Exponential Fermi acceleration in general time-dependent billiards

Abstract

It is shown, that under very general conditions, a generic time-dependent billiard, for which a phase-space of corresponding static (frozen) billiards is of the mixed type, exhibits the exponential Fermi acceleration in the adiabatic limit. The velocity dynamics in the adiabatic regime is represented as an integral over a path through the abstract space of invariant components of corresponding static billiards, where the paths are generated probabilistically in terms of transition-probability matrices. We study the statistical properties of possible paths and deduce the conditions for the exponential Fermi acceleration. The exponential Fermi acceleration and theoretical concepts presented in the paper are demonstrated numerically in four different time-dependent billiards.

11 pages, 9 figures

References in corpus (11)

• Chaotic Dirac billiard in graphene quantum dots
• High-Power Directional Emission from Microlasers with Chaotic Resonators
• The Astrophysics of Ultrahigh Energy Cosmic Rays
• Tunable Fermi acceleration in the driven elliptical billiard
• The Fermi accelerator in atom optics
• Quantum localization of chaotic eigenstates and the level spacing distribution
• Evolutionary phase space in driven elliptical billiards
• Stochastic acceleration by multi-island contraction during turbulent magnetic reconnection
• Phase Space Interpretation of Exponential Fermi Acceleration
• Fermi acceleration in chaotic shape-preserving billiards
• Analysis of resonant population transfer in time-dependent elliptical quantum billiards

Cited by in corpus (17)

• Super-exponential diffusion in nonlinear non-Hermitian systems
• Oscillating mushrooms: adiabatic theory for a non-ergodic system
• Exponential energy growth in adiabatically changing Hamiltonian Systems
• Equilibration of energy in slow-fast systems
• Driven power-law oscillator
• Universal energy diffusion in a quivering billiard
• Transition from normal to ballistic diffusion in a one-dimensional impact system
• Superexponential Self-Interacting Oscillator
• Exponential energy growth due to slow parameter oscillations in quantum mechanical systems
• Explaining a changeover from normal to super diffusion in time-dependent billiards
• Leaky Fermi accelerators
• Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving
• Dynamical thermalization in time-dependent Billiards
• Many-Body Effects in Models with Superexponential Interactions
• Discussing a transition from bounded to unbounded energy in a time-dependent billiard
• Perturbative solution of Vlasov equation for periodically driven systems
• Acceleration in a nonplanar time-dependent billiard