistical mechanics. Most of the emphasis is put on open setups, where energy is exchanged with the environment. With reference to a few models of classical coupled anharmonic oscillators, we review anomalous but general properties such as extremely slow relaxation processes, or non-Fourier heat transport.
We study the non-equilibrium dynamics of two component bosonic atoms in a one-dimensional optical lattice in the presence of spin-orbit coupling. In the Mott insulating regime, the two-component bosonic system at unity filling can be described by the quantum spin XXZ model. The atoms are initially prepared in their lower spin states. The system becomes out of equilibrium by suddenly introducing spin-orbit coupling to the atoms. The system shows the relaxation and non-stationary dynamics, respectively, in the different interaction regimes. We find that the time average of magnetization is usefu…
We studied the critical behavior of the $J_{1}-J_{2}$ spin-{1/2} Ising model in the square lattice by considering $J_{1}$ fixed and $J_{2}$ as random interactions following discrete and continuous probability distribution functions. The configuration of $J_{2}$ in the lattice evolves in time through a competing kinetics using Monte Carlo simulations leading to a steady state without reaching the free-energy minimization. However, the resulting non-equilibrium phase diagrams are, in general, qualitatively similar to those obtained with quenched randomness at equilibrium in past works. According…
We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in non-stationary diffusive lattice gases. We identify two universality classes of these fluctuations which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of \emph{effective fluid}, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the Symmetric Simple Exclusion Process where, for some initial conditions,…
We consider several one-dimensional driven lattice gas models that show a phase transition in the stationary state between a high-density fluid phase in which the particles are homogeneously distributed and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterise the scaling of the saturation width and the relaxation ti…
In his comment, Dhar (cond-mat/0106349) claims that the existence and uniqueness of a nonequilibrium stationary state has been proved by Lebowitz et al. We should point out that our observation does not contradict the proof. They have only proved that when a (mass) disordered harmonic chain is placed in contact with stochastic reservoirs of the Langevin type, a nonequilibrium stationary state can be reached. However, they didn't prove the existence and uniqueness of the nonequilibrium stationary state for the general case, namely, when the chain is in contact with general thermostated reservoi…
Nonequilibrium reaction networks (NRNs) underlie most biological functions. Despite their diverse dynamic properties, NRNs share the signature characteristics of persistent probability fluxes and continuous energy dissipation even in the steady state. Dynamics of NRNs can be described at different coarse-grained levels. Our previous work showed that the apparent energy dissipation rate at a coarse-grained level follows an inverse power law dependence on the scale of coarse-graining. The scaling exponent is determined by the network structure and correlation of stationary probability fluxes. Ho…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a new universality class. The critical point is characterized by ultraslow activated dy…
We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in arbitrary dimensions and for any stochastic prescription. We apply this general formalism to study noise-induced phase transitions. We focus on a class of multiplicative stochastic lattice models and compute the steady state phase diagram in terms of the noise intensity and the lattice coupling. We obtain, under appropriate conditions, an ordered phase induced by …
An ultracold gas is considered, loaded into a lattice, each site of which is formed by a double-well potential. Initial conditions, after the loading, correspond to a nonequilibrium state. The nonlinear dynamics of the system, starting with a nonequilibrium state, is analysed in the local-field approximation. The importance of taking into account attenuation, caused by particle collisions, is emphasized. The presence of this attenuation dramatically influences the system dynamics.
We introduce a nonequilibrium off--lattice model for anisotropic phenomena in fluids. This is a Lennard--Jones generalization of the driven lattice--gas model in which the particles' spatial coordinates vary continuously. A comparison between the two models allows us to discuss some exceptional, hardly realistic features of the original discrete system --which has been considered a prototype for nonequilibrium anisotropic phase transitions. We thus help to clarify open issues, and discuss on the implications of our observations for future investigation of anisotropic phase transitions.
The driven lattice gas (DLG) evolving at low temperature helps understanding the kinetics of pattern formation in unstable mixtures under anisotropic conditions. We here develop a simple theoretical description of kinetics in Monte Carlo simulations of the DLG. A Langevin continuum analog is also studied which is shown to exhibit the same behavior. We demonstrate that pattern growth is mainly a consequence of single-particle processes and that, after a short transient time, in which a surface evaporation/condensation mechanism is important, hole diffusion in the bulk becomes dominant. Conseque…
We study in detail the dynamic scaling of the three-dimensional (3D) Ising model driven through its critical point on finite-size lattices and show that a series of new critical exponents are needed to account for the anomalous scalings originating from breaking of self-similarity of the so-called phases fluctuations. Our results demonstrate that new exponents are generally required for scaling in the whole driven process once the lattice size or an externally applied field are taken into account. These open a new door in critical phenomena and suggest that much is yet to be explored in driven…
Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g. in the channel system of some zeolites or in artificial optical lattices. In our model involving two species of particles a steady-state particle current is maintained by a density gradient between the channel boundaries and by the influence of an external driving force. This leads to the development of a fluctuating but always microscopically sharp interfac…
We study the diffusion of a tracer particle driven out-of-equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the t…
I report on an extensive numerical investigation of various discrete growth models describing equilibrium and nonequilibrium interfaces on a substrate of a finite Bethe lattice. An unusual logarithmic scaling behavior is observed for the nonequilibrium models describing the scaling structure of the infinite dimensional limit of the models in the Kardar-Parisi-Zhang (KPZ) class. This gives rise to the classification of different growing processes on the Bethe lattice in terms of logarithmic scaling exponents which depend on both the model and the coordination number of the underlying lattice. T…
We study numerically an inhomogeneous Ising lattice gas with short-range interactions where different sectors are in contact with thermal baths at different temperatures. Inside the different sectors particles jump to empty sites following the familiar Kawasaki dynamics. In addition, particles can freely hop from one sector to the other. This crossing between the sectors breaks detailed balance and yields a local energy influx that drives the system to a nonequilibrium steady state. When the low-temperature sector is cooled below the equilibrium critical temperature, a complicated nonequilibri…
Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle
Institute of Physics, NAS of Ukraine（乌克兰国家科学院物理研究所）
We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature T_{th}^{-1}. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.
