Single-File diffusion in a Box

TL;DR

This paper derives an exact analytical solution for the diffusion of interacting particles in a finite 1D system, revealing three distinct temporal regimes and validating results with simulations, with potential applications in bio-nano sensors.

Contribution

It provides the first exact analytical expression for tagged particle diffusion in a finite 1D system with hard-core interactions using Bethe-ansatz.

Findings

Identification of three distinct diffusion regimes

Excellent agreement with stochastic simulations

Potential applications in bio-nano sensor development

Abstract

We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density using a coordinate Bethe-ansatz, from which the mean square displacement is calculated. The analysis show the existence of three regimes of drastically different behavior for short, intermediate and large times. The results show excellent agreement with stochastic simulations (Gillespie algorithm). The findings of the Letter holds promise for the development of novel bio-nano sensors.