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

Abstract

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 first-passage 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.