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 firstpassage 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.

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

“…Abrupt drops of stock-market prices at times of economic crashes and other sudden catastrophic events 60 can also be viewed as reset-related phenomena. (•) Recent experimental (wo-)man-made particletracking resetting setups involve a manipulation of micron-sized beads in optical traps 122 and "tweezers" 66,67 and can potentially yield time series amenable for a single-trajectory-based time-averaging analysis to decipher the underlying diffusion process, as in the theory developed below.…”

“…Resetting a stochastic process, either normal or anomalous 1-10 , via restart events-abrupt or taking a finite time, stochastic/random but distributed, or entirely deterministic in time-returns the particle to its initial position (or a set of positions) according to a certain rule. In recent years, the field of resetting has experienced a wave of new theoretical developments as well as some experimental progress 66,67 . There bouncing-back, often rare, restart events might obey different distributions of waiting times, take place in space-dependent and spacetime-coupled manner, with space-time coupled returns, with power-law-like time-dependent resetting rates, with probabilities depending on the offset position, in different geometries and higher dimensions, in comb-like structures, in confining potential wells, under spatial constraints, in nonexponential resetting protocols, with interactions, in coagulation-diffusion processes, in reactiondiffusion protocols, in the presence of space-dependent diffusivity, for the over-and under-damped particle dynamics, to mention a few recent directions of resetting studies.…”

Experimental Realization of Diffusion with Stochastic Resetting

“…Despite a long catalogue of theoretical studies on stochastic resetting, no attempt to experimentally study resetting in a controlled environment has been made to date (but see very recent work that appeared after our arXiv submission 41 ). This is needed as resetting in the real world is never “clean” as in theoretical models which glance over physical complications for the sake of analytical tractability and elegance.…”

Controlling particle currents with evaporation and resetting from an interval

“…In words, the control is exerted on the particle at a rate r only when the particle is located within the interval [−a, a]. This choice of the resetting profile turns out to be more realistic for experimental realizations [13,14] with respect to the ideal, spatially homogeneous case, which can be retrieved as a → ∞. We will discuss a collection of transport phenomena described by Eqs.…”

“…Stochastic processes whereby incremental changes are interspersed with sudden and large changes occurring at unpredictable times are common in nature [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Examples range from epidemics (e.g., to financial markets (e.g., the 2008 crisis) and biology (e.g., the catastrophic events of sudden shrinkage during the polymerization of a microtubule [1,3,4], the flashing ratchet mechanism of molecular motors [2], etc.).…”