Abstract
The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvaluesλ j of the unperturbed Hamiltonian grows asλ j -λ j-1 ≃j α and the multiplicity ofλ j grows asj β with α>β≥0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.
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