Intermittent resetting potentials

We study the non-equilibrium steady states (NESS) 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.