Asymmetric simple exclusion process with tree-like network branches

Abstract

The asymmetric simple exclusion process (ASEP) is a fundamental stochastic model describing asymmetric many-particle diffusion with hard-core interactions on a one-dimensional lattice, and has been widely applied in the study of nonequilibrium transport phenomena. Motivated by the modeling of proton transport along oxygen networks in proton-conducting solid oxides, we extend the ASEP to a model defined on a one-dimensional backbone lattice with tree-like network branches. We derive the exact stationary distribution of this network ASEP and investigate its transport properties. By considering two representative network geometries for which physical quantities can be expressed in terms of certain hypergeometric series, we elucidate how the network geometry influences transport properties.