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Dynamical Localization in Kicked Rotator as a Paradigm of Other Systems: Spectral Statistics and the Localization Measure

  • Thanos Manos
  • Marko Robnik
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

We study the intermediate statistics of the spectrum of quasi-energies and of the eigenfunctions in the kicked rotator, in the case when the corresponding system is fully chaotic while quantally localized. As for the eigenphases, we find clear evidence that the spectral statistics is well described by the Brody distribution, notably better than by the Izrailev’s one, which has been proposed and used broadly to describe such cases. We also studied the eigenfunctions of the Floquet operator and their localization. We show the existence of a scaling law between the repulsion parameter with relative localization length, but only as a first order approximation, since another parameter plays a role. We believe and have evidence that a similar analysis applies in time-independent Hamilton systems.

Notes

Acknowledgements

The financial support of the Slovenian Research Agency (ARRS) is gratefully acknowledged.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Thanos Manos
    • 1
    • 2
  • Marko Robnik
    • 1
  1. 1.Center for Applied Mathematics and Theoretical PhysicsUniversity of MariborMariborSlovenia
  2. 2.School of Applied SciencesUniversity of Nova GoricaAjdovščinaSlovenia

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