Quasienergy spectra of quantum dynamical systems

We present a technique that yields in analytic fashion the quasienergy spectrum of bounded quantum systems in the presence of time-periodic perturbations. It also allows for the calculation of statistical averages using simple algebraic manipulations and provides tractable solutions even for systems with a large number of levels. We also report on numerical calculations for systems with few number of levels in and out of resonance, and which show the recurrences predicted by the Hogg-Huberman theorem [Phys. Rev. Lett. 48, 711 (1982); Phys. Rev. A 28, 22 (1983)].