Stochastic resetting in the Kramers problem: A Monte Carlo approach

TL;DR

This paper investigates how stochastic resetting affects escape times in the Kramers problem with a cubic potential, using Monte Carlo simulations to identify optimal resetting rates and conditions where resetting accelerates escape.

Contribution

It introduces a Monte Carlo method to analyze stochastic resetting in complex potentials, revealing optimal rates and counterintuitive benefits of resetting.

Findings

Optimal resetting rate is linked to the escape time distribution.

Resetting can accelerate escape even from unfavorable positions.

Monte Carlo approach is effective for complex potential analysis.

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.