Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries

TL;DR

This paper analyzes the density profile of a one-dimensional partially asymmetric simple exclusion process with open boundaries, using q-orthogonal polynomials to compute the average density and confirm the phase diagram of correlation length.

Contribution

It introduces a novel application of q-orthogonal polynomials to analyze the stationary state and density profile of the process, confirming previous conjectures about phase behavior.

Findings

Average density profile computed using q-Hermite polynomials

Phase diagram for correlation length confirmed

Stationary state constructed via matrix product form

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 the previous work[J. Phys. A {\bf 32} (1999) 7109], is confirmed.