Synchronous asymmetric exclusion processes

Abstract

For a fully synchronous asymmetric exclusion process with open or closed boundaries only partial analytic results are known owing to the appearance of strong-short range correlations, which invalidate simple mean-field approximations. Here we present a new method for calculating basic properties of nonequilibrium steady states, and calculate densities, fluxes, travel times, spatial and temporal correlation functions, phase diagrams, profiles and widths of boundary layers and interfaces between phases in coexistence, as well as their microstructures. This paper is based on two new elements: (i) a microscopic characterization of order parameters and local configurations in the relevant phases, based on the microdynamics of the model, and (ii) an improved mean-field approximation, which neglects certain four-point - and higher-order correlation functions. It is conjectured that the density profiles, obtained here, are exact up to terms that are exponentially small in the system size.