Quasi-energy statistics for regular and chaotic regimes in quantum systems with Hamiltonians periodic in time

Quantum mechanical systems with Hamiltonians varying periodically in time are considered. it is assumed that the spectrum of the Floquet operator has no absolutely continuous part and spacings between quasi-energies may be statistically described by means of a continuous density. It is shown that the induced statistical density of spacings between fractional parts of the quasi-energies defined with respect to mod (hw), suitably normalized, approaches arbitrarily close to an exponential distribution when the number of levels is infinitely increased. This result does not depend on the original distribution, An alternate method of statistically describing fractional parts is proposed which makes it possible to distinguish between the original quasi-energy distribution laws for regular and chaotic regimes.