First passage time distribution of active thermal particles in potentials

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.

arXiv comment25 pages, 10 figures

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• Extinctions of coupled populations, and rare-event dynamics under non-Gaussian noise
• Evidence and quantification of memory effects in competitive first passage events
• Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes
• Correlated escape of active particles across a potential barrier