$N$-tag Probability Law of the Symmetric Exclusion Process

TL;DR

This paper provides a comprehensive analytical study of the joint probability distribution and cumulants of tagged particles in the symmetric exclusion process, revealing universal scaling and large deviation functions.

Contribution

It offers the first full quantitative determination of spatial correlations in SEP, including analytical results for cumulants and their dynamics at high density.

Findings

Analytical large time limit of all cumulants for arbitrary density

Universal scaling form shared by cumulants

Time-dependent large deviation function derived

Abstract

The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of strong spatial correlations induced by the requirement that the particles cannot overtake each other. Even if this fact has been recognised qualitatively for a long time, up to now there is no full quantitative determination of these correlations. Here we study the joint probability distribution of an arbitrary number of tagged particles in the SEP. We determine analytically the large time limit of all cumulants for an arbitrary density of particles, and their full dynamics in the high density limit. In this limit, we unveil a universal scaling form shared by the cumulants and obtain the time-dependent large deviation function of the problem.