External force affected escape of Brownian particles from a potential well

TL;DR

This paper investigates how an external force influences the escape kinetics of Brownian particles from a potential well, extending the two-state model to include force effects and deriving simple expressions for escape rates.

Contribution

The study generalizes the two-state model to account for external forces, providing accurate expressions for escape kinetics under various force conditions.

Findings

Escape rate depends on the parameter  = Fa/(2k_b T)

Derived expressions are valid for different well shapes and force strengths

Analyzed limiting behaviors for weak and strong external forces

Abstract

The effect of an external force on the kinetics of diffusion-assisted escaping of Brownian particles from a potential well is analyzed in detail. The analysis is made within the two-state model of the process which is known to be valid in the deep well limit in the absence of external force. The generalized variant of this model, taking into account the effect of the force, is shown to be quite accurate as well for some shapes of the well. Within the generalized two-state model simple expressions for the well depopulation kinetics and, in particular, the for the escape rate are obtained. These expressions show that the effect of the force ($F$) manifests itself in the escape rate dependence on the only parameter $\varphi = Fa/(2k_b T)$, where $a$ is the Onzager radius of the attractive part of the well $U(r)$, defined by the relation $|U(a)| = k_b T$. The limiting behavior of this dependence in the cases of weak and strong force is analyzed in detail. Possible applications as well as the relation of the results of the analysis to those obtained earlier are briefly discussed.