Large deviation functional of the weakly asymmetric exclusion process

TL;DR

This paper derives the large deviation functional for the density profile in a weakly asymmetric exclusion process with open boundaries, unifying symmetric and asymmetric cases and analyzing the differential equation using a WKB-like method.

Contribution

It provides the explicit large deviation functional for the weakly asymmetric exclusion process, bridging symmetric and asymmetric cases with a novel analytical approach.

Findings

Derived the large deviation functional for the weakly asymmetric exclusion process.

Unified the expressions for symmetric and asymmetric cases.

Analyzed the differential equation using a WKB-like method.

Abstract

We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like 1/L. We recover as limiting cases the expressions derived recently for the symmetric (SSEP) and the asymmetric (ASEP) cases. In the ASEP limit, the non linear differential equation one needs to solve can be analysed by a method which resembles the WKB method.