Two-Species Asymmetric Simple Exclusion Process with Open Boundaries

TL;DR

This paper analyzes the steady state of a two-species ASEP with open boundaries, deriving explicit formulas for physical quantities and identifying three distinct phases in the thermodynamic limit.

Contribution

It introduces a matrix product approach combined with big q-Hermite polynomials to explicitly compute stationary distributions and phase behavior in the two-species ASEP.

Findings

Identification of three phases: low-density, high-density, and maximal current.

Explicit integral formulas for partition function and n-point functions.

Application of matrix product method with polynomial relations.

Abstract

We study the steady state of the two-species Asymmetric Simple Exclusion Process (ASEP) with open boundary conditions. The matrix product method works for the determination of the stationary probability distribution. Several physical quantities are calculated through an explicit representation for the matrix products. By making full use of the relation with the continuous big q-Hermite polynomials, we arrive at integral formulae for the partition function and the n-point functions. We examine the thermodynamic limit and find three phases: the low-density phase, the high-density phase and the maximal current phase.