The heat conduction behavior of one dimensional momentum conserving lattice systems with asymmetric interparticle interactions is numerically investigated. It is found that with certain degree of interaction asymmetry, the heat conductivity measured in nonequilibrium stationary states converges in the thermodynamical limit, in clear contrast to the well accepted viewpoint that Fourier's law is generally violated in low dimensional momentum conserving systems. It suggests in nonequilibrium stationary states the mass gradient resulted from the asymmetric interactions may provide an additional ph…
Axelrod's model in the square lattice with nearest-neighbors interactions exhibits culturally homogeneous as well as culturally fragmented absorbing configurations. In the case the agents are characterized by $F=2$ cultural features and each feature assumes $k$ states drawn from a Poisson distribution of parameter $q$ these regimes are separated by a continuous transition at $q_c = 3.10 \pm 0.02$. Using Monte Carlo simulations and finite size scaling we show that the mean density of cultural domains $μ$ is an order parameter of the model that vanishes as $μ\sim \left ( q - q_c \right)^β$ with …
We study the nonequilibrium properties of directed Ising models with non conserved dynamics, in which each spin is influenced by only a subset of its nearest neighbours. We treat the following models: (i) the one-dimensional chain; (ii) the two-dimensional square lattice; (iii) the two-dimensional triangular lattice; (iv) the three-dimensional cubic lattice. We raise and answer the question: (a) Under what conditions is the stationary state described by the equilibrium Boltzmann-Gibbs distribution? We show that for models (i), (ii), and (iii), in which each spin "sees" only half of its neighbo…
We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths $L_{x,y}$ in the directions ($x,y)$ of velocity and velocity gradient. Apparent scaling exponents are estimated as $L_{x}\sim\dotγ^{-2/3}$ and $L_{y}\sim\dotγ^{-3/4}$. We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.
We study nonequilibrium steady states of the driven lattice gas with two particles, using the most general stochastic transition rules that satisfy the local detailed balance condition. We observe that i) the universal $1/r^d$ long range correlation may be found already in the two-particle models, but ii) the magnitude (or even the existence/absence) of the long range correlation depends crucially on the rule for transition rates. The latter is in stark contrast with equilibrium dynamics, where all rules give essentially the same results provided that the detailed balance condition is satisfie…
Nonequilibrium behavior and dynamic phase transition properties of a kinetic Ising model under the influence of periodically oscillating random-fields have been analyzed within the framework of effective field theory (EFT) based on a decoupling approximation (DA). Dynamic equation of motion has been solved for a simple cubic lattice ($q=6$) by utilizing a Glauber type stochastic process. Amplitude of the sinusoidally oscillating magnetic field is randomly distributed on the lattice sites according to bimodal and trimodal distribution functions. For a bimodal type of amplitude distribution, it …
We present results for the nonequilibrium dynamics of collapse for a model flexible homopolymer on simple cubic lattices with fixed and fluctuating bonds between the monomers. Results from our Monte Carlo simulations show that, phenomenologically, the sequence of events observed during the collapse are independent of the bond criterion. While the growth of the clusters (of monomers) at different temperatures exhibits a nonuniversal power-law behavior when the bonds are fixed, the introduction of fluctuations in the bonds by considering the existence of diagonal bonds produces a temperature ind…
Exact solutions for local equilibrium and nonequilibrium out-of-time-ordered correlation (OTOC) functions are obtained for a lattice fermion model with on-site interactions, namely the Falicov-Kimball (FK) model, in the large dimensional and thermodynamic limit. Our approach is based on the nonequilibrium dynamical mean-field theory generalized to an extended Kadanoff-Baym contour. We find that the density-density OTOC is most enhanced at intermediate coupling around the metal-insulator phase transition. In the high-temperature limit, the OTOC remains nontrivially finite and interaction-depend…
We study analytically the dynamics and the micro-structural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active micro-rheology experiments, we consider here a minimal model comprising a geometrically confined lattice system -- a two-dimensional strip-like or a three-dimensional capillary-like -- populated by two types of hard-core particles with stochastic dynamics -- a tracer particle driven by a constant external force and bath particles moving completely at random. Resorting to a dec…
Dynamic behaviour of an isotropic Ashkin-Teller model in the presence of a periodically oscillating magnetic field has been analysed by means of the mean field approximation. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a square lattice. After defining the possible dynamical phases of the system, phase diagrams have been given and the behaviour of the hysteresis loops has been investigated in detail. The hysteresis loop for specific order parameter of isotropic Ashkin-Teller model has been defined and characteristics of t…
An ensemble of particles in thermal equilibrium at temperature $T$, modeled by Nosè-Hoover dynamics, moves on a triangular lattice of oriented semi-disk elastic scatterers. Despite the scatterer asymmetry a directed transport is clearly ruled out by the second law of thermodynamics. Introduction of a polarized zero mean monochromatic field creates a directed stationary flow with nontrivial dependence on temperature and field parameters. We give a theoretical estimate of directed current induced by a microwave field in an antidot superlattice in semiconductor heterostructures.
