Cumulants of the current in the weakly asymmetric exclusion process

TL;DR

This paper analyzes the fluctuations of the total current in a weakly asymmetric exclusion process using Bethe Ansatz, deriving explicit formulas for all cumulants including leading and next-to-leading terms.

Contribution

It provides a comprehensive calculation of all current cumulants in the weak asymmetry regime using Bethe Ansatz, including higher-order corrections.

Findings

Explicit formulas for all cumulants of the current.

Leading and next-to-leading order contributions derived.

Advances understanding of current fluctuations in weakly asymmetric systems.

Abstract

We study the fluctuations of the total current for the partially asymmetric exclusion process in the scaling of a weak asymmetry (asymmetry of order the inverse of the size of the system) using Bethe Ansatz. Starting from the functional formulation of the Bethe equations, we obtain for all the cumulants of the current both the leading and next-to-leading contribution in the size of the system.