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Méthodes exactes pour le modèle d'exclusion asymétrique

Abstract : In this thesis, we study some properties of the one-dimensional Asymmetric Simple Exclusion Process, an exactly solvable model of interacting particles featuring an out of equilibrium stationary state.
In a first part, we explain the relations between the asymmetric exclusion process and other models of statistical physics, in particular growth models, models of a directed polymer in a random medium, and vertex models. After recalling a few known results, we explain how the exclusion process can be studied through the use of the Bethe Ansatz.
The second part deals with Bethe Ansatz calculations of the fluctuations of the total current in the partially asymmetric exclusion process with periodic boundary conditions. Using a functional formulation of the Bethe equations, we obtain exact expressions for the three first cumulants of the current. Then, starting from these exact expressions and also from calculations performed for small systems, we conjecture an explicit combinatorial expression for all the cumulants of the current.
In the third part, we present the exclusion process with several species of particles, which generalizes the model studied in the two first parts. We show that its stationary probabilities can be written as traces of products of matrices. Then, we explain the algebraic formulation of the Bethe Ansatz for this model.
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Contributor : Sylvain Prolhac <>
Submitted on : Tuesday, October 13, 2009 - 2:20:59 PM
Last modification on : Wednesday, December 9, 2020 - 3:16:25 PM
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  • HAL Id : tel-00423952, version 1


Sylvain Prolhac. Méthodes exactes pour le modèle d'exclusion asymétrique. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2009. Français. ⟨tel-00423952⟩



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