Diffusion with stochastic resetting.

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r*. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.

• Publication year

  2011

• Venue

  Physical Review Letters

• Publication date

  2011-02-14

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevLett.106.160601arXiv 1102.2704PMID 21599344
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• For multiple searchers, the typical survival probability of a stationary target decays exponentially in time, while the average survival probability decays as a power law with an exponent that varies continuously with searcher density.

  Confidence 0.96

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• The mean time for a diffusive searcher to find a stationary target is finite and is minimized at an optimal resetting rate `r*`.

  Confidence 0.97

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• Finite resetting produces a nonequilibrium stationary state for the diffusing particle, with non-Gaussian position fluctuations.

  Confidence 0.98

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review

• diffusion with stochastic resetting

  processes

  A diffusion process in which a particle is intermittently returned to its starting position at a constant rate.

  Aliases: stochastic resetting diffusion, diffusion with resetting

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• mean time to find a stationary target

  quantities

  The average time required for a diffusive searcher to reach a fixed target that does not move.

  Aliases: mean first-passage time to a stationary target, MFPT

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• multiple searchers

  populations

  A setting with many independent diffusive searchers competing to find the same target.

  Aliases: many searchers

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• nonequilibrium stationary state

  states

  A steady state maintained away from equilibrium by the resetting dynamics.

  Aliases: NESS

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• non-gaussian fluctuations

  fluctuations

  Position fluctuations whose distribution is not Gaussian in the stationary regime.

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• optimal resetting rate

  parameters

  The resetting rate that optimizes the target-finding time in the search problem.

  Aliases: r*, optimal rate

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• searcher density

  quantities

  The number of searchers per unit length or volume used to characterize the many-searcher setting.

  Aliases: density of searchers

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• stationary target

  targets

  A target location that remains fixed while being searched for by the diffusing particle.

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review
• survival probability

  probabilities

  The probability that the target has not yet been found by a given time.

  Aliases: target survival probability

  박진우 (dztg5apj7m) extraction뀨 (7c402c1b98) reviewAK (4715169a40) review

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