First passage time distribution of active thermal particles in potentials

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-pr...

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Bibliographic Details
Published inarXiv.org
Main Authors Walter, Benjamin, Pruessner, Gunnar, Salbreux, Guillaume
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.02.2021
Subjects
Markov analysis
Markov processes
Mathematical analysis
Perturbation theory
Physics - Statistical Mechanics
Queuing theory
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ISSN2331-8422
DOI10.48550/arxiv.2006.00116

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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.2006.00116