Analytic profiles and correlation functions in synchronous asymmetric exclusion processes

TL;DR

This paper develops a microscopic characterization and an improved mean field approximation for analyzing correlation functions and density profiles in synchronous asymmetric exclusion processes, addressing challenges posed by complex short-range correlations.

Contribution

It introduces a new microscopic approach and an enhanced mean field method for fully parallel dynamics in exclusion processes, providing more accurate analytical results.

Findings

Density profiles are conjectured to be exact up to exponentially small corrections.

The method captures strong short-range correlations that invalidate simple mean field approximations.

Provides new insights into phase behavior and correlation functions in synchronous exclusion models.

Abstract

The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as density profiles and spatial and temporal correlation functions for models with a dynamics that is updated in (random) sequential and sublattice-parallel order. Here we consider fully parallel or synchronous dynamics, for which only partial results are known, due to the appearance of complicated strong short range correlations, that invalidate simple mean field approximations. This paper is based on two new ingredients: (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.