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Intermittent resetting potentials

2020; Institute of Physics; Volume: 2020; Issue: 11 Linguagem: Inglês

10.1088/1742-5468/abc1d9

1742-5468

Gabriel Mercado-Vásquez, Denis Boyer, Satya N. Majumdar, Grégory Schehr,

Mathematical and Theoretical Epidemiology and Ecology Models

Abstract 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 ) = 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, 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 μ is varied across non-trivial values. A discontinuous transition with metastable behavior is also observed for the optimal strength at fixed rates.