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

Wednesday 23rd April 2008 - 15:30 to 16:30
INI Seminar Room 1

The Asymmetric Simple Exclusion Process (ASEP) plays the role of a paradigm in Non-Equilibrium Statistical Mechanics: it is one of the simplest interacting N-body systems far from equilibrium that can be solved analytically. By using the Bethe Ansatz, we calculate the spectral gap of the model and predict global spectral properties such as the existence of multiplets. We then discuss the fluctuations of the current in the stationary state. Finally, we explain that the stationary state of the ASEP and of some of its generalizations with multiple classes of particles has an underlying combinatorial structure that leads naturally to a matrix product representation.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons