The onset of chaotic motion in externally driven classical systems is a key problem in nonlinear dynamics that is now well understood in its essential aspects. In many physically interesting cases, as the perturbation strength increases beyond some critical value, the system starts absorbing energy in a diffusive way. The question whether “diffusive” excitation processes can take place also in externally driven quantum systems is then a very interesting one for the physics of atoms and molecules in external electromagnetic fields. This is a deep question involving the nature and the validity of the quasiclassical approximation when the underlying classical dynamics is chaotic.

The question of “quantum diffusion” was first addressed in a simple model system, the kicked rotator. It was chosen because the features of classical chaos in it were relatively clean and well understood. Besides that, the numerical simulation of its quantum dynamics could be easily accomplished. The major indication of this model was that quantum mechanics suppresses the classical chaotic diffusion in action via a destructive interference effect similar to that responsible for the Anderson localization well known in condensed matter physics.