Related papers: Solvable stationary non equilibrium states
We consider invariant measures for the stochastic Burgers equation on $\mathbb{R}$, forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth in space. An invariant measure is indecomposable, or…
In this paper the author reviews a version of the global Galerkin that was developed and applied in a series of earlier publications. The method is based on divergence-free basis functions satisfying all the linear and homogeneous boundary…
We study invariant boundary conditions for one dimensional discrete Gaussian Markov processes, basic toy models of spatial Markov processes in statistical mechanics. More precisely, we give a decomposition of boundary objects in a non…
We consider the invariant measure of a homogeneous continuous- time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be…
We implement the recently developed influence functional matrix product states approach as impurity solver in equilibrium and nonequilibrium dynamical mean field theory (DMFT) calculations of the single-band Hubbard model. The method yields…
We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in one dimension are studied both analytically and numerically,…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…
In this paper, the compressible quantum model with the given mass source and the external force of general form in three-dimensional whole space is considered. Based on the weighted $L^2$ method and $L^\infty$ estimates, the existence and…
In a recent paper [16], the authors proposed a BGK model for relativistic gas mixtures based on the Marle-type approximation, which satisfies the fundamental kinetic properties: non-negativity of distribution functions, conservation laws,…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary…
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…
A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to…
We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold. Our main abstract result provides sufficient conditions for…
In this paper we detail the mechanisms that drive substitutional binary diffusion and derive appropriate governing equations. We focus on the one-dimensional case with insulated boundary conditions. Asymptotic expansions are used in order…
We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transfered from large velocity scales to small velocity scales. These steady-states exist for arbitrary collision rules and…
Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional…
We consider the multiparticle asymmetric diffusion model (MADM) introduced by Sasamoto and Wadati with integrability preserving reservoirs at the boundaries. In contrast to the open asymmetric simple exclusion process (ASEP) the number of…
There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…