Activated decay of a metastable state: transient times for small and large dissipation

Abstract

The time evolution of the thermally activated decay rates is considered. This evolution is of particular importance for the recent nanoscale experiments discussed in the literature, where the potential barrier is relatively low (or the temperature is relatively high). The single-molecule pulling is one example of such experiments. The decay process is modeled in the present work through computer solving the stochastic (Langevin) equations. Altogether about a hundred of high precision rates have been obtained and analyzed. The rates are registered at the absorption point located far beyond the barrier to exclude the influence of the backscattering on the value of the quasistationary decay rate. The transient time, i.e. the time lapse during which the rate attains half of its quasistationary value, has been extracted. The dependence of the transient times upon a damping parameter is compared with that of the inverse quasistationary decay rate. Two analytical formulas approximating the time-dependences of the numerical rates are proposed and analyzed.