Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process
Statistical Mechanics
2009-10-30 v1
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, Evans, Hakim and Pasquier [J. Phys. A 26, 1493 (1993)] have shown 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.
Keywords
Cite
@article{arxiv.cond-mat/9705152,
title = {Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process},
author = {Kirone Mallick and Sven Sandow},
journal= {arXiv preprint arXiv:cond-mat/9705152},
year = {2009}
}
Comments
18 pages, Latex, 1 EPS figure