Exponential energy growth in adiabatically changing Hamiltonian Systems

Abstract

Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time, the energy is no longer conserved, which makes the acceleration possible. One of the main problems is how to generate a sustained and robust energy growth. We show that the non-ergodicity of any chaotic Hamiltonian system must universally lead to the exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of a Geometric Brownian Motion with a positive drift, and relate it to the entropy increase.

References in corpus (6)

• Tunable Fermi acceleration in the driven elliptical billiard
• Stable chaos
• Ergodicity breaking in geometric Brownian motion
• Exponential Fermi acceleration in general time-dependent billiards
• Classical Dissipation and Asymptotic Equilibrium via Interaction with Chaotic Systems
• Oscillating mushrooms: adiabatic theory for a non-ergodic system

Cited by in corpus (10)

• The Chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration
• Fermi-like acceleration and power-law energy growth in nonholonomic systems
• Oscillating mushrooms: adiabatic theory for a non-ergodic system
• Equilibration of energy in slow-fast systems
• Driven power-law oscillator
• Diffusion Phenomena in a Mixed Phase Space
• Exponential energy growth due to slow parameter oscillations in quantum mechanical systems
• Leaky Fermi accelerators
• Many-Body Effects in Models with Superexponential Interactions
• Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically