Finite-dimensional representations of the quadratic algebra: Applications to the exclusion process

1997/05/15 by Kirone Mallick, K Mallick, Sven Sandow +1 · 4 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/30/13/008

18 pages, Latex, 1 EPS figure

arxiv created 1997/05/15 · openalex publication_date 1997/07/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We study the one-dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillator-algebra. We construct all finite-dimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density as well as all correlation lengths for the ASEP on a set of special curves of the phase diagram.

Citations

• An exact solution of a one-dimensional asymmetric exclusion model with open boundaries

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