Floquet operators without singular continuous spectrum

Let U be a unitary operator defined on a infinite-dimensional separable complex Hilbert spaceH. Assume there exists a self-adjoint operator A on H such that U∗AU − A cI +K for some positive constant c and compact operator K. Then, assuming the commutators U∗AU − A and [A,U∗AU] admit a bounded extension over H, we prove the spectrum of the operator U has no singular continuous component and only a finite number of eigenvalues of finite multiplicity. We give a localized version of this result and apply it to study the spectrum of the Floquet operator of periodic time-dependent kicked quantum systems. © 2006 Elsevier Inc. All rights reserved.