Optimal Resetting Brownian Bridges via Enhanced Fluctuations

Benjamin De Bruyne, Satya N. Majumdar, and Grégory Schehr
Phys. Rev. Lett. 128, 200603 – Published 17 May 2022
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Abstract

We introduce a resetting Brownian bridge as a simple model to study search processes where the total search time tf is finite and the searcher returns to its starting point at tf. This is simply a Brownian motion with a Poissonian resetting rate r to the origin which is constrained to start and end at the origin at time tf. We unveil a surprising general mechanism that enhances fluctuations of a Brownian bridge, by introducing a small amount of resetting. This is verified for different observables, such as the mean-square displacement, the hitting probability of a fixed target and the expected maximum. This mechanism, valid for a Brownian bridge in arbitrary dimensions, leads to a finite optimal resetting rate that minimizes the time to search a fixed target. The physical reason behind an optimal resetting rate in this case is entirely different from that of resetting Brownian motions without the bridge constraint. We also derive an exact effective Langevin equation that generates numerically the trajectories of a resetting Brownian bridge in all dimensions via a completely rejection-free algorithm.

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  • Received 6 January 2022
  • Revised 6 April 2022
  • Accepted 25 April 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.200603

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Benjamin De Bruyne1, Satya N. Majumdar1, and Grégory Schehr2

  • 1LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
  • 2Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France

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Issue

Vol. 128, Iss. 20 — 20 May 2022

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