Anomalous diffusion under stochastic resettings: A general approach

Masoliver, Jaume; Montero, Miquel

doi:10.1103/physreve.100.042103

Cited by 57 publications

(58 citation statements)

References 43 publications

(99 reference statements)

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“…(41). Upon inserting the expression for ρ(N, R, t) into the discrete Laplace transform (45) and taking the trace of both sides of the equality, one eventually gets…”

Section: The Non-markovian Tilted Generator From Quantum Trajectoriesmentioning

confidence: 99%

“…The more general case, where the times between consecutive resets are distributed according to a generic waiting time distribution p(τ ), can be analyzed within the so-called renewal equation approach, which relates the dynamics in the presence of resetting to the one where resets are absent, as shown in Refs. [41][42][43][44][45][46][47][48][49]. At the level of the master equation, non-Poissonian resetting is typically harder to treat than the Poissonian case.…”

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confidence: 99%

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Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Perfetto,

Carollo,

Lesanovsky

2021

Preprint

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We consider Markovian open quantum systems subject to stochastic resetting, which means that the dissipative time evolution is reset at randomly distributed times to the initial state. We show that the ensuing dynamics is non-Markovian and has the form of a generalized Lindblad equation. Interestingly, the statistics of quantum-jumps can be exactly derived. This is achieved by combining techniques from the thermodynamics of quantum-jump trajectories with the renewal structure of the resetting dynamics. We consider as an application of our analysis a driven two-level and an intermittent three-level system. Our findings show that stochastic resetting may be exploited as a tool to tailor the statistics of the quantum-jump trajectories and the dynamical phases of open quantum systems.

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“…(41). Upon inserting the expression for ρ(N, R, t) into the discrete Laplace transform (45) and taking the trace of both sides of the equality, one eventually gets…”

Section: The Non-markovian Tilted Generator From Quantum Trajectoriesmentioning

confidence: 99%

mentioning

confidence: 99%

Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Perfetto,

Carollo,

Lesanovsky

2021

Preprint

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“…The system under resetting can feature a nonequilibrium stationary state, depending on the parameters of the resetting process [22]. Characterisation of such a non-equilibrium stationary sate has recently become a major focus of activity in statistical physics [23][24][25]. The field enjoys a broad range of applications including RNA polymerisation processes [26,27], active matter [28][29][30] and randomised searching problems [31] (see the review [32] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Non-conserving zero-range processes with extensive rates under resetting

Grange

2020

J. Phys. Commun.

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We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and vanish with a uniform annihilation rate. On a fully-connected lattice with a large number of sites, the meanfield geometry leads to a negative binomial law for the number of particles at each site, with parameters depending on the hopping, creation and annihilation rates. This model can be mapped to population dynamics (if the creation rates are reproductive fitnesses in a haploid population, and the hopping rate is the mutation rate). It can also be mapped to a Bianconi-Barabási model of a growing network with random rewiring of links (if creation rates are the rates of acquisition of links by nodes, and the hopping rate is the rewiring rate). The steady state has recently been worked out and gives rise to occupation numbers that reproduce Kingman's house-of-cards model of selection and mutation. In this paper we solve the master equation using a functional method, which yields integral equations satisfied by the occupation numbers. The occupation numbers are shown to forget initial conditions at an exponential rate that decreases linearly with the fitness level. Moreover, they can be computed exactly in the Laplace domain, which allows to obtain the steady state of the system under resetting. The result modifies the house-of-cards result by simply adding a skewed version of the initial conditions, and by adding the resetting rate to the hopping rate.

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“…While this "optimal resetting" paradigm has been tested and verified in a large number of recent theoretical and numerical studies [9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] (see also the review [5]), it still needs to be verified experimentally (see, however, the recent preprint [29], where the authors use a holographic optical tweezer setup. Their resetting protocols though are quite different from ours).…”

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confidence: 99%

Optimal mean first-passage time for a Brownian searcher subjected to resetting: Experimental and theoretical results

Besga

Bovon

Petrosyan

et al. 2020

Phys. Rev. Research

180

162

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We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the resetting position are Gaussian distributed with width σ. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full firstpassage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period and rate for different values of the ratio b = L/σ and find an interesting phase transition at a critical value b = b c. For b c < b < ∞, there is a metastable optimum time which disappears for b < b c. The intrinsic difficulties in implementing these protocols in experiments are also discussed.

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Anomalous diffusion under stochastic resettings: A general approach

Cited by 57 publications

References 43 publications

Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting

Non-conserving zero-range processes with extensive rates under resetting

Optimal mean first-passage time for a Brownian searcher subjected to resetting: Experimental and theoretical results

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