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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 (one of the alternative locations)
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Copyright: 2021 IOP Publishing
Appears in Collections:Research Papers (TP)

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