Langevin formulation for single-file diffusion

TL;DR

This paper presents a Langevin equation model for single-file diffusion that accurately captures the three key temporal regimes—ballistic, diffusive, and subdiffusive—using a diffusion noise approach, providing a compact and quantitative description.

Contribution

It introduces a stochastic Langevin equation for a tagged particle in single-file diffusion, unifying multiple properties and regimes in a single framework.

Findings

Reproduces three temporal regimes with accurate time scales

Provides a compact representation of fluctuation-dissipation relations

Quantitatively matches system behavior across regimes

Abstract

We introduce a stochastic equation for the microscopic motion of a tagged particle in the single file model. This equation provides a compact representation of several of the system's properties such as Fluctuation-Dissipation and Linear Response relations, achieved by means of a diffusion noise approach. Most important, the proposed Langevin Equation reproduces quantitatively the \emph{three} temporal regimes and the corresponding time scales: ballistic, diffusive and subdiffusive.