Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials

TL;DR

This paper explores the ASEP with open boundaries, revealing its steady state connection to Askey-Wilson polynomials and providing explicit formulas for key physical quantities.

Contribution

It establishes a novel link between ASEP steady states and Askey-Wilson polynomials, deriving integral formulas for the partition function and correlation functions.

Findings

Partition function expressed via four boundary parameters.

Thermodynamic current confirms the phase diagram.

Steady state characterized by Askey-Wilson polynomials.

Abstract

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