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

Alexis Poncet; Aurélien Grabsch; Olivier Bénichou

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arXiv · 2505.21446

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

Alexis Poncet·Aurélien Grabsch·Olivier Bénichou

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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.

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Alexis Poncet, Aurélien Grabsch, Olivier Bénichou. 2025-05-27. Full stochastic dynamics of a tracer in a dense single-file system. https://arxiv.org/abs/2505.21446

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