Matrix Product Solution of the Stationary State of Two-Species Open Zero Range Processes

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.