Escape of harmonically forced classical particle from an infinite-range potential well

TL;DR

This paper analyzes the escape of a classical particle from an infinite-range potential well under harmonic forcing, providing an analytic prediction for the minimal forcing amplitude needed for escape and validating it with numerical simulations.

Contribution

It introduces a simplified analytical framework for predicting particle escape thresholds in a well with adjustable parameters, combining action-angle variables and resonance analysis.

Findings

Analytic expression for minimal forcing amplitude as a function of frequency.

Identification of a frequency at which the escape threshold is minimized.

Qualitative and quantitative agreement between theory and numerical simulations.

Abstract

The paper considers a process of escape of classical particle from a one-dimensional potential well by virtue of an external harmonic forcing. We address a particular model of the infinite-range potential well that allows independent adjustment of the well depth and of the frequency of small oscillations. The problem can be conveniently reformulated in terms of action-angle variables. Further averaging provides a nontrivial conservation law for the slow flow. Thus, one can consider the problem in terms of averaged dynamics on primary 1:1 resonance manifold. This simplification allows efficient analytic exploration of the escape process, and yields a theoretical prediction for minimal forcing amplitude required for the escape, as a function of the excitation frequency. This function exhibits a single minimum for certain intermediate frequency value. Numeric simulations are in complete qualitative and reasonable quantitative agreement with the theoretical predictions.