# Testing the energy diffusion approximation for the escape of a Brownian particle from a potential pocket

## TL;DR

This study rigorously compares the energy diffusion approximation with exact numerical models for thermal decay of metastable states, revealing limitations of the approximation at higher damping levels.

## Contribution

The paper constructs and validates a Langevin-type equation for the action, providing a detailed comparison with exact decay rates across various potentials and parameters.

## Key findings

- Action diffusion approach agrees within 50% at low damping
- Exact numerical modeling uses Langevin equations for coordinate and momentum
- Limitations of the energy diffusion approximation are identified at higher damping

## Abstract

For the first time, the energy diffusion approximation is confronted at the percent level with the exact numerical modeling of thermal decay of a metastable state. The latter is performed using the quasistationary decay rates resulting from the Langevin equations for the coordinate and conjugated momentum. For the energy (or action) diffusion approach, a Langevin-type equation for the action is constructed, validated, and solved numerically. The comparison of two approaches is performed for four potentials (two of which are anharmonic) in a wide range of two dimensionless scaling parameters: the governing parameter $G$ reflecting how high is the barrier with respect to the temperature and the damping parameter $\varphi$ expressing the friction strength. It turns out that the action diffusion approach produces the rate which is in 50% agreement with the exact one only at $\varphi<0.02$ contrary to $\varphi<1$ as claimed in the literature.

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Source: https://tomesphere.com/paper/1908.03940