Singular Continuous Floquet Operator for Systems with Increasing Gaps

Consider the Floquet operator of a time independent quantum system, periodically perturbed by a rank one kick, acting on a separable Hilbert space: e0 e |φ〉〈φ| where T and κ are the period and the coupling constant respectively. Assume the spectrum of the self adjoint operator H0 is pure point, simple, bounded from below and the gaps between the eigenvalues (λn) grow like: λn+1 − λn ∼ Cn with d ≥ 2. Under some hypotheses on the arithmetical nature of the eigenvalues and on the vector φ, cyclic for H0, we prove the Floquet operator of the perturbed system has purely singular continuous spectrum.