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

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.

24 pages, 5 figures, published in the "special issue on recent advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and J. Feinberg editors

References in corpus (5)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Traffic of molecular motors through tube-like compartments
• Bethe ansatz solution of zero-range process with nonuniform stationary state
• Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
• Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates

Cited by in corpus (17)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Matrix representation of the stationary measure for the multispecies TASEP
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Total Current Fluctuations in ASEP
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Cumulants of the current in the weakly asymmetric exclusion process
• Current Fluctuations in the exclusion process and Bethe Ansatz
• Single-file dynamics with different diffusion constants
• Fluctuations and skewness of the current in the partially asymmetric exclusion process
• All orders asymptotic expansion of large partitions
• Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model
• A Matrix model for plane partitions
• Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
• Family of Commuting Operators for the Totally Asymmetric Exclusion Process
• Connected Operators for the Totally Asymmetric Exclusion Process
• A combinatorial solution for the current fluctuations in the exclusion process