Evolution equation for tagged particle density and correlations in single file diffusion

TL;DR

This paper develops a theoretical framework for single file diffusion that captures particle correlations and anomalous diffusion, validated by numerical and simulation methods, providing deeper insights into the underlying processes.

Contribution

It introduces a novel approach to derive correlations between a tagged particle and others in single file diffusion systems.

Findings

Correlation functions match Monte Carlo simulations

The approach explains anomalous diffusion behavior

Numerical integration agrees with simulation results

Abstract

We derive and study a theoretical description for single file diffusion, i.e., diffusion in a one dimensional lattice of particles with hard core interaction. It is well known that for this system a tagged particle has anomalous diffusion for long times. The novelty of the present approach is that it allows for the derivation of correlations between a tagged particle and other particles of the system at a given distance with empty sites in between. The behavior of the correlation gives deeper insights into the processes involved. Numerical integration of differential equations are in good agreement with Monte Carlo simulations.