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.