Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries

TL;DR

This paper derives Bethe ansatz equations for the asymmetric exclusion process with open boundaries, analyzing spectral properties and boundary effects on scaling regimes.

Contribution

It provides the complete spectrum solution for the process with general open boundaries and investigates boundary-induced crossovers between different scaling regimes.

Findings

Spectral gap calculated for totally asymmetric diffusion.

Identification of boundary-induced crossovers in scaling regimes.

Analysis of approach to stationarity at large times.

Abstract

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive and KPZ scaling regimes.