Thermal escape from a trap over the parabolic barrier: Langevin type approach to energy diffusion regime

Thermally activated escape from a metastable state is a useful tool to account for some features of the micro/nano-motors or superconducting nanowires. In the present work, we consider the case of week friction (action diffusion regime) which corresponds to the latter example. To describe the thermal decay, we apply two approaches both based on the Langevin type equations: the action diffusion (approximate) and the phase space diffusion (exact). For the first time, the quasistationary decay rates obtained numerically for the parabolic barrier from these two approaches are compared quantitatively with each other as well as with the analytical formula.