Evolutionary phase space in driven elliptical billiards

TL;DR

This paper investigates the long-term classical dynamics of a driven elliptical billiard, revealing a transition from chaotic to diffusive behavior and a dynamic crossover from subdiffusion to normal diffusion in momentum space.

Contribution

It provides the first long-time analysis of a driven elliptical billiard's phase space, uncovering a dynamic crossover in diffusion behavior not induced by parameters.

Findings

Transition from chaotic sea to thin chaotic channels

Observation of Fermi acceleration due to diffusive motion

Dynamic crossover from subdiffusion to normal diffusion

Abstract

We perform the first long-time exploration of the classical dynamics of a driven billiard with a four dimensional phase space. With increasing velocity of the ensemble we observe an evolution from a large chaotic sea with stickiness due to regular islands to thin chaotic channels with diffusive motion leading to Fermi acceleration. As a surprising consequence, we encounter a crossover, which is not parameter induced but rather occurs dynamically, from amplitude dependent tunable subdiffusion to universal normal diffusion in momentum space. In the high velocity case we observe particle focusing in phase space.