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

Aurélien Grabsch; Alexis Poncet; Pierre Rizkallah; Pierre Illien; Olivier Bénichou

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arXiv · 2110.09269

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

Aurélien Grabsch·Alexis Poncet·Pierre Rizkallah·Pierre Illien·Olivier Bénichou

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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.

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Aurélien Grabsch, Alexis Poncet, Pierre Rizkallah, Pierre Illien, Olivier Bénichou. 2021-10-18. Exact closure and solution for spatial correlations in single-file diffusion. https://arxiv.org/abs/2110.09269

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