Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution

TL;DR

This paper analyzes the phase transition in the current distribution of the weakly asymmetric simple exclusion process using Bethe ansatz, providing insights into the behavior before and after the transition.

Contribution

It introduces a Bethe ansatz method to study the large deviation function of the current across the phase transition in the weak asymmetry regime.

Findings

Identification of the phase transition in current distribution.

Analysis of large deviation function on both sides of the transition.

Extension of Bethe ansatz techniques to this regime.

Abstract

The probability distribution of the current in the asymmetric simple exclusion process is expected to undergo a phase transition in the regime of weak asymmetry of the jumping rates. This transition was first predicted by Bodineau and Derrida using a linear stability analysis of the hydrodynamical limit of the process and further arguments have been given by Mallick and Prolhac. However it has been impossible so far to study what happens after the transition. The present paper presents an analysis of the large deviation function of the current on both sides of the transition from a Bethe ansatz approach of the weak asymmetry regime of the exclusion process.