Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-11-28
J. Phys. A: Math. Gen. 39 (2006) 12679-12705
Physics
Condensed Matter
Statistical Mechanics
24 pages, 5 figures, published in the "special issue on recent advances in low-dimensional quantum field theories", P. Dorey,
Scientific paper
10.1088/0305-4470/39/41/S03
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.
Golinelli Olivier
Mallick Kirone
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