Matrix product solution of the stationary states of two-species open zero range processes

TL;DR

This paper presents a matrix product approach to exactly solve the steady-state distributions of a two-species open zero range process, simplifying the matrices involved and enabling potential generalizations to more species.

Contribution

It introduces a novel matrix product ansatz solution for the two-species zero range process under specific hop rate constraints, simplifying the matrix structure.

Findings

Steady-state distribution is expressed as an inhomogeneous factorized form.

Matrices at each site are tensor products of two matrix sets.

Method can be extended to more than two species.

Abstract

Using the matrix product ansatz, we obtain solutions of the steady-state distribution of the two-species open one-dimensional zero range process. Our solution is based on a conventionally employed constraint on the hop rates, which eventually allows us to simplify the constituent matrices of the ansatz. It is shown that the matrix at each site is given by the tensor product of two sets of matrices and the steady-state distribution assumes an inhomogeneous factorized form. Our method can be generalized to the cases of more than two species of particles.