Bethe Ansatz solution of the stochastic process with nonuniform stationary state

TL;DR

This paper solves a stochastic zero-range process with nonuniform stationary states exactly using Bethe ansatz, revealing a transition from positive to negative driving through a purely diffusive point.

Contribution

It provides an exact Bethe ansatz solution for a zero-range process with nonuniform stationary states, including the characterization of a transition in driving behavior.

Findings

Eigenfunctions and eigenvalues are obtained exactly.

A parameter controls the transition from positive to negative driving.

The model's relation to other Bethe ansatz solvable models is discussed.

Abstract

The eigenfunctions and eigenvalues of the master-equation for zero range process on a ring are found exactly via the Bethe ansatz. The rates of particle exit from a site providing the Bethe ansatz applicability are shown to be expressed in terms of single parameter. Continuous variation of this parameter leads to the transition of driving diffusive system from positive to negative driving through purely diffusive point. The relation of the model with other Bethe ansatz solvable models is discussed.