  We explore the dynamical evolution of an ensemble of non-interacting
particles propagating freely in an elliptical billiard with harmonically driven
boundaries. The existence of Fermi acceleration is shown thereby refuting the
established assumption that smoothly driven billiards whose static counterparts
are integrable do not exhibit acceleration dynamics. The underlying mechanism
based on intermittent phases of laminar and stochastic behavior of the strongly
correlated angular momentum and velocity motion is identified and studied with
varying parameters. The diffusion process in velocity space is shown to be
anomalous and we find that the corresponding characteristic exponent depends
monotonically on the breathing amplitude of the billiard boundaries. Thus it is
possible to tune the acceleration law in a straightforwardly controllable
manner.
