  We explore Fermi acceleration in a driven oval billiard which shows unlimited
to limited diffusion in energy when passing from the free to the dissipative
case. We provide evidence for a second-order phase transition taking place
while detuning the corresponding restitution coefficient from one responsible
for the degree of dissipation. A corresponding order parameter is suggested,
and its susceptibility is shown to diverge at the transition point. We also
discuss the underlying symmetry breaking and the elementary excitation of the
controlled diffusion process.
