Intermittent resetting potentials

TL;DR

This paper investigates a stochastic resetting process driven by an intermittently switched confining potential, revealing complex optimal switching behaviors and phase transitions in mean first passage times.

Contribution

It introduces a novel model of stochastic resetting with an intermittently activated potential, uncovering rich phase transition phenomena in optimal control parameters.

Findings

Optimal switching rates minimize mean first passage time.

Transitions in optimal rates are continuous or discontinuous depending on potential strength.

Discontinuous transitions with metastability are observed at fixed rates.

Abstract

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 $V(X)=\mu|X|$, and that is switched on and off stochastically. Applying the potential intermittently generates a physically realistic diffusion process with stochastic resetting toward the origin, a topic which has recently attracted a considerable interest in a variety of theoretical contexts but has remained challenging to implement in lab experiments. The present system exhibits rich features, not observed in previous 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. The optimal rates undergo continuous or discontinuous transitions as the potential strength $\mu$ is varied across non-trivial values. A discontinuous transition with metastable behavior is also observed for the optimal strength at fixed rates.