Linear response approach to active Brownian particles in time-varying activity fields

TL;DR

This paper develops a linear response framework to analytically describe active Brownian particles in time-varying activity fields, validated by simulations, with potential applications in particle sorting and targeted control.

Contribution

It introduces a fully analytical linear response approach for ABPs in dynamic activity fields, bridging theory and simulation for the first time.

Findings

Analytical expressions accurately predict polarization profiles.

The formalism works best for small, highly Brownian particles.

Simulations confirm the validity of the linear response approach.

Abstract

In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of the particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.