Kramers escape of a self-propelled particle

TL;DR

This study analyzes the escape rate of a self-propelled particle from a potential well, revealing how particle size influences escape dynamics through analytical and numerical methods.

Contribution

It introduces a simplified 1D model for active particle escape and derives approximate formulas for different particle sizes, aligning well with detailed 2D simulations.

Findings

Escape rate depends on particle radius and timescales of translational and rotational motion.

Analytical expressions match numerical results within their validity ranges.

Particle size critically influences the escape dynamics of active particles.

Abstract

We investigate the escape rate of an overdamped, self-propelled spherical Brownian particle on a surface from a metastable potential well. Within a modeling in terms of a 1D constant speed of the particle's active dynamics we consider the associated rate using both numerical and analytical approaches. Regarding the properties of the stationary state in the potential well, two major timescales exist, each governing the translational and the rotational dynamics of the particle, respectively. The particle radius is identified to present the essential quantity in charge of regulating the ratio between those timescales. For very small and very large particle radii, approximate analytic expressions for the particle's escape rate can be derived, which, within their respective range of validity, compare favorably with the precise escape numerics of the underlying full two-dimensional Fokker-Planck description.