# Intermittent resetting potentials – Archive ouverte HAL

### Gabriel Mercado-VásquezDenis BoyerSatya N. Majumdar 1 Grégory Schehr 1

#### Gabriel Mercado-Vásquez, Denis Boyer, Satya N. Majumdar, Grégory Schehr. Intermittent resetting potentials. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2020, 2020 (11), pp.113203. ⟨10.1088/1742-5468/abc1d9⟩. ⟨hal-03010255⟩

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.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques