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Diffusion with two resetting points.

Pedro Julián-Salgado1, Leonardo Dagdug1, Denis Boyer2

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This study reveals that optimal search strategies with two resetting locations exhibit discontinuous transitions in mean search time. A critical point exists, influencing search efficiency in Brownian particle target searches.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Brownian motion is fundamental to understanding particle diffusion.
  • Stochastic resetting enhances search efficiency by periodically returning particles to specific locations.
  • Previous studies primarily focused on single-site resetting, leaving multi-site scenarios less explored.

Purpose of the Study:

  • To investigate the impact of stochastic resetting to a pair of sites on target search efficiency.
  • To analyze the behavior of the mean search time and identify optimal resetting strategies.
  • To characterize the phase transitions and critical phenomena in a two-site resetting system.

Main Methods:

  • Mathematical modeling of a Brownian particle undergoing stochastic resetting to two distinct sites.
  • Analysis of the mean search time as a function of resetting rate and site positions.
  • Identification of conditions for discontinuous transitions and critical points.

Main Results:

  • The optimal resetting rate exhibits a discontinuous transition, unlike the smooth variation in single-site resetting.
  • A
  • liquid-gas
  • critical point in position space is identified, dependent on the relative weight of the sites.
  • Discontinuous transitions in optimal rates occur when initial positions follow the resetting distribution, contingent on a critical weight parameter.

Conclusions:

  • Distributed stochastic resetting introduces complex behaviors, including discontinuous transitions, not observed in single-site scenarios.
  • The identified critical point and parameter dependencies offer insights into optimizing search strategies in complex environments.
  • This model serves as a foundation for studying intermittent search problems with dynamic diffusion coefficients.