Brownian motion under non-instantaneous resetting in higher dimensions

Abstract

We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the mean-squared displacement (MSD) in this process. We study two different resetting protocols: exponentially distributed time intervals between the resetting events (Poissonian resetting) and resetting at fixed time intervals (deterministic resetting). We moreover discuss a general problem of the invariance of the PDF with respect to the return speed, as observed in the one-dimensional system for Poissonian resetting, and show, that this one dimensional situation is the only one in which such an invariance can be found. However, the invariance of the MSD can still be observed in higher dimensions.

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Cited by in corpus (17)

• Intermittent resetting potentials
• Brownian motion under intermittent harmonic potentials
• Resetting with stochastic return through linear confining potential
• The cost of stochastic resetting
• Continuous time random walks under Markovian resetting
• Diffusion with Partial Resetting
• First passage in the presence of stochastic resetting and a potential barrier
• Resetting transition is governed by an interplay between thermal and potential energy
• Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes
• Dynamically emergent correlations between particles in a switching harmonic trap
• Role of dimensions in first passage of a diffusing particle under stochastic resetting and attractive bias
• Non-linear diffusion with stochastic resetting
• Search with stochastic home-returns can expedite classical first passage under resetting
• Universal performance bounds of restart
• The cost of resetting discrete-time random walks
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• Drift-diffusive resetting search process with stochastic returns: speed-up beyond optimal instantaneous return