Phase Space Interpretation of Exponential Fermi Acceleration

Abstract

Recently, the occurrence of exponential Fermi acceleration has been reported in a rectangular billiard with an oscillating bar inside [K. Shah, D. Turaev, and V. Rom-Kedar, Phys. Rev. E {\bf 81}, 056205 (2010)]. In the present work, we analyze the underlying physical mechanism and show that the phenomenon can be understood as a sequence of highly correlated motions, consisting of alternating phases of free propagation and motion along the invariant spanning curves of the well-known one-dimensional Fermi-Ulam model. The key mechanism for the occurrence of exponential Fermi acceleration can be captured in a random walk model in velocity space with step width proportional to the velocity itself. The model reproduces the occurrence of exponential Fermi acceleration and provides a good ab initio prediction of the value of the growth rate including its full parameter-dependency. Our analysis clearly points out the requirements for exponential Fermi acceleration, thereby opening the perspective of finding other systems exhibiting this unusual behaviour.

References in corpus (5)

• Hyperacceleration in a stochastic Fermi-Ulam model
• In-flight dissipation as a mechanism to suppress Fermi acceleration
• Dynamical trapping and chaotic scattering of the harmonically driven barrier
• Classical Dynamics of the Time-Dependent Elliptical Billiard
• Scattering Dynamics of Driven Closed Billiards

Cited by in corpus (10)

• Exponential Fermi acceleration in general time-dependent billiards
• Recurrence of particles in static and time varying oval billiards
• Super-exponential diffusion in nonlinear non-Hermitian systems
• Oscillating mushrooms: adiabatic theory for a non-ergodic system
• Driven power-law oscillator
• Analysis of resonant population transfer in time-dependent elliptical quantum billiards
• Statistical properties of 1D parametrically kicked Hamilton systems
• Exponential energy growth due to slow parameter oscillations in quantum mechanical systems
• Superexponential Self-Interacting Oscillator
• Many-Body Effects in Models with Superexponential Interactions