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We explore the dynamical evolution of an ensemble of non-interactingparticles propagating freely in an elliptical billiard with harmonically drivenboundaries. The existence of Fermi acceleration is shown thereby refuting theestablished assumption that smoothly driven billiards whose static counterpartsare integrable do not exhibit acceleration dynamics. The underlying mechanismbased on intermittent phases of laminar and stochastic behavior of the stronglycorrelated angular momentum and velocity motion is identified and studied withvarying parameters. The diffusion process in velocity space is shown to beanomalous and we find that the corresponding characteristic exponent dependsmonotonically on the breathing amplitude of the billiard boundaries. Thus it ispossible to tune the acceleration law in a straightforwardly controllablemanner.

Tunable Fermi acceleration in the driven elliptical billiard