Matrix product solution of a left-permeable two-species asymmetric exclusion process

TL;DR

This paper presents an exact matrix product solution for a two-species asymmetric exclusion process with a permeable left boundary, revealing detailed phase behavior and boundary accumulation phenomena.

Contribution

It introduces a novel matrix product approach to solve the stationary state of a two-species exclusion process with asymmetric boundary conditions.

Findings

Exact stationary phase diagram derived

Slower species can accumulate at the far boundary

Boundary densities influence phase structure

Abstract

We study a two-species partially asymmetric exclusion process where the left boundary is permeable for the `slower' species but the right boundary is not. We find a matrix product solution for the stationary state, and the exact stationary phase diagram for the densities and currents. By calculating the density of each species at the boundaries, we find further structure in the stationary phases. In particular, we find that the slower species can reach and accumulate at the far boundary, even in phases where the bulk density of these particles approaches zero.