First passage in the presence of stochastic resetting and a potential barrier

Ahmad, Saeed; Rijal, Krishna; Das, Dibyendu

doi:10.1103/physreve.105.044134

Cited by 20 publications

(20 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We quantify this transition via direct optimization of the mean FPT and then provide a cross-verification of the same using the restart transition theory of optimal resetting rate [60]. Such resetting transition has been observed in various other systems such as diffusion in confinement [73] or channel [74], gated reaction [75], diffusion in potential [52,[76][77][78][79][80][81][82], random walks [83,84] and the universal applicability of the general condition [61,63] that dictates such transition is quite remarkable.…”

Section: Discussionmentioning

confidence: 86%

First-passage functionals for Ornstein–Uhlenbeck process with stochastic resetting

Dubey,

Pal

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We study the statistical properties of first-passage Brownian functionals (FPBFs) of an Ornstein-Uhlenbeck (OU) process in the presence of stochastic resetting. We consider a one dimensional set-up where the diffusing particle sets off from $x_0$ and resets to $x_R$ at a certain rate $r$. The particle diffuses in a harmonic potential (with strength $k$) which is centered around the origin. The center also serves as an absorbing boundary for the particle and we denote the first passage time of the particle to the center as $t_f$. In this set-up, we investigate the following functionals: (i) local time $T_{loc} = \int _0^{t_f}d \tau ~ \delta (x-x_R)$ i.e., the time a particle spends around $x_R$ until the first passage, (ii) occupation or residence time $T_{res} = \int _0^{t_f} d \tau ~\theta (x-x_R)$ i.e., the time a particle typically spends above $x_R$ until the first passage and (iii) the first passage time $t_f$ to the origin. We employ the Feynman-Kac formalism for renewal process to derive the analytical expression for the first moment of all the three FPBFs mentioned above. In particular, we find that resetting can either prolong or shorten the mean residence and first passage time depending on the system parameters. The transition between these two behaviors or phases can be characterized precisely in terms of optimal resetting rates, which interestingly undergo a continuous transition as we vary the trap stiffness $k$. We characterize this transition and identify the critical -parameter \& -coefficient for both the cases. We also showcase other interesting interplay between the resetting rate and potential strength on the statistics of these observables. Our analytical results are in excellent agreement with the numerical simulations.

show abstract

Section: Discussionmentioning

confidence: 86%

First-passage functionals for Ornstein–Uhlenbeck process with stochastic resetting

Dubey,

Pal

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…R,L (a) = τ depending on whether the system has (i) an absorbing boundary or (ii) a reflecting boundary at x = (see, for instance, Ref. [63]).…”

Section: Discussionmentioning

confidence: 99%

Run-and-tumble motion in a linear ratchet potential: analytic solution, power extraction and first-passage properties

Roberts¹,

Zhen²

2023

Preprint

View full text Add to dashboard Cite

We explore the properties of a system of run-and-tumble (RnT) particles moving in a piecewiselinear "ratchet" potential, and subject to non-negligible diffusion, by deriving exact analytical results for its steady-state probability density, current, entropy production rate, power output, and thermodynamic efficiency. The current, and thus the extractable power and efficiency, have non-monotonic dependencies on the diffusion strength, ratchet height, and particle self-propulsion speed, peaking at finite values in each case. In the case where the particles' self-propulsion is completely suppressed by the force from the ratchet, and thus a current can be generated only by diffusion-mediated barrier crossings, the system's entropy production rate remains finite in the limit of vanishing diffusion. In the final part of this work, we consider RnT motion in a linear ratchet potential on a bounded interval, allowing the derivation of mean first-passage times and splitting probabilities for different boundary and initial conditions. The present work resides at the interface of exactly solvable models of run-and-tumble motion and the study of work extraction from active matter by providing exact expressions pertaining to the feasibility and future design of active engines. Our results are in agreement with Monte Carlo simulations.

show abstract

“…Introducing a potential bias towards the target always expedite the first passage. The simultaneous presence of both resetting and potential bias has been studied in different models [33,37,[55][56][57][58][59][60][61][62]. It is generically found that the ORR is strongly regulated by the strength of the potential and the reset location.…”

Section: Introductionmentioning

confidence: 99%

Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting

Ahmad

Das

2023

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

The strategy of stochastic resetting is known to expedite the first passage to a target, in diffusive systems. Consequently, the mean first passage time is minimized at an optimal resetting parameter. With Poisson resetting, vanishing transitions in the optimal resetting rate r∗ → 0 (continuously or discontinuously) have been found for various model systems, under the further influence of an external potential. In this paper, we explore how the discontinuous transitions in this context are regulated by two other factors — the first one is spatial dimensions within which the diffusion is embedded, and the second is the time delay introduced before restart. We investigate the effect of these factors by studying analytically two types of models, one with an ordinary drift and another with a barrier, and both types having two absorbing boundaries. In the case of barrier potential, we find that the effect of increasing dimensions on the transitions is quite the opposite of increasing refractory period.

show abstract

First passage in the presence of stochastic resetting and a potential barrier

Cited by 20 publications

References 38 publications

First-passage functionals for Ornstein–Uhlenbeck process with stochastic resetting

First-passage functionals for Ornstein–Uhlenbeck process with stochastic resetting

Run-and-tumble motion in a linear ratchet potential: analytic solution, power extraction and first-passage properties

Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting

Contact Info

Product

Resources

About