Title:	Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap
Authors:	Basu, Urna Majumdar, Satya N Sabhapandit, Sanjib +2 Co-Authors
Keywords:	stochastic processes active particles exact solution
Issue Date:	4-Feb-2020
Publisher:	IOP Publishing Ltd
Citation:	Journal of Physics A: Mathematical and Theoretical, 2020, Vol.53, p09LT01
Abstract:	We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness [ image ] The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate [ image ]. We compute the stationary position distribution exactly for arbitrary values of [ image ] and [ image ] which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as [ image ] is changed. For [ image ] the distribution has a double-concave shape and shows algebraic divergences with an exponent [ image ] both at the origin and at the boundaries. For [ image ] the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case [ image ] the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.
Description:	Restricted Access.
URI:	http://hdl.handle.net/2289/7454
ISSN:	0305-4470 1361-6447(Online)
Alternative Location:	https://ui.adsabs.harvard.edu/abs/2020JPhA...53iLT01B/abstract https://arxiv.org/abs/1910.10083 https://doi.org/10.1088/1751-8121/ab6af0
Copyright:	2020 IOP Publishing Ltd
Appears in Collections:	Research Papers (TP)

Items in RRI Digital Repository are protected by copyright, with all rights reserved, unless otherwise indicated.