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We study quantum kicked rotator in the classically fully chaotic regime, inthe domain of the semiclassical behaviour. We use Izrailev's N-dimensionalmodel for various N<=4000, which in the limit N-> infinity tends to thequantized kicked rotator, not only for K=5 as studied previously, but for manydifferent values of the classical kick parameter 5<=K<=35, and also of thequantum parameter k. We describe the dynamical localization of chaoticeigenstates as a paradigm for other both time-periodic and time-independentfully chaotic or/and mixed type Hamilton systems. We generalize thelocalization length L and the scaling variable (L/N) to the case of anomalousclassical diffusion. We study the generalized classical diffusion also in theregime where the simple minded theory of the normal diffusion fails. We greatlyimprove the accuracy of the numerical calculations with the followingconclusions: The level spacings distribution of the eigenphases is very welldescribed by the Brody distribution, systematically better than by otherproposals, for various Brody exponents. When N->infinity and L is fixed we havealways Poisson, even in fully chaotic regime. We study the eigenfunctions ofthe Floquet operator and characterize their localization properties using theinformation entropy measure describing the degree of dynamical localization ofthe eigenfunction. The resulting localization parameter is found to be almostequal to the Brody parameter. We show the existence of a scaling law betweenthe localization parameter and the scaling variable L/N, now including theregimes of anomalous diffusion. The above findings are important also intime-independent Hamilton systems, like in mixed type billiards, where theBrody distribution is confirmed to a very high degree of precision fordynamically localized chaotic eigenstates.

physical review. e, statistical, nonlinear and soft matter physics

Dynamical localization in chaotic systems: spectral statistics and  localization measure in the kicked rotator as a paradigm for time-dependent  and time-independent systems