Accuracy of the analytical escape rate for a cusp barrier in the overdamping regime

Abstract

For the first time, the accuracy of the approximate analytical Kramers formula for the thermal decay rate over a cusp barrier, , is checked numerically for the overdamping regime. The numerical quasistationary rate, , which is believed to be exact within the statistical errors is evaluated by means of computer modeling of the stochastic Langevin-type dynamical equations. The agreement between and significantly depends upon the friction strength and the height of the barrier in comparison to the thermal energy. The difference between and decreases with the dimensionless damping parameter , however, does not become smaller than 10-20%. The unexpected growth of the difference between and with the governing parameter is observed.