Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials

Details Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials

2003-12-18

arxiv.org/abs/cond-mat/0312457v1

J. Phys. A: Math. Gen. 37 (2004) 4985-5002

Physics

Condensed Matter

Statistical Mechanics

21 pages, 2 figures

Scientific paper

10.1088/0305-4470/37/18/006

We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the Askey-Wilson polynomials. The partition function and the $n$-point functions are obtained in the integral form with four boundary parameters. The thermodynamic current is evaluated to confirm the conjectured phase diagram.

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