How active field theories couple to external potentials

TL;DR

This paper develops a systematic method to incorporate external potentials into active field theories, revealing non-trivial couplings that explain various nonequilibrium behaviors of active particles.

Contribution

It introduces a perturbative expansion approach to couple active Brownian particles with external potentials, capturing key nonequilibrium phenomena.

Findings

Derived a coupling between density and potential gradients in active particles.

Explained boundary accumulation and far-field density modulation.

Extended the method to interacting particles and spatial propulsion speed variations.

Abstract

We study the simplest terms that need to be included in active field theories to couple them to external potentials. To do so, we consider active Brownian particles and implement a systematic perturbative expansion in the particle persistence time. The result is a non-trivial coupling between density and potential gradients, which accounts for the nonequilibrium features of active particles in the presence of an external potential, from boundary accumulation to far-field density modulation. We show how the method can be applied to particles interacting via pairwise forces and to spatial modulations of the propulsion speed.