Exponential Fermi Acceleration in a Switching Billiard

TL;DR

This paper demonstrates the existence of exponentially escaping orbits in a resonant Fermi accelerator modeled as a square billiard with a periodically oscillating platform, using normal forms and hyperbolic system techniques.

Contribution

It introduces a novel analysis of energy growth in a resonant billiard system, revealing exponential acceleration mechanisms.

Findings

Existence of an infinite measure set of exponentially escaping orbits.

Application of normal forms to describe energy changes.

Use of hyperbolic systems techniques to prove exponential drift.

Abstract

In this paper we show an infinite measure set of exponentially escaping orbits for a resonant Fermi accelerator, which is realised as a square billiard with a periodically oscillating platform. We use normal forms to describe how the energy changes in a period and we employ techniques for hyperbolic systems with singularities to show the exponential drift of these normal forms on a divided time-energy phase.