Title:	Universal framework for the long-time position distribution of free active particles
Authors:	Santra, Ion Basu, Urna Sabhapandit, Sanjib
Issue Date:	23-Aug-2022
Publisher:	IOP Publishing Ltd
Citation:	Journal of Physics A : Mathematical and Theoretical, 2022, Vol.55, p385002
Abstract:	Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times much larger than the persistence time. Here we develop a general framework for studying the long-time behavior for a class of active particle dynamics and illustrate it using the examples of run-and-tumble particle, active Ornstein–Uhlenbeck particle, active Brownian particle, and direction reversing active Brownian particle. Treating the ratio of the persistence-time to the observation time as the small parameter, we show that the position distribution generically satisfies the diffusion equation at the leading order. We further show that the sub-leading contributions, at each order, satisfies an inhomogeneous diffusion equation, where the source term depends on the previous order solutions. We explicitly obtain a few sub-leading contributions to the Gaussian position distribution. As a part of our framework, we also prescribe a way to find the position moments recursively and compute the first few explicitly for each model.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/7988
ISSN:	1751-8113 1751-8121 (Online)
Alternative Location:	https://arxiv.org/abs/2202.12117 https://doi.org/10.1088/1751-8121/ac864c https://ui.adsabs.harvard.edu/abs/2022JPhA...55L5002S/abstract
Copyright:	2022 IOP Publishing Ltd.
Appears in Collections:	Research Papers (TP)

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