Quantum resonance for a rotator in a nonlinear periodic field

Behaviour of a plane quantum ratator under a timeperiodic perturbation given as delta-like “kicks” nonlinearly dependent on a phase is studied. The case of so-called quantum resonance is investigated both analytically and numerically. It is shown that for large times the rotator energy is proportional to $t^2$. The structure of quasi-energy spectrum is analysed and its continuity is proved.