Asymmetric simple exclusion process with open boundaries and Askey–Wilson polynomials

Abstract

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