QUANTUM NEKHOROSHEV THEOREM FOR QUASI-PERIODIC FLOQUET HAMILTONIANS

A quantum version of Nekhoroshev estimates for Floquet Hamiltonians as sociated to quasi-periodic time dependent perturbations is developped. If the unperturbed energy operator has a discrete spectrum and under finite Diophantine conditions, an effective Floquet Hamiltonian with p ure point spectrum is constructed. For analytic perturbations, the eff ective time evolution remains close to the original Floquet evolution up to exponentially long times. We also treat the case of differentiab le perturbations.