First passage time distribution of active thermal particles in potentials

TL;DR

This paper develops a perturbative approach to compute the moments of the first-passage time distribution for non-Markovian active thermal particles in potentials, bridging stochastic process theory and active matter physics.

Contribution

It introduces a novel perturbation method for non-Markovian processes to analyze first-passage times in active thermal particles, with applications to harmonic traps and rings.

Findings

Analytical first-order corrections to moments of first-passage times

Validation of analytical results against numerical simulations

Extension of methods to non-Markovian active matter systems

Abstract

We introduce a perturbative method to calculate all moments of the first-passage time distribution in stochastic one-dimensional processes which are subject to both white and coloured noise. This class of non-Markovian processes is at the centre of the study of thermal active matter, that is self-propelled particles subject to diffusion. The perturbation theory about the Markov process considers the effect of self-propulsion to be small compared to that of thermal fluctuations. To illustrate our method, we apply it to the case of active thermal particles (i) in a harmonic trap (ii) on a ring. For both we calculate the first-order correction of the moment-generating function of first-passage times, and thus to all its moments. Our analytical results are compared to numerics.