Partially Asymmetric Simple Exclusion Model in the Presence of an Impurity on a Ring

Details Partially Asymmetric Simple Exclusion Model in the Presence of an Impurity on a Ring Partially Asymmetric Simple Exclusion Model in the Presence of an Impurity on a Ring

1999-08-24

arxiv.org/abs/cond-mat/9908327v2

Physics

Condensed Matter

Statistical Mechanics

Adding more references and doing minor corrections, 16 pages and 3 Eps figures

Scientific paper

10.1088/0305-4470/33/9/306

We study a generalized two-species model on a ring. The original model [1] describes ordinary particles hopping exclusively in one direction in the presence of an impurity. The impurity hops with a rate different from that of ordinary particles and can be overtaken by them. Here we let the ordinary particles hop also backward with the rate q. Using Matrix Product Ansatz (MPA), we obtain the relevant quadratic algebra. A finite dimensional representation of this algebra enables us to compute the stationary bulk density of the ordinary particles, as well as the speed of impurity on a set of special surfaces of the parameter space. We will obtain the phase structure of this model in the accessible region and show how the phase structure of the original model is modified. In the infinite-volume limit this model presents a shock in one of its phases.

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