Thermal decay rate of a metastable state with two degrees of freedom: dynamical modeling versus approximate analytical formula

TL;DR

This paper compares the accuracy of the Kramers approximate formula with dynamical modeling for the thermal decay rate of a metastable state in a two-dimensional potential, highlighting conditions where the approximation holds or fails.

Contribution

It provides a detailed comparison between the Kramers formula and dynamical modeling for decay rates in a 2D potential, clarifying the formula's validity range.

Findings

Kramers rate agrees with dynamical modeling when the absorptive border is far from the potential ridge.

The Kramers formula underestimates the decay rate as the border approaches the ridge.

Discrepancies can reach a factor of 2 when the border coincides with the ridge.

Abstract

Accuracy of the Kramers approximate formula for the thermal decay rate of the metastable state is studied for the two-dimensional potential pocket. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. It is shown that the Kramers rate is in agreement with the quasistationary rate within the statistical errors provided the absorptive border is far enough from the potential ridge restricting the metastable state. As the absorptive border (or its part) gets closer to the ridge the Kramers formula underestimate the quasistationary rate. The difference reaches approximately the factor of 2 when the absorptive border coincides with the ridge.