Abstract
We introduce a resetting Brownian bridge as a simple model to study search processes where the total search time is finite and the searcher returns to its starting point at . This is simply a Brownian motion with a Poissonian resetting rate to the origin which is constrained to start and end at the origin at time . 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.
- Received 6 January 2022
- Revised 6 April 2022
- Accepted 25 April 2022
DOI:https://doi.org/10.1103/PhysRevLett.128.200603
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