Experimental realization of diffusion with stochastic resetting

Tal-Friedman, Ofir; Pal, A.; Sekhon, Amandeep; Reuveni, Shlomi; Roichman, Yael

doi:10.1117/12.2596165

Cited by 7 publications

(9 citation statements)

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“…An interesting follow-up involves extending our analysis to a many-particle setup with exclusion interaction [68] and employing reset-setups using optical tweezers [69,70] We provide here the details on deriving the recursion relation between branch-site probabilities along with the definition of Γ M . Let us first exhibit the explicit form of the ME, Eq.…”

Section: (B))mentioning

confidence: 99%

Biased random walk on random networks in presence of stochastic resetting: Exact results

Sarkar,

Gupta

2022

Preprint

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We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as also when the model is subject to stochastic resetting, whereby the walkers on the branches reset with a constant rate to the respective backbone sites, we obtain exact stationary-state static and dynamic properties for a given disorder realization of branch lengths sampled following an arbitrary distribution. We derive a criterion to observe in the stationary state a non-zero drift velocity along the backbone. For the bare model, we discuss the occurrence of a drift velocity that is non-monotonic as a function of the bias, becoming zero beyond a threshold bias because of walkers trapped at very long branches. Further, we show that resetting allows the system to escape trapping, resulting in a drift velocity that is finite at any bias.

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Section: (B))mentioning

confidence: 99%

Biased random walk on random networks in presence of stochastic resetting: Exact results

Sarkar,

Gupta

2022

Preprint

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“…Tuning such parameters, it is (in principle) possible to invert such effect of resetting on the dynamics [28][29][30][31][32][33][34][35]. Due to its appearance in a plethora of natural systems and drastic effect on the dynamics, study of first-passage problems with resetting has gained overwhelming attention in recent years [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Surprisingly, the effect of resetting on Feller process still remains scarcely explored.…”

Section: Introductionmentioning

confidence: 99%

Expediting Feller process with stochastic resetting

Ray¹

2022

Preprint

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We explore the effect of stochastic resetting on the first-passage properties of Feller process. The Feller process can be envisioned as space-dependent diffusion, with diffusion coefficient D(x) = x, in a potential U(x) = x x 2 − θ that owns a minimum at θ . This restricts the process to the positive side of the origin and therefore, Feller diffusion can successfully model a vast array of phenomena in biological and social sciences, where realization of negative values is forbidden. In our analytically tractable model system, a particle that undergoes Feller diffusion is subject to Poissonian resetting, i.e., taken back to its initial position at a constant rate r, after random time epochs. We addressed the two distinct cases that arise when the relative position of the absorbing boundary (x a ) with respect to the initial position of the particle (x 0 ) differ, i.e., for (a) x 0 < x a and (b) x a < x 0 . Utilizing the Fokker-Planck description of the system, we obtained closed-form expressions for the Laplace transform of the survival probability and hence derived the exact expressions of the mean first-passage time T r . Performing a comprehensive analysis on the optimal resetting rate (r ) that minimize T r and the maximal speedup that r renders, we identify the phase space where Poissonian resetting facilitates first-passage for Feller diffusion. We observe that for x 0 < x a , resetting accelerates first-passage when θ < θ c , where θ c is a critical value of θ that decreases when x a is moved away from the origin. In stark contrast, for x a < x 0 , resetting accelerates first-passage when θ > θ c , where θ c is a critical value of θ that increases when x 0 is moved away from the origin. Our study opens up the possibility of a series of subsequent works with more case-specific models of Feller diffusion with resetting.

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“…The optimal mean time needed by a freely diffusing particle to reach a target in presence of resetting has been studied experimentally and theoretically [31,32]. In another experimental realization of resetting, it is shown that the energetic cost of resetting in first-passage scenarios cannot be made arbitrarily small [33]. Resetting has also been studied in interacting particle systems such as fluctuating surfaces [34,35,36] and coagulationdiffusion process [37], in non-diffusive processes such as Lévy flights [38,39] and run and tumble dynamics [40], in telegraphic process [41], in active Brownian process [42], in symmetric exclusion process [43], in Ising model [44], as well as in quantum systems [45,46].…”

Section: Introductionmentioning

confidence: 99%

Discrete space-time resetting model: Application to first-passage and transmission statistics

Das¹,

Giuggioli²

2022

Preprint

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We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability r. We construct a discrete renewal equation and present closed-form expressions for different quantities of the resetting dynamics in terms of the underlying reset-free propagator or Green's function. We apply our formalism to the biased random walk dynamics in one-dimensional unbounded space and show how one recovers in the continuous limits results for diffusion with resetting. The resetting dynamics of biased random walker in one-dimensional domain bounded with periodic and reflecting boundaries is also analyzed. Depending on the bias the first-passage probability in periodic domain shows multi-fold non-monotonicity as r is varied. Finally, we apply our formalism to study the transmission dynamics of two lattice walkers with resetting in one-dimensional domain bounded by periodic and reflecting boundaries. The probability of a definite transmission between the walkers shows non-monotonic behavior as the resetting probabilities are varied.

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Experimental realization of diffusion with stochastic resetting

Cited by 7 publications

References 0 publications

Biased random walk on random networks in presence of stochastic resetting: Exact results

Biased random walk on random networks in presence of stochastic resetting: Exact results

Expediting Feller process with stochastic resetting

Discrete space-time resetting model: Application to first-passage and transmission statistics

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