Dynamical trapping and chaotic scattering of the harmonically driven barrier

TL;DR

This paper analyzes the classical nonlinear dynamics of a harmonically driven potential barrier, revealing chaotic scattering, dynamical trapping, and classical analogs of quantum tunneling resonances.

Contribution

It provides a detailed classical analysis of a driven barrier, highlighting dynamical trapping, chaos, and classical origins of tunneling-like resonances.

Findings

Existence of stable islands in phase space

Chaotic scattering with stickiness near stable islands

Classical transmission resonances similar to quantum tunneling

Abstract

A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM-structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.