Bethe ansatz approach for the steady state of the asymmetric simple exclusion process with open boundaries

TL;DR

This paper applies the Bethe ansatz method to analyze the steady state of an asymmetric simple exclusion process with open boundaries, deriving explicit expressions for the steady state, current, and density profile.

Contribution

It introduces a Bethe ansatz approach with a symmetric chiral basis to explicitly solve for the steady state of the ASEP with non-diagonal boundaries.

Findings

Explicit steady state expression derived

Current and density profiles analyzed

Bethe ansatz method successfully applied

Abstract

We study the asymmetric simple exclusion process with non-diagonal boundary terms under a specific constraint. A symmetric chiral basis is constructed and a special string solution of the Bethe ansatz equations corresponding to the steady state is presented. Using the coordinate Bethe ansatz method, we derive a concise expression for the steady state. The current and density profile in the steady state are also studied.