Matrix product solution of the multispecies partially asymmetric exclusion process

TL;DR

This paper presents an exact matrix product solution for the stationary state of a multispecies partially asymmetric exclusion process on a ring, extending previous models to multiple species with a recursive matrix construction.

Contribution

It introduces a recursive matrix product framework for solving the stationary states of multispecies exclusion processes, providing a complete proof and transfer matrix interpretation.

Findings

Exact stationary state measure derived for multispecies model

Recursive matrix construction for N species based on N-1 species

Complete proof using quadratic relations and transfer matrix interpretation

Abstract

We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product representation where the matrices for a system of N species are defined recursively in terms of the matrices for a system of N-1 species. A complete proof is given, based on the quadratic relations verified by these matrices. This matrix product construction is interpreted in terms of the action of a transfer matrix.