Optimal mean firstpassage 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 a tolerance radius R _{tol}, a target at a distance L from an initial position in the presence of resetting. The reset position is 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 firstpassage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean firstpassage time as a function of the resetting period/rate for different target distances (values of the ratios b = L/σ) and target size (a = R _{tol}/L). We find an interesting phase transition at a critical value of b, both in one and two dimensions. The details of the calculations as well as the experimental setup and limitations are discussed.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 November 2021
 DOI:
 10.1088/17425468/ac2cc7
 arXiv:
 arXiv:2106.09113
 Bibcode:
 2021JSMTE2021k3203F
 Keywords:

 Brownian motion;
 diffusion;
 fluctuation phenomena;
 Condensed Matter  Statistical Mechanics
 EPrint:
 arXiv admin note: substantial text overlap with arXiv:2004.11311