Stochastic resetting in the Kramers problem: A Monte Carlo approach

Abstract

The theory of stochastic resetting asserts that restarting a search process at certain times may accelerate the finding of a target. In the case of a classical diffusing particle trapped in a potential well, stochastic resetting may decrease the escape times due to thermal fluctuations. Here, we numerically explore the Kramers problem for a cubic potential, which is the simplest potential with a escape. Both deterministic and Poisson resetting times are analyzed. We use a Monte Carlo approach, which is necessary for generic complex potentials, and we show that the optimal rate is related to the escape times distribution in the case without resetting. Furthermore, we find rates for which resetting is beneficial even if the resetting position is located on the contrary side of the escape.

References in corpus (21)

• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Stochastic resetting in backtrack recovery by RNA polymerases
• Diffusion with stochastic resetting at power-law times
• Stochastic Search with Poisson and Deterministic Resetting
• Effects of refractory period on stochastic resetting
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Diffusion with resetting in a logarithmic potential
• Stochastic resetting with stochastic returns using external trap
• Ising model with stochastic resetting
• Transport properties of random walks under stochastic non-instantaneous resetting
• Schrödinger potentials solvable in terms of the general Heun functions
• Kramers problem for nonequilibrium current-induced chemical reactions
• Formulating the Kramers problem in field theory

Cited by in corpus (6)

• The inspection paradox in stochastic resetting
• Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting
• Diversity of Sharp Restart
• Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting
• Chaotic resetting: A resetting strategy for deterministic chaotic systems
• Interplay of noise induced stability and stochastic resetting