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

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 ref. 1 [J. Phys. A 32 (1999) 7109], is confirmed.