Applicability of Kramers rate formulas in the energy diffusion regime

The work of nanomachines, which is a contemporary subject of the numerous investigations, is permanently affected by thermal fluctuations. Some aspects of this phenomenon might be reduced to the so-called Kramers problem concerning the decay rate of a metastable state. In the present work we compare the result of computer modelling, performed by solving the Langevin equations, with the analytical formulas for the decay rate for the case of energy diffusion regime (relatively small values of the friction strength). Qualitatively the agreement between these two approaches is rather good. However, the quantitative analysis reveals a difference of 10-20% which depends upon the thermal energy of the system.