Thermal decay of a metastable state: Influence of rescattering on the quasistationary dynamical rate.

Abstract

We study the effect of backscattering of the Brownian particles as they escape out of a metastable state overcoming the potential barrier. For this aim, we model this process numerically using the Langevin equations. This modeling is performed for the wide range of the friction constant covering both the energy and spatial diffusion regimes. It is shown how the influence of the descent stage on the quasistationary decay rate gradually disappears as the friction constant decreases. It is found that, in the energy diffusion regime, the rescattering absents and the descent stage does not influence the decay rate. As the value of friction increases, the descent alters the value of the rate by more than 50% for different values of thermal energy and different shapes of the potential. To study the influence of the backscattering on the decay rate, four potentials have been considered which coincide near the potential well and the barrier but differ beyond the barrier. It is shown that the potential for which the well and the barrier are described by two smoothly joined parabolas ("the parabolic potential") plays a role of a dividing range for the mutual layout of the quasistationary dynamical rate and the widely used in the literature Kramers rate. Namely, for the potentials with steeper tails, the Kramers rate R_{KM} underestimates the true quasistationary dynamical rate R_{D}, whereas for the less steep tails the opposite holds (inversion of R_{D}/R_{KM}). It is demonstrated that the mutual layout of the values of R_{D} for different potentials is explained by the rescattering of the particles from the potential tail.