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

A V Zakharov,M V Chushnyakova,I I Gontchar

doi:10.1088/1742-6596/1441/1/012181

Abstract

For the first time, the accuracy of the approximate analytical Kramers formula for the thermal decay rate over a cusp barrier, RK, is checked numerically for the overdamping regime. The numerical quasistationary rate, RD, 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 RK and RD significantly depends upon the friction strength and the height of the barrier in comparison to the thermal energy. The difference between RK and RD decreases with the dimensionless damping parameter φ, however, does not become smaller than 10-20%. The unexpected growth of the difference between RK and RD with the governing parameter is observed.

Highlights

The problem of the thermal decay of a metastable state is significant for different branches of natural sciences: in chemistry [1,2,3], biophysics [4,5], astrophysics [6], electronics [7,8], nuclear physics [9,10] etc
We consider a general physical problem, all the results are presented in the dimensionless form
In the present work, for the first time, the accuracy of the Kramers decay rate, RK, for the cusp potential has been explored quantitatively. This is achieved by means of the numerical solution of the stochastic Langevin type equations

Summary

Introduction

The problem of the thermal decay of a metastable state (escape of a Brownian particle from a trap due to thermal fluctuations) is significant for different branches of natural sciences: in chemistry [1,2,3], biophysics [4,5], astrophysics [6], electronics [7,8], nuclear physics [9,10] etc. The decay rate is the principal characteristics of this process. Approximate analytical formulas for the rate accounting for dissipation were derived by Kramers in his seminal work [11]. The problem is often referred to as the Kramers problem [12,13]. In [14] it was shown that the decay rate depends mostly upon two dimensionless parameters, namely a governing parameter G and damping parameter φ.

Ub θ

Results

Conclusions