Exact solution of an exclusion process with three classes of particles and vacancies

TL;DR

This paper provides an exact analytical solution for a complex exclusion process involving three classes of particles and vacancies, using a matrix product approach with tensor product quadratic algebras.

Contribution

It introduces a novel exact solution method for a multi-class exclusion process with explicit configuration weights.

Findings

Explicit stationary state weights derived

Matrix product Ansatz with tensor quadratic algebras used

Solution applicable to asymmetric exclusion processes with multiple classes

Abstract

We present an exact solution for an asymmetric exclusion process on a ring with three classes of particles and vacancies. Using a matrix product Ansatz, we find explicit expressions for the weights of the configurations in the stationary state. The solution involves tensor products of quadratic algebras.