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

Abstract

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.

Fission rate of excited nuclei at variable friction in the energy diffusion regime

“…Recently, we proposed to model the process in this regime by means of a Langevin equation for the action as the stochastic variable [16]. This approach is more efficient with respect to the time of computer modeling, however, the approach based on equations (1), ( 2) is more accurate though more computer time-consuming.…”

“…To find this quasistationary rate 𝑅 𝐷 we choose several bins beginning from the end of 𝑅 𝑎𝑡 -array and make averaging over these bins. This procedure and its errors are discussed in detail in [16,18].…”

“…Thus, one can expect that the nuclear motion at small deformation happens in the regime which is called in the literature "the energy diffusion regime" [1,[14][15][16]]. An approximate analytical formula for the fission rate in this regime, obtained in [1] and modified in [17], was not carefully compared with the exact quasistationary numerical rate so far.…”