Time-dependent correlation functions in a one-dimensional asymmetric exclusion process

TL;DR

This paper analyzes a one-dimensional asymmetric exclusion process, deriving exact steady-state properties, correlation functions, and phase diagram, providing insights into particle dynamics and boundary effects.

Contribution

It presents the first exact solutions for steady-state density profiles and correlation functions in a boundary-driven asymmetric exclusion process.

Findings

Exact steady-state density profile obtained.

Explicit expressions for correlation functions derived.

Phase diagram characterized and compared with scaling predictions.

Abstract

We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of $L$ sites and being removed at the (right) boundary. We construct the steady state and compute the density profile, exact expressions for all equal-time n-point density correlation functions and the time-dependent two-point function in the steady state as functions of the injection and absorption rates. We determine the phase diagram of the model and compare our results with predictions from dynamical scaling and discuss some conjectures for other exclusion models.