The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
By O. Golinelli, Kirone Mallick. 2006
157 citations recorded by the source corpus.
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 the 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 the Bethe ansatz.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/cd1c057932d92754c98fb856e2213122922a7603
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In Condensed Matter Physics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport (2011, unknown): “These mappings suggest the use of the Bethe Ansatz 985 to derive spectral information about the evolution operator, such as the spectral gap 986 [132, 135, 136, 137, 138, 139] and large deviation functions [140, 141].”
- Non-equilibrium steady states: fluctuations and large deviations of the density and of the current (2007, background): “On the ring too, Bethe ansatz calculations [66, 97, 98], [142]–[ 150 ], allow us to calculate the large deviation function of the current which exhibits a universal shape in the scaling regime.”
- An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, methodology): “Asymmetric simple exclusion process The asymmetric simple exclusion process (ASEP), one of the paradigmatic models in non-equilibrium statistical physics [79, 80], has also played a central role in the exact studies of the 1D KPZ class.”
- A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, methodology): “The generalization is highly nontrivial, because the ASEP for general q is not a determinantal process [133], and it requires a novel set of techniques based on the Bethe ansatz [53, 105, 118].”
- Nonequilibrium steady states of matrix-product form: a solver's guide (2007, background): “Some of these topics, however, have recently been reviewed elsewhere [28,29].”