Interacting single-file system: Fractional Langevin formulation versus diffusion-noise approach

TL;DR

This paper reviews recent analytical models of single-file diffusion, comparing the fractional Langevin equation approach with the diffusion-noise formalism, highlighting their equivalence and providing insights into particle motion.

Contribution

It introduces an alternative derivation of the fractional Langevin equation from the diffusion-noise formalism, connecting two different analytical approaches for single-file diffusion.

Findings

Demonstrates equivalence of fractional Langevin and diffusion-noise models

Provides a new derivation of the Langevin equation from diffusion-noise formalism

Enhances understanding of stochastic modeling in single-file systems

Abstract

We review the latest advances in the analytical modelling of single file diffusion. We focus first on the derivation of the fractional Langevin equation that describes the motion of a tagged file particle. We then propose an alternative derivation of the very same stochastic equation by starting from the diffusion-noise formalism for the time evolution of the file density.