Absence of point spectrum for unitary operators

Abstract: Let us consider the time-dependent Schrödinger equation, on the Hilbert space , where is a repulsive periodic time-dependent potential, with period T. We denote by its associated propagator. First, using a multiplier method, we rule out the existence of regular eigenvectors of the Floquet operator . Secondly, strengthening the hypotheses on the potential V, we prove that the spectrum of does not contain any eigenvalues, by means of positive commutator methods. [Copyright &y& Elsevier]