Oscillating mushrooms: adiabatic theory for a non-ergodic system

TL;DR

This paper demonstrates that a mushroom billiard with oscillating boundaries can cause particles to accelerate exponentially, supported by theoretical estimates and numerical experiments, suggesting broader applicability to systems with mixed phase space.

Contribution

It introduces a novel adiabatic theory explaining exponential acceleration in non-ergodic systems with oscillating boundaries, specifically in mushroom billiards.

Findings

Particles accelerate exponentially in oscillating mushroom billiards

Theoretical estimates match numerical simulations

Mechanism likely applies to other systems with mixed phase space

Abstract

Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a periodically oscillating boundary accelerates the particle inside it exponentially fast. We provide an estimate for the rate of acceleration. Our numerical experiments confirms the theory. We suggest that a similar mechanism applies to general systems with mixed phase space.