Denis Boyer

Date: 11 February 2021

Title: Intermittent resetting potentials

Abstract:

Resetting from time to time a diffusive particle to its starting position typically reduces the time needed to reach a given position for the first time. The idea that the completion of a task or the encounter with a hidden target can be accelerated by restart finds many applications in random search problems. Stochastic processes under resetting is thus a topic that has recently attracted considerable attention in a variety of theoretical contexts, but which has remained challenging to implement in lab experiments. Here, we study the non-equilibrium steady states and first passage properties of a Brownian particle with position X subject to an external confining potential of the form V(X)= μ |X|, and that is switched on and off stochastically. Applying the potential intermittently generates a physically realistic diffusion process with stochastic resetting toward the origin. Our system, although simple, exhibits rich features not observed in idealized resetting models. The mean time needed by a particle starting from the potential minimum to reach an absorbing target located at a certain distance can be minimized with respect to the switch-on and switch-off rates. This optimal time is in general shorter than the well-studied equilibrium Kramers' escape time. The optimal rates also undergo continuous or discontinuous transitions as the potential strength μ is varied across non-trivial values. A discontinuous transition with metastable behavior is also observed for the optimal strength at fixed rates.

Youtube link: https://www.youtube.com/watch?v=MsHYjNpwI8U