Solution of classical stochastic one dimensional many-body systems

TL;DR

This paper introduces a straightforward method to exactly solve a broad class of one-dimensional classical stochastic many-body systems far from equilibrium, exemplified by asymmetric diffusion with sources and annihilation.

Contribution

The authors develop a novel approach that transforms the Master equation into solvable integro-differential equations for density and correlation functions.

Findings

Exact solutions for density and correlation functions

Method applicable to various one-dimensional stochastic systems

Numerical and analytical solutions demonstrated

Abstract

We propose a simple method that allows, in one dimension, to solve exactly a wide class of classical stochastic many-body systems far from equilibrium. For the sake of illustration and without loss of generality, we focus on a model that describes the asymmetric diffusion of hard core particles in the presence of an external source and instantaneous annihilation. Starting from a Master equation formulation of the problem we show that the density and multi-point correlation functions obey a closed set of integro-differential equations which in turn can be solved numerically and/or analytically