Suppression of Fermi Acceleration in the Oval Billiard

We consider in this chapter the introduction of drag force in the oval billiard. As we have seen in Chap. 13 from the LRA conjecture, the chaotic dynamics in the static billiard is a sufficient condition to produce unlimited diffusion in the energy, i.e, Fermi acceleration, when a time perturbation to the boundary is introduced. We show in this chapter that the introduction of a drag force of the type F∝ - V, or F∝ ± V2 or F∝ - Vδ with δ≠ 1 and δ≠ 2 destroys the unlimited energy growth for an ensemble of particles. This result is a clear indication that Fermi acceleration is not a robust phenomena.