The 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 supposed that spectrum of Floquet operator has no absolutely continuous part, and spacings between quasienergies may be described statistically by means of a continuous density. It is shown that statistical density induced for spacings between the fractions $\mod(\hbar\omega)$ renormalized in the suitable manner comes arbitrarily close to exponential distribution as soon as the level number is infinitely increased. The result does not depend on the original statistical law. The alternative method of statistical description of fractions is proposed. This makes it possible to distinguish between the statistical laws of the regular and chaotic regimes.