First-passage time of run-and-tumble particles with non-instantaneous resetting

Tucci, Gennaro; Gambassi, Andrea; Majumdar, Satya N.; Schehr, Grégory

doi:10.48550/arxiv.2203.16066

Cited by 3 publications

(3 citation statements)

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“…When the distance to the target is of the order of the width of this distribution, the MFPT exhibits a metastable behavior as the resetting periodicity is varied. These results were further generalized to the case of a one-dimensional persistent random walks in a harmonic potential, for which the distribution of resetting positions is non-Boltzmann [53]. Metastability is also the outcome of other protocols that use intermittent potentials to mimic non-ideal resetting processes [54].…”

Section: Discussionmentioning

confidence: 91%

Freezing transitions of Brownian particles in confining potentials

Mercado-Vásquez¹,

Boyer²,

Majumdar³

2022

J. Stat. Mech.

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We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential v(x) in a finite domain. We focus on the cases in which the external potential is confining, of the form v(x) = k|x − x 0| n /n, and where the particle’s initial position coincides with x 0. We first consider a particle between an absorbing target at x = 0 and a reflective wall at x = c. At fixed x 0, we show that when the target distance c exceeds a critical value, there exists a nonzero optimal stiffness k opt that minimizes the MFPT to the target. However, when c lies below the critical value, the optimal stiffness k opt vanishes. Hence, for any value of n, the optimal potential stiffness undergoes a continuous ‘freezing’ transition as the domain size is varied. On the other hand, when the reflective wall is replaced by a second absorbing target, the freezing transition in k opt becomes discontinuous. The phase diagram in the (x 0, n)-plane then exhibits three dynamical phases and metastability, with a ‘triple’ point at (x 0/c ≃ 0.171 85, n ≃ 0.395 39). For harmonic or higher order potentials (n ⩾ 2), the MFPT always increases with k at small k, for any x 0 or domain size. These results are contrasted with problems of diffusion under optimal resetting in bounded domains.

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Section: Discussionmentioning

confidence: 91%

Freezing transitions of Brownian particles in confining potentials

Mercado-Vásquez¹,

Boyer²,

Majumdar³

2022

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…When the distance to the target is of the order of the width of this distribution, the MFPT exhibits a metastable behavior as the resetting periodicity is varied. These results were further generalized to the case of a one-dimensional persistent random walks in a harmonic potential, for which the distribution of resetting positions is non-Boltzmann [52]. Metastability is also the outcome of other protocols that use intermittent potentials to mimic non-ideal resetting processes [53].…”

Section: Discussionmentioning

confidence: 91%

Freezing transitions of Brownian particles in confining potentials

Mercado-Vásquez,

Boyer,

Majumdar

2022

Preprint

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We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential v(x) in a finite domain. We focus on the cases in which the external potential is confining, of the form v(x) = k|x − x 0 | n /n, and where the particle's initial position coincides with x 0 . We first consider a particle between an absorbing target at x = 0 and a reflective wall at x = c. At fixed x 0 , target encounter is accelerated by increasing the potential stiffness k from zero, but only when the size of the domain c is above a critical value. In this case, the MFPT gets minimized at an optimal stiffness k opt > 0. Conversely, if the size of the system is below the critical size, pure diffusion (k opt = 0) becomes optimal. Hence, for any value of n, the optimal potential stiffness undergoes a continuous "freezing" transition as the domain size is varied. On the other hand, when the reflective wall is replaced by a second absorbing target, the freezing transition in k opt becomes discontinuous. The phase diagram in the (x 0 , n)-plane then exhibits three dynamical phases and metastability, with a "triple" point at (x 0 /c 0.17185, n 0.39539). For harmonic or higher order potentials (n ≥ 2), the MFPT always increases with k at small k, for any x 0 or domain size. These results are contrasted with problems of diffusion under optimal resetting in bounded domains.

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“…Moreover, in view of the importance of resetting phenomena in the context of search problems, we can speculate that the heterogeneous telegrapher's equation with resetting represents a toy model of random search in a turbulent environment. We also note that run-and-tumble particle motion under stochastic resetting [82,[86][87][88] and more generalized models of Lévy walks under resetting [89,90] are of current interest. By Laplace transform of equation ( 48), it follows that Pr (x, s) = s + r s P (x, s + r).…”

Section: Finite-velocity Hdp With Stochastic Resetting a Probability ...mentioning

confidence: 99%