Relaxation rate of the reverse biased asymmetric exclusion process

TL;DR

This paper calculates the exact relaxation rate of a partially asymmetric exclusion process with reverse bias, revealing a crossover between exponential and algebraic relaxation due to boundary effects, using Bethe ansatz analysis.

Contribution

It provides the first exact computation of relaxation rates in a reverse biased exclusion process with open boundaries, highlighting the impact of boundary conditions on relaxation dynamics.

Findings

Identifies a length scale where relaxation behavior changes

Shows crossover from exponential to algebraic relaxation

Uses Bethe ansatz to analyze root structure

Abstract

We compute the exact relaxation rate of the partially asymmetric exclusion process with open boundaries, with boundary rates opposing the preferred direction of flow in the bulk. This reverse bias introduces a length scale in the system, at which we find a crossover between exponential and algebraic relaxation on the coexistence line. Our results follow from a careful analysis of the Bethe ansatz root structure.