Quantum suppression of chaos in the Fermi accelerator

We address the question of how a quantum particle exchanges energy with a moving wall with an imposed smooth, periodic motion law. In the semiclassical region of parameter space, the energy gain of the particle is initially consistent with the classical result. This correspondence is maintained for some time, until quantum localization effects suppress the classical diffusion. We discuss similarities with the well studied case of the Quantum Kicked Rotor.