Oscillating mushrooms: adiabatic theory for a non-ergodic system

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.

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References in corpus (6)

• Hyperacceleration in a stochastic Fermi-Ulam model
• Exponential Fermi acceleration in general time-dependent billiards
• Phase Space Interpretation of Exponential Fermi Acceleration
• Exponential energy growth in adiabatically changing Hamiltonian Systems
• Fermi acceleration in chaotic shape-preserving billiards
• Resonant phenomena in slowly perturbed elliptic billiards

Cited by in corpus (11)

• Exponential energy growth in adiabatically changing Hamiltonian Systems
• Equilibration of energy in slow-fast systems
• Elliptic Flowers: simply connected billiard tables with chaotic or non-chaotic flows moving around chaotic or non-chaotic cores
• Universal energy diffusion in a quivering billiard
• A Rectangular Billiard with Moving Slits
• Quasistatic transfer protocols for atomtronic superfluid circuits
• Exponential energy growth due to slow parameter oscillations in quantum mechanical systems
• Quantum irreversibility of quasistatic protocols for finite-size quantized systems
• Leaky Fermi accelerators
• Exponential Fermi Acceleration in a Switching Billiard
• Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically