Absence of point spectrum for unitary operators

Let us consider the time-dependent Schrödinger equation,iφt=−Δφ+V(x,t)φ,iφt=−Δφ+V(x,t)φ, on the Hilbert space L2(Rn)L2(Rn), where V(x,t)V(x,t) is a repulsive periodic time-dependent potential, with period T  . We denote by (U(t,s))(t,s)∈R×R(U(t,s))(t,s)∈R×R its associated propagator. First, using a multiplier method, we rule out the existence of regular eigenvectors of the Floquet operator U(T,0)U(T,0). Secondly, strengthening the hypotheses on the potential V  , we prove that the spectrum of U(T,0)U(T,0) does not contain any eigenvalues, by means of positive commutator methods.