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Energy level distributions and chaos in quantum mechanics

  • III. Aspects Of Quantizations
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Differential Geometric Methods in Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1139))

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References

  1. J.E. Bayfield and P.M. Koch, Phys.Rev. 33, 258 (1974), J.E. Bayfield, L.D. Gardner and P.M. Koch, Phys.Rev.Lett. 39, 76 (1977), P.M. Koch, J.Phys. (Paris), Coolq. 43, C2-187 (1982), R.J. Damburg and V.V. Kolosov, J.Phys. B12, 2637 (1979), P.M. Koch and D.R. Mariani, Phys.Rev.Lett. 46, 1275 (1981)

    Google Scholar 

  2. V.M. Alexeev and M.V. Yakobson, Phys. Reports, 5 (1981) 287

    Google Scholar 

  3. H.P. Baltes and E.R. Hilf, Spectra of finite Systems, (Wissenschaftsverlag, Mannheim 1976)

    MATH  Google Scholar 

  4. M.L. Mehta, Randon Matrices, Academic, New York, 1967

    Google Scholar 

  5. J. Ford, Phys. Today, April 1983

    Google Scholar 

  6. E.P. Wigner, Math.Ann. 53 (1951) 36, 62 (1955) 548, 65 (1957) 203, 67 (1958) 325

    Article  MathSciNet  Google Scholar 

  7. L.D. Landau and Ya. A. Smorodinsky, Lect. on the theory of atomic nuclei (GOSTEHIZDAT, Moscow, 1955) "English translation published by Plenum Press, New York 1959"

    Google Scholar 

  8. S.S.M. Wong, in "Chaotic Behaviour in Quantum systems", edited by G. Casati, (Plenum, New York), in press

    Google Scholar 

  9. Statistical Theory of spectra: Fluctuations ed. C.E. Porter (Academic Press, New York, 1965)

    Google Scholar 

  10. F.J. Dyson, J.Math.Phys. 3 (1962) 140, 157, 166

    Article  MathSciNet  Google Scholar 

  11. H.S. Camarda and P.D. Georgopulos, Phys.Rev.Lett. 50 (1983), 215

    Article  Google Scholar 

  12. E. Haller, H. Koppel and L.S. Cederbaum, Chem.Phys.Letters 101 (1983), 215

    Article  Google Scholar 

  13. G.M. Zaslavsky, N.N. Filonenko, Sov.Phys. JETP 38 (1974) 317

    Google Scholar 

  14. M.V. Berry and M. Tabor, Proc.Roy.Soc. London 356 (1977) 375

    Article  Google Scholar 

  15. S.W. Mc Donald and A. N, Kaufman, Phys.Rev.Lett. 42 (1979) 1189

    Article  Google Scholar 

  16. O. Bohigas, M.S. Giannoni and C. Schmit, in Chaotic Behaviour in Quantum Systems, edited by G. Casati, (Plenum, New York, in press)

    Google Scholar 

  17. G. Casati, F. Valz-Gris and I. Guarneri, Lett.Nuov.Cim. 28 (1980) 279

    Article  MathSciNet  Google Scholar 

  18. G.M. Zaslavsky, Phys.Rep. 80 (1981) 157

    Article  MathSciNet  Google Scholar 

  19. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, S.S.M. Wong, Rev.Mod.Phys. 53 (1981) 385

    Article  MathSciNet  Google Scholar 

  20. V. Buch, R.B. Gerber and M.A. Ratner, J.Chem.Phys. 76 (1982) 5397

    Article  Google Scholar 

  21. M. Robnik, J.Phys. A.: math. Gen. (to appear)

    Google Scholar 

  22. L.D. Landau, E.M. Lifshitz, Theoretical Phys. Vol. 3-MIR Editions

    Google Scholar 

  23. M.V. Berry, Ann.Phys. 131 (1981) 163, Proceedings of the "Les Houches" Summer School on Chaotic behaviour of deterministic systems (Amsterdam North Holland)

    Article  Google Scholar 

  24. G. Mantica, Thesis, Pavia University (1982), Italy

    Google Scholar 

  25. G. Casati, I. Guarneri and F. Valz-Gris, "Degree of randomness of the sequence of eigenvalues", Phys.Rev. A. Rapid Comm. (in press)

    Google Scholar 

  26. A.N. Kolmogorov, IEEE Trans. Information Theory 14 (1968) 662

    Article  MathSciNet  Google Scholar 

  27. P. Martin-Loef, J. Information and Control 9 (1966) 602

    Article  Google Scholar 

  28. F.J. Dyson and M.L. Mehta, J.Math.Phys. 4 (1963) 701

    Article  MathSciNet  Google Scholar 

  29. G. Casati, B.V. Chirikov and I. Guarneri, "Energy level statistic of integrable quantum systems", preprint

    Google Scholar 

  30. A.I. Shnirelman, Usp.Mat. Nauk 29 (1974) 181

    Google Scholar 

  31. B.V. Chirikov, private communication

    Google Scholar 

  32. G. Casati, I. Guarneri and G. Mantica, in "Chaotic Behaviour in Quantum Systems", edited by G. Casati (Plenum, New York), in press

    Google Scholar 

  33. G. Casati in Lectures Notes in Mathematics 1055 1984, 62–75 edited by L. Accardi, A. Frigerio, V. Gorini (Springer-Verlag, Berlin), proceedings of the workshop on Quantum probability and applications to the Quantum theory of Irreversible Processes, Rome, 1982

    Article  MathSciNet  Google Scholar 

  34. G. Casati in "Trends and developments in the eighties", Bielefeld symposium 1983, World Publishing Company, Singapore, Eds. S. Albeverio and Ph. Blanchard, in press.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica dell'Università, Via Celoria 16, 20133, Milano, Italy

    Giulio Casati

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  1. Giulio Casati
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Heinz-Dietrich Doebner Jörg-Dieter Hennig

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© 1985 Springer-Verlag

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Casati, G. (1985). Energy level distributions and chaos in quantum mechanics. In: Doebner, HD., Hennig, JD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074578

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  • DOI: https://doi.org/10.1007/BFb0074578

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  • Print ISBN: 978-3-540-15666-6

  • Online ISBN: 978-3-540-39585-0

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