Quantum chaos and peculiarities of diffusion in Wigner representation

Peculiarities of energy diffusion in the well-known model of a quantum rotator excited by an external periodic δ-like field are investigated in the Wigner representation. It is shown that in a semi-classical region of parameters quantum diffusion can be approximatelydescribed means of classical mappings in discrete phase space. Both the phenomenon of the quantum limitation of classical diffusion and the quantum resonance for which the mean energy is increasing quadratically in the time manifests itself in the motion of such classical models.