First passage of a particle in a potential under stochastic resetting: A vanishing transition of optimal resetting rate

Ahmad, Saeed; Nayak, Indrani; Bansal, A.S.; Nandi, Amitabha; Das, Dibyendu

doi:10.1103/physreve.99.022130

Cited by 97 publications

(125 citation statements)

References 40 publications

(71 reference statements)

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“…The example of diffusion with resetting falls into the restorative category. Transitions between the different categories have been studied in [110][111][112]. It was also shown in [110] how the equation for the optimal resetting rate (5.19) generalises in the case of a refractory period with mean τ tõ φ 0 (r)(1 −φ 0 (r)) r 2φ 0 (r) − 1 r = τ (5.33) at r = r * .…”

Section: Michaelis-menton Reaction Scheme (Mmrs)mentioning

confidence: 99%

Stochastic resetting and applications

Evans

Majumdar

Schehr

2020

J. Phys. A: Math. Theor.

503

600

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In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.

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Section: Michaelis-menton Reaction Scheme (Mmrs)mentioning

confidence: 99%

Stochastic resetting and applications

Evans

Majumdar

Schehr

2020

J. Phys. A: Math. Theor.

503

600

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“…This issue can be addressed e.g. by incorporating an overhead time (refractory period) that follows each resetting event [8,9,29,38,61]; but all these attempts assumed that the overhead time and the position of the particle at the resetting moment are not coupled directly-which is again non-physical since returning from afar usually takes longer. To address this point, we have recently introduced a comprehensive theory for first-passage under space-time coupled resetting [63].…”

Section: Introductionmentioning

confidence: 99%

Invariants of motion with stochastic resetting and space-time coupled returns

2019

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Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the resetting moment. However, in our world, getting from one place to another always takes time and places that are further away take more time to be reached. We thus set off to extend the theory of stochastic resetting such that it would account for this inherent spatio-temporal coupling. We consider a particle that starts at the origin and follows a certain law of stochastic motion until it is interrupted at some random time. The particle then returns to the origin via a prescribed protocol. We study this model and surprisingly discover that the shape of the steady-state distribution which governs the stochastic motion phase does not depend on the return protocol. This shape invariance then gives rise to a simple, and generic, recipe for the computation of the full steady state distribution. Several case studies are analyzed and a class of processes whose steady state is completely invariant with respect to the speed of return is highlighted. For processes in this class we recover the same steady-state obtained for resetting with instantaneous returns-irrespective of whether the actual return speed is high or low. Our work significantly extends previous results on motion with stochastic resetting and is expected to find various applications in statistical, chemical, and biological physics.

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“…The simple model of diffusion with stochastic resetting has been extended and generalized to cover: diffusion in the presence of a potential [6][7][8], in a domain [9][10][11][12], and arbitrary dimensions [13]; diffusion in the presence of non-exponential resetting time distributions e.g., deterministic [14], intermittent [4], non-Markovian [15], non-stationary [16], with general time dependent resetting rates [17], as well as other protocols [18]; and diffusion in the presence of interactions [19][20][21]. The effect of resetting on random walks [22,23], continuous time random walks [24][25][26], Lévy flights [27,28], and other forms of stochastic motion [29][30][31][32][33], has also been studied.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent density of diffusion with stochastic resetting is invariant to return speed

2019

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The canonical Evans-Majumdar model for diffusion with stochastic resetting to the origin assumes that resetting takes zero time: upon resetting the diffusing particle is teleported back to the origin to start its motion anew. However, in reality getting from one place to another takes a finite amount of time which must be accounted for as diffusion with resetting already serves as a model for a myriad of processes in physics and beyond. Here we consider a situation where upon resetting the diffusing particle returns to the origin at a finite (rather than infinite) speed. This creates a coupling between the particle's random position at the moment of resetting and its return time, and further gives rise to a non-trivial cross-talk between two separate phases of motion: the diffusive phase and the return phase. We show that each of these phases relaxes to the stead-state in a unique manner; and while this could have also rendered the total relaxation dynamics extremely non-trivial our analysis surprisingly reveals otherwise. Indeed, the time-dependent distribution describing the particle's position in our model is completely invariant to the speed of return. Thus, whether returns are slow or fast, we always recover the result originally obtained for diffusion with instantaneous returns to the origin.

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First passage of a particle in a potential under stochastic resetting: A vanishing transition of optimal resetting rate

Cited by 97 publications

References 40 publications

Stochastic resetting and applications

Stochastic resetting and applications

Invariants of motion with stochastic resetting and space-time coupled returns

Time-dependent density of diffusion with stochastic resetting is invariant to return speed

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