Characterizing a transition from limited to unlimited diffusion in energy for a time-dependent billiard

TL;DR

This paper investigates how energy diffusion in a driven oval billiard transitions from unlimited to limited as dissipation varies, revealing a second-order phase transition with diverging susceptibility and symmetry breaking.

Contribution

It introduces a phase transition framework to describe the change in energy diffusion behavior in a dissipative billiard system, including an order parameter and analysis of symmetry breaking.

Findings

Identifies a second-order phase transition in energy diffusion behavior.

Shows susceptibility diverges at the transition point.

Discusses symmetry breaking and elementary excitations in the process.

Abstract

We explore Fermi acceleration in a driven oval billiard which shows unlimited to limited diffusion in energy when passing from the free to the dissipative case. We provide evidence for a second-order phase transition taking place while detuning the corresponding restitution coefficient from one responsible for the degree of dissipation. A corresponding order parameter is suggested, and its susceptibility is shown to diverge at the transition point. We also discuss the underlying symmetry breaking and the elementary excitation of the controlled diffusion process.