# Nonadiabatic escape and stochastic resonance

## TL;DR

This paper develops an asymptotic method to analyze particle escape from metastable states under weak periodic forcing, extending to a double well potential to model stochastic resonance in the nonadiabatic limit.

## Contribution

It introduces a novel asymptotic approach for solving the Fokker-Planck equation with mixed boundary conditions, applicable to nonadiabatic stochastic resonance scenarios.

## Key findings

- Derived an approximate escape rate for weak periodic forcing
- Extended the method to double well potentials with white noise
- Formulated a two-state stochastic model in the nonadiabatic limit

## Abstract

We analyze the fluctuation-driven escape of particles from a metastable state under the influence of a weak periodic force. We develop an asymptotic method to solve the appropriate Fokker-Planck equation with mixed natural and absorbing boundary conditions. The approach uses two boundary layers flanking an interior region; most of the probability is concentrated within the boundary layer near the metastable point of the potential and particles transit the interior region before exiting the domain through the other boundary layer, which is near the unstable maximal point of the potential. The dominant processes in each region are given by approximate time-dependent solutions matched to construct the approximate composite solution, which gives the rate of escape with weak periodic forcing. Using reflection we extend the method to a double well potential influenced by white noise and weak periodic forcing, and thereby derive a two-state stochastic model--the simplest treatment of stochastic resonance theory--in the nonadiabatic limit