Fractional generalized Langevin equation approach to single-file diffusion

TL;DR

This paper models single-file diffusion using a fractional generalized Langevin equation with external force, deriving analytic expressions for mean square displacement that capture both short and long time behaviors.

Contribution

It introduces a fractional Langevin equation approach with external force to accurately describe single-file diffusion dynamics.

Findings

Correct short and long time behavior of mean square displacement

New analytic expressions for mean square displacement

Effective Fokker-Planck equation for single-file diffusion

Abstract

Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short and long time behavior for the mean square displacement of single-file diffusion when appropriate choice of parameters associated with fractional generalized Langevin equation are used. By considering some special cases of the fractional generalized Langevin equation, a new class of closed analytic expressions for the mean square displacement of single-file diffusion can be obtained. The effective Fokker-Planck equation associated with single-file diffusion is briefly considered.