Singular continuous Floquet operator for systems with increasing gaps. (Q1856962)

The paper under review investigates the Hamiltonian \(H_0\) of a quantum mechanical harmonic oscillator that is periodically perturbed by a time-dependent potential of the form \[ V(t)=P_{\phi}\sum_{n\in{\mathbb Z}}\delta(t-nT), \] where \(P_{\phi}\) denotes the projection operator onto an arbitrary state vector \(\phi\). In [J. Stat. Phys. 59, 679--690 (1990; Zbl 0713.58044)], \textit{M. Combescure} showed that if \(\phi\) is cyclic with respect to \(H_0\) and if the oscillator frequency \(\omega\) is ``sufficiently irrational'' in the sense that \(\omega T/(2\pi)\) is a Diophantine number, the spectrum of the system's Floquet operator is purely singular continuous for all \(\kappa\in {\mathbb R\backslash \mathbb Z}\). The present paper generalizes this result by admitting a larger class of oscillator frequencies.