Breaking down the Fermi acceleration with inelastic collisions

TL;DR

This paper investigates how inelastic collisions in a dissipative bouncing ball model prevent Fermi acceleration, showing a phase transition from unbounded to bounded energy growth as dissipation varies.

Contribution

It demonstrates that energy dissipation via inelastic collisions halts Fermi acceleration and characterizes the phase transition in energy behavior.

Findings

Inelastic collisions prevent Fermi acceleration.

A phase transition from unbounded to bounded energy occurs.

Dissipation is sufficient to break Fermi acceleration.

Abstract

The phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving wall) is a sufficient condition to break down the process of Fermi acceleration. The phase transition from bounded to unbounded energy growth in the limit of vanishing dissipation is characterized.