Title:	Brownian motion under intermittent harmonic potentials
Authors:	Santra, Ion Das, Santanu Nath, Sujit Kumar
Issue Date:	Jul-2021
Publisher:	IOP Publishing
Citation:	Journal of Physics A: Mathematical and Theoretical, 2021, Vol. 54, p334001
Abstract:	We study the effects of an intermittent harmonic potential of strength μ = μ0ν—that switches on and off stochastically at a constant rate γ, on an overdamped Brownian particle with damping coefficient ν. This can be thought of as a realistic model for realisation of stochastic resetting. We show that this dynamics admits a stationary solution in all parameter regimes and compute the full time dependent variance for the position distribution and find the characteristic relaxation time. We find the exact non-equilibrium stationary state distributions in the limits—(i) γ Lt μ0 which shows a non-trivial distribution, in addition as μ0 → ∞, we get back the result for resetting with refractory period; (ii) γ Gt μ0 where the particle relaxes to a Boltzmann distribution of an Ornstein–Uhlenbeck process with half the strength of the original potential and (iii) intermediate γ = 2nμ0 for n = 1, 2. The mean first passage time (MFPT) to find a target exhibits an optimisation with the switching rate, however unlike instantaneous resetting the MFPT does not diverge but reaches a stationary value at large rates. MFPT also shows similar behavior with respect to the potential strength. Our results can be verified in experiments on colloids using optical tweezers.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/7810
Alternative Location:	https://arxiv.org/abs/2104.00609 https://doi.org/10.1088/1751-8121/ac12a0 https://ui.adsabs.harvard.edu/abs/2021arXiv210400609S/abstract
Copyright:	2021 IOP Publishing
Appears in Collections:	Research Papers (TP)

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