Confined active particles with spatially dependent Lorentz force: an odd twist to the "best Fokker-Planck approximation"

TL;DR

This paper develops a generalized Fokker-Planck approximation to analyze the spatial behavior of active particles under magnetic fields, revealing how Lorentz forces influence particle distribution and accumulation.

Contribution

It introduces a new approach extending the BFPA to include Lorentz forces, enabling analytic characterization of active particle distributions in magnetic fields.

Findings

Lorentz force reduces particle accumulation near repulsive walls.

The theory agrees with simulations on particle distribution.

Inhomogeneous magnetic fields affect accumulation regions.

Abstract

We derive a version of the so-called "best Fokker-Planck approximation" (BFPA) to describe the spatial properties of interacting active Ornstein-Uhlenbeck particles (AOUPs) in arbitrary spatial dimensions. In doing so, we also take into account the odd-diffusive contribution of the Lorentz force acting on a charged particle in a spatially dependent magnetic field, sticking to the overdamped limit. While the BFPA itself does not turn out to be widely useful, our general approach allows to deduce an appropriate generalization of the Fox approximation, which we use to characterize the stationary behavior of a single active particle in an external potential by deriving analytic expressions for configurational probability distributions (or effective potentials). In agreement with computer simulations, our theory predicts that the Lorentz force reduces the effective attraction and thus the probability to find an active particle in the vicinity of a repulsive wall. Even for an inhomogeneous magnetic field, our theoretical findings provide useful qualitative insights, specifically regarding the location of accumulation regions.