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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
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 (one of the alternative locations)
ISSN: 1742-5468
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Copyright: 2018 IOP Publishing and SISSA Medialab srl
Appears in Collections:Research Papers (TP)

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