Exact spatial correlations in single-file diffusion

TL;DR

This paper derives exact equations for bath-tracer correlations in single-file diffusion, revealing the underlying strong correlations causing subdiffusive behaviour, and extends these results to different models, connecting with recent inverse scattering solutions.

Contribution

It provides a full derivation of the exact correlation equations and extends the analysis to the double exclusion process, linking different theoretical approaches.

Findings

Derived exact closed equations for bath-tracer correlations.

Extended the analysis to the double exclusion process.

Connected results with recent inverse scattering solutions.

Abstract

Single-file diffusion refers to the motion of diffusive particles in narrow channels, so that they cannot bypass each other. This constraint leads to the subdiffusion of a tagged particle, called the tracer. This anomalous behaviour results from the strong correlations that arise in this geometry between the tracer and the surrounding bath particles. Despite their importance, these bath-tracer correlations have long remained elusive, because their determination is a complex many-body problem. Recently, we have shown that, for several paradigmatic models of single-file diffusion such as the Simple Exclusion Process, these bath-tracer correlations obey a simple exact closed equation. In this paper, we provide the full derivation of this equation, as well as an extension to another model of single-file transport: the double exclusion process. We also make the connection between our results and the ones obtained very recently by several other groups, and which rely on the exact solution of different models obtained by the inverse scattering method.