Tunable Fermi acceleration in the driven elliptical billiard

TL;DR

This paper demonstrates that smoothly driven elliptical billiards can exhibit Fermi acceleration, with the acceleration rate tunable by adjusting the boundary's breathing amplitude, challenging previous assumptions about integrable billiards.

Contribution

It reveals the occurrence of Fermi acceleration in driven elliptical billiards and identifies the mechanism and controllability of the acceleration process.

Findings

Fermi acceleration occurs in driven elliptical billiards.

The acceleration rate depends on the boundary's breathing amplitude.

The velocity diffusion is anomalous and tunable.

Abstract

We explore the dynamical evolution of an ensemble of non-interacting particles propagating freely in an elliptical billiard with harmonically driven boundaries. The existence of Fermi acceleration is shown thereby refuting the established assumption that smoothly driven billiards whose static counterparts are integrable do not exhibit acceleration dynamics. The underlying mechanism based on intermittent phases of laminar and stochastic behavior of the strongly correlated angular momentum and velocity motion is identified and studied with varying parameters. The diffusion process in velocity space is shown to be anomalous and we find that the corresponding characteristic exponent depends monotonically on the breathing amplitude of the billiard boundaries. Thus it is possible to tune the acceleration law in a straightforwardly controllable manner.