Accuracy of analytical calculation of the heat decay rate of metastable state in the energy diffusion mode

Background. The problem of the thermal decay of a metastable state appears in many branches of natural sciences: from chemistry and nuclear physics till electromagnetism and astrophysics. The energy diffusion regime (regime of week friction) is of the special interest since it is less intensively studied in the literature. The aim of the present research is the analysis of accuracy of approximate analytical formulas for the rate of a metastable state thermal decay in the energy diffusion regime Materials and methods. The numerical modeling of a metastable state thermal decay is performed by means of the stochastic differential equations (Langevin equations). Results. The quasistationary decay rate is calculated for the energy diffusion regime as well as for the spatial diffusion regime. The decay rates obtained using the numerical modeling are exact within the statistical errors. These dynamical (numerical) rates are compared with the approximate formulas for the energy diffusion regime in a wide range of friction parameter. All the results are presented in the dimensionless form in order to make them useful for a wider range of readers. Conclusions. It is found that within the present model (parabolic potential, ratio of the barrier height to thermal energy is equal to 2.4), it is possible to choose such a value of a single free parameter of the approximate formula that the deviation of the approximate rate from the exact one does not exceed 5 %. The obtained value of the free parameter does not depend upon the friction strength and does not contradict to the physical sense of the parameter intended by authors.