Microscopic theory for the diffusion of an active particle in a crowded environment

TL;DR

This paper develops a microscopic theoretical approach to calculate the diffusion coefficient of an active particle in a crowded environment, capturing nonequilibrium effects and environmental perturbations.

Contribution

It introduces a closure approximation that accurately predicts diffusion coefficients for various densities, surpassing mean-field methods.

Findings

Accurate diffusion coefficient predictions across a wide density range

Captures nonequilibrium effects due to activity

Explicit expressions for low and high density regimes

Abstract

We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean-field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.