Exact closure and solution for spatial correlations in single-file diffusion

TL;DR

This paper derives and solves an exact equation for spatial correlations in single-file diffusion, providing new insights into the fundamental anomalous transport behavior in confined systems.

Contribution

It introduces a closed-form exact equation for correlations in the Symmetric Exclusion Process, advancing understanding of single-file diffusion beyond previous hierarchical approaches.

Findings

Derived a closed exact equation for correlations.

Solved the equation for the Symmetric Exclusion Process.

Applicable to out-of-equilibrium and other single-file systems.

Abstract

Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in 1D, which, despite extensive effort, have however remained elusive, because they involve an infinite hierarchy of equations. Here, for the Symmetric Exclusion Process, a paradigmatic model of single-file diffusion, we break the hierarchy and unveil a closed exact equation satisfied by these correlations, which we solve. Beyond quantifying the correlations, the central role of this key equation as a novel tool for interacting particle systems is further demonstrated by showing that it applies to out-of equilibrium situations, other observables and other representative single-file systems.