Dynamics of a Classical Particle in a Quasi Periodic Potential

TL;DR

This paper analyzes the short-term dynamics of a classical particle in a quasi-periodic potential, revealing a model of random walk between resonances, with analytical and numerical insights relevant for optics and atom optics.

Contribution

It introduces an analytical model for short-time particle dynamics in quasi-periodic potentials and validates it with numerical simulations.

Findings

Momentum dynamics described by a random walk model between resonances

Analytical expression for momentum at short times

Numerical results confirm the resonance hopping behavior

Abstract

We study the dynamics of a one-dimensional classical particle in a space and time dependent potential with randomly chosen parameters. The focus of this work is a quasi-periodic potential, which only includes a finite number of Fourier components. The momentum is calculated analytically for short time within a self-consistent approximation, under certain conditions. We find that the dynamics can be described by a model of a random walk between the Chirikov resonances, which are resonances between the particle momentum and the Fourier components of the potential. We use numerical methods to test these results and to evaluate the important properties, such as the characteristic hopping time between the resonances. This work sheds light on the short time dynamics induced by potentials which are relevant for optics and atom optics.