Title:	Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
Authors:	Malakar, Kanaya Jemseena, V Kundu, Anupam Kumar, Vijay K Sabhapandit, Sanjib Majumdar, Satya N. Redner, S. Dhar, Abhishek
Keywords:	active matter Brownian motion diffusion
Issue Date:	Apr-2018
Publisher:	IOP Publishing and SISSA
Citation:	Journal of Statistical Mechanics: Theory and Experiment, 2018, p043215
Abstract:	We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/7119
ISSN:	1742-5468
Alternative Location:	https://arxiv.org/abs/1711.08474 https://doi.org/10.1088/1742-5468/aab84f
Copyright:	2018 IOP Publishing and SISSA Medialab srl
Appears in Collections:	Research Papers (TP)

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