Theory of Single File Diffusion in a Force Field

TL;DR

This paper develops a theoretical framework for understanding the diffusion behavior of interacting particles in a force field, providing a simple formula linking single-particle reflection and transmission to the motion of a tagged particle.

Contribution

It introduces a general formula connecting the tagged particle's dynamics with single-particle reflection and transmission coefficients in a one-dimensional force field.

Findings

The formula applies to both equilibrium and non-equilibrium states.

It captures complex physical behaviors in single file diffusion.

Provides insights into the approach to equilibrium in many-body systems.

Abstract

The dynamics of hard-core interacting Brownian particles in an external potential field is studied in one dimension. Using the Jepsen line we find a very general and simple formula relating the motion of the tagged center particle, with the classical, time dependent single particle reflection ${\cal R}$ and transmission ${\cal T}$ coefficients. Our formula describes rich physical behaviors both in equilibrium and the approach to equilibrium of this many body problem.