Woosok Moon: Nonadiabatic asymptotic escape

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 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 asymptotically to construct the approximate composite solution, which gives the rate of escape with weak periodic forcing. By extending the method to a double well potential influenced by white noise and weak periodic forcing, we derive a two-state stochastic model--the simplest treatment of stochastic resonance theory--in the nonadiabatic limit.