Trapping Instability of an Active Particle in Steering Potential Fields

TL;DR

This paper develops an analytical framework to understand how active particles get trapped or escape in steering potential fields, revealing critical thresholds for trapping stability.

Contribution

It introduces a projection operator method to derive explicit solutions for trapping dynamics of active particles in symmetric potentials, addressing a complex coupling problem.

Findings

Derived analytical expressions for mean first passage time in trapping scenarios

Identified critical steering potential strength thresholds for trapping stability

Analyzed trapping and release dynamics in active particle systems

Abstract

A particle driven by active self-propulsion can be subject to inhomogeneous potential fields, steering its orientation and leading to confinement and eventual trapping. Analytical treatment of capture and/or release dynamics for general steering potentials presents a challenge due to its coupling between external potential fields and intrinsic active noise. By using the projection operator method we obtain the coarse-grained Dynkin equations with orientation integrated out in the large fluctuations limit, and derive explicit analytical solutions for the mean first passage time in radially symmetric point source trapping potentials. We analyze the ensuing trapping instabilities related to a critical value of the steering potential strength below which the particle either cannot be lured into the trap, or above which it is unable to leave the trap after being lured into it.