Density profile of the one-dimensional partially asymmetric simple exclusion process with open boundaries

Abstract

The one-dimensional partially asymmetric simple exclusion process with open boundaries is considered. The stationary state, which is known to be constructed in a matrix product form, is studied by applying the theory of q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the average density profile is computed in the thermodynamic limit. The phase diagram for the correlation length, which was conjectured in [1](J. Phys. A 32 (1999) 7109), is confirmed. [Keywords: asymmetric simple exclusion, exact solution, density profile, q-orthogonal polynomials]

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