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, $R_K$, is checked numerically for the overdamping regime. The numerical quasistationary rate, $R_D$, 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 $R_K$ and $R_D$ significantly depends upon the friction strength and the height of the barrier in comparison to the thermal energy. The difference between $R_K$ and $R_D$ decreases with the dimensionless damping parameter $\phi$, however, does not become smaller than 10-20%. The unexpected growth of the difference between $R_K$ and $R_D$ with the governing parameter is observed.