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 $\sigma$. 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/rate for different values of the ratio b = L/$\sigma$ and find an interesting phase transtion at a critical value b = bc. For bc < b < $\infty$, there is a metastable optimum time which disappears for b < bc. The intrinsic diffculties in implementing these protocols in experiments are also discussed.
Highlights
When searching for a lost object in vain for a while, intuition tells us that maybe one should stop the current search and restart the search process all over again
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
Searching a target via resetting is an example of the so-called intermittent search strategy [6] that consists of a mixture of short-range moves with intermittent long-range moves where the searcher relocates to a new place and starts a local search in the new place
Summary
Optimal mean first-passage time for a Brownian searcher subjected to resetting: Experimental and theoretical results. These studies have led to the paradigm that resetting typically makes the search process more efficient, and, there often exists an optimal resetting rate r∗ (or period T ∗) that makes the search time minimal [7,8] While this “optimal resetting” paradigm has been tested and verified in a large number of recent theoretical and numerical studies [9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] (see the review [5]), it still needs to be verified experimentally The stiffness is controlled by changing the optical power in the chamber directly by laser current
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