Mean first passage time of active Brownian particle in one dimension

TL;DR

This paper studies the mean first passage time of a one-dimensional active Brownian particle with stochastic orientation switching, analyzing the effects of resetting and external potentials through simulations and effective modeling.

Contribution

It introduces a two-state model for active Brownian motion in one dimension and explores the impact of resetting and external potentials on first passage times.

Findings

Existence of an optimal resetting rate minimizing first passage time.

Effective diffusion and potential models accurately predict simulation results.

External potentials align theory with numerical simulations.

Abstract

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate $r$ on the mean first passage time to a fixed target of a single free Active Brownian Particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate $r^*$ for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.