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.
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References
Haake F (2001) Quantum signatures of chaos. Springer, Berlin
Stöckmann HJ (1999) Quantum chaos—an introduction. Cambridge University Press, Cambridge
Casati G, Chirikov BV, Izraelev FM, Ford J (1979) Stochastic behavior of a quantum pendulum under a periodic perturbation. In: Casati eG, Ford J (eds) stochastic behaviour in classical and quantum Hamiltonian systems, Proc Como conf, 1997. Lecture notes in physics, vol 93. Springer, Berlin, pp 334–352
Izrailev FM (1988) Quantum localization and statistics of quasienergy spectrum in a classically chaotic system. Phys Lett A 134:13–18
Izrailev FM (1990) Simple models of quantum chaos: spectrum and eigenfunctions. Phys Rep 196:299–392
Prosen T, Robnik M (1994) Semiclassical energy level statistics in the transition region between integrability and chaos: transition from Brody-like to Berry-Robnik behaviour. J Phys A, Math Gen 27:8059–8077
Izrailev FM (1995) Quantum chaos, localization and band random matrices. In: Casati G, Chirikov B (eds) Quantum chaos: between order and disorder. Cambridge University Press, Cambridge, pp 557–576
Batistić B, Robnik M (2010) Semiempirical theory of level spacing distribution beyond the Berry-Robnik regime: modeling the localization and the tunneling effects. J Phys A, Math Theor 43:215101
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The financial support of the Slovenian Research Agency (ARRS) is gratefully acknowledged.
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Manos, T., Robnik, M. (2013). Dynamical Localization in Kicked Rotator as a Paradigm of Other Systems: Spectral Statistics and the Localization Measure. In: Gilbert, T., Kirkilionis, M., Nicolis, G. (eds) Proceedings of the European Conference on Complex Systems 2012. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-00395-5_3
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DOI: https://doi.org/10.1007/978-3-319-00395-5_3
Publisher Name: Springer, Cham
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