The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics

TL;DR

This paper reviews the ASEP model in non-equilibrium statistical mechanics, highlighting its integrability via Bethe ansatz, spectral properties, large deviation functions, and solvable variants.

Contribution

It provides a comprehensive review of exact Bethe ansatz solutions for ASEP, including spectral analysis, large deviations, and extensions to variants.

Findings

Bethe equations derived for ASEP eigenvalues

Spectral gap and multiplet structures predicted

Analytic expression for large deviation function obtained

Abstract

The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by Bethe ansatz. Keywords: ASEP, integrable models, Bethe ansatz, large deviations.