Two ways for finding the thermal decay rate at weak friction

Abstract

We model the thermal decay of a metastable state at weak friction (the underdamped regime), the phenomenon which might be met in many branches of natural and technical sciences. The profile of the metastable state is considered as a pure parabola. We quantitatively compare the decay rate obtained from the phase space dynamics with the rate coming from the approximate energy diffusion approach which should be correct in the case of relatively weak friction. Both the phase space and energy diffusion dynamics employ the Langevin-type equations, however for the different stochastic variables. The results of the comparison reveal that the level of agreement between these two approaches depends not only upon the damping parameter (as qualitatively expected) but also upon the thermal energy.