Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests

Abstract We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within tolerance radius R tol , target at distance L from an initial position presence of resetting. The reset is Gaussian distributed with width ? . derived tested resetting protocols, periodic random (Poissonian) times. computed measured full first-passage probability distribution that displays spectacular spikes immediately after each for close targets. as function period/rate different distances (values ratios b = / ) size ( ). find interesting phase transition critical value both dimensions. details calculations well experimental setup limitations are discussed.