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 (5)

• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Stochastic Search with Poisson and Deterministic Resetting
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Cited by in corpus (1)

• Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher's equation, anomalous crossovers and resetting