Full stochastic dynamics of a tracer in a dense single-file system

TL;DR

This paper investigates the detailed multi-time correlations of a tracer in a dense single-file system, revealing significant memory effects and extending understanding beyond Gaussian and single-time statistics.

Contribution

It derives explicit multi-time correlation functions for a tracer in a dense symmetric exclusion process, linking non-Markovian dynamics to Markovian probabilities and exploring various extensions.

Findings

Explicit four-time correlation expressions derived

Significant memory effects identified in dense regimes

Initial conditions strongly influence long-time dynamics

Abstract

Tracer diffusion in single-file systems, where particles are restricted to move on a line without passing each other, has been a fertile ground to investigate anomalous diffusion and strong memory effects. While the long-time behavior of such a tracer has been well studied, with a known subdiffusive dynamics and a Gaussian description for the rescaled position, the finer details of multi-time correlations remain poorly understood. This work focuses on the limit where almost all sites of a Symmetric Exclusion Process (SEP), a paradigmatic lattice model, are occupied. It extends beyond Gaussian descriptions and single-time statistics to address the multi-time correlation functions of the tracer in the SEP. In this dense limit, we present a general relation between all $n$-time correlations of the non-Markovian tracer position process and the conditional probabilities of a single Markovian random walker. Using this relation, we derive explicit expressions for the four-time correlations and further explore important extensions: multiple tracers, non-equilibrium situations, and finite observation times. Our results underscore significant memory effects, strong temporal correlations, and the influence of initial conditions on long-time dynamics.