Title:	Run-and-tumble particle in inhomogeneous media in one dimension
Authors:	Singh, Prashant Sabhapandit, Sanjib Kundu, Anupam
Keywords:	stationary states active matter persistence Brownian motion
Issue Date:	Aug-2020
Publisher:	IOP Publishing and SISSA
Citation:	Journal of Statistical Mechanics:Theory and Experiment, 2020, Article No.083207
Abstract:	We investigate the run and tumble particle (RTP), also known as persistent Brownian motion, in one dimension. A telegraphic noise σ(t) drives the particle which changes between ±1 values with some rates. Denoting the rate of flip from 1 to −1 as R1 and the converse rate as R2 , we consider the position and direction dependent rates of the form R1(x)=(∣x∣l)α[γ1 θ(x)+γ2 θ(−x)] and R2(x)=(∣x∣l)α[γ2 θ(x)+γ1 θ(−x)] with α≥0 . For γ1>γ2 , we find that the particle exhibits a steady-state probability distriution even in an infinite line whose exact form depends on α . For α=0 and 1 , we solve the master equations exactly for arbitrary γ1 and γ2 at large t . From our explicit expression for time-dependent probability distribution P(x,t) we find that it exponentially relaxes to the steady-state distribution for γ1>γ2 . On the other hand, for γ1<γ2 , the large t behaviour of P(x,t) is drastically different than γ1=γ2 case where the distribution decays as t−12 . Contrary to the latter, detailed balance is not obeyed by the particle even at large t in the former case. For general α , we argue that the approach to the steady state in γ1>γ2 case is exponential which we numerically demonstrate....
Description:	Restricted Access.
URI:	http://hdl.handle.net/2289/7531
ISSN:	1742-5468
Alternative Location:	https://ui.adsabs.harvard.edu/abs/2020arXiv200411041S/abstract https://arxiv.org/abs/2004.11041 https://doi.org/10.1088/1742-5468/aba7b1
Copyright:	2020, IOP Publishing and SISSA
Appears in Collections:	Research Papers (TP)

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