One-dimensional partially asymmetric simple exclusion process with open boundaries: orthogonal polynomials approach

The stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered. The so-called matrix product ansatz is employed. This enables us to construct the stationary state in the form of the product of the matrices D and E. Noticing the fact that the matrix C(= D + E) for the model is related to certain q-orthogonal polynomials, the model is analysed for a wide range of parameters. The current and the correlation length are evaluated in the thermodynamic limit. It turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case.