Advertisement

Quantum Chaos and Spectral Transitions in the Kicked Harper Model

  • Karsten Kruse
  • Roland Ketzmerick
  • Theo Geisel
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 547)

Abstract

In contrast to bounded systems, quantum chaos in extended systems may be associated with fractal spectra, metal-insulator transitions due to avoided band crossings, and spreading wave packets. In this lecture we point out the role of avoided band crossings for spectral transitions in the example of the kicked Harper model. We explain the coexistence of localized and extended eigenfunctions off the critical line as well as changes of the fractal dimension on the critical line. Avoided band crossings thus provide a common cause for various phenomena observed numerically in the spectrum of the kicked Harper model.

Keywords

Fractal Dimension Anderson Model Pure Point Spectral Transition Quantum Chaos 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.-M. C. Gutzwiller (1991) Chaos in classical and quantum mechanics. Springer-Verlag, New York.Google Scholar
  2. 2.
    F. Haake (1991) Quantum signatures of chaos, Springer Series in Synergetics Vol. 54. Springer-Verlag, Berlin Heidelberg.Google Scholar
  3. 3.
    For a review see R. Artuso, G. Casati, F. Borgonovi, L. Rebuzzini, and I. Guarneri (1994). Int. J. Mod. Phys. B 8, 207.Google Scholar
  4. 4.
    P. Leboeuf, J. Kurchan, M. Feingold, and D. P. Arovas (1990). Phys. Rev. Lett. 65, 3076.CrossRefGoogle Scholar
  5. 5.
    R. Lima and D. Shepelyansky (1991). Phys. Rev. Lett. 67, 1377.CrossRefGoogle Scholar
  6. 6.
    T. Geisel, R. Ketzmerick, and G. Petschel (1991). Phys. Rev. Lett. 67, 3635.CrossRefGoogle Scholar
  7. 7.
    R. Artuso, G. Casati, and D. Shepelyansky (1992). Phys. Rev. Lett. 68, 3826.CrossRefGoogle Scholar
  8. 8.
    R. Artuso, F. Borgonovi, I. Guarneri, L. Rebuzzini, and G. Casati (1992). Phys. Rev. Lett. 69, 3302.CrossRefGoogle Scholar
  9. 9.
    I. Guarneri and F. Borgonovi (1993). J. Phys. A: Math. Gen. 26, 119.CrossRefGoogle Scholar
  10. 10.
    R. Roncaglia, L. Bonci, F. M. Izrailev, B. J. West, and P. Grigolini (1994). Phys. Rev. Lett. 73, 802.CrossRefGoogle Scholar
  11. 11.
    P. Leboeuf and A. Mouchet (1994). Phys. Rev. Lett. 73, 1360.CrossRefGoogle Scholar
  12. 12.
    I. Dana (1994). Phys. Rev. Lett. 73, 1609.CrossRefGoogle Scholar
  13. 13.
    F. Borgonovi and D. Shepelyansky (1995). Europhys. Lett. 29, 117.CrossRefGoogle Scholar
  14. 14.
    R. Ketzmerick, K. Kruse, and T. Geisel (1999). Physica D 131, 247.Google Scholar
  15. 15.
    F. M. Izraelev and D. L. Shepelyanskii (1979). Sov. Phys. Dokl. 24, 996.Google Scholar
  16. 16.
    P. G. Harper (1955). Proc. Roy. Soc. London A68, 874.Google Scholar
  17. 17.
    M. Ya. Azbel (1964). Sov. Phys. JETP 19, 634.Google Scholar
  18. 18.
    D. R. Hofstadter (1976). Phys. Rev. B14, 2239.Google Scholar
  19. 19.
    F. Delyon (1987). J. Phys. A 20, L21.Google Scholar
  20. 20.
    B. Simon (1982). Adv. Appl. Math. 3, 463.CrossRefGoogle Scholar
  21. 21.
    J. Avron and B. Simon (1983). Duke Math. J. 50, 369.CrossRefGoogle Scholar
  22. 22.
    J. Bellissard and B. Simon (1982). J. Funct. Anal. 48, 408.CrossRefGoogle Scholar
  23. 23.
    S. C. Bell and R. B. Stinchcombe (1989). J. Phys. A: Math. Gen. 22, 717.CrossRefGoogle Scholar
  24. 24.
    C. Tang and M. Kohmoto (1986). Phys. Rev. B 34, 2041.CrossRefGoogle Scholar
  25. 25.
    M. Wilkinson and E. J. Austin (1994). Phys. Rev. B 50, 1420.CrossRefGoogle Scholar
  26. 26.
    A. Rüdinger and F. Piéchon (1997). J. Phys. A: Math. Gen. 30, 117.CrossRefGoogle Scholar
  27. 27.
    R. Ketzmerick, K. Kruse, F. Steinbach, and T. Geisel (1998). Phys. Rev. B 58, 9881.CrossRefGoogle Scholar
  28. 28.
    S. Aubry and G. André (1980). Ann. Isr. Phys. Soc. 3, 133.Google Scholar
  29. 29.
    R. Ketzmerick, K. Kruse, and T. Geisel (1998). Phys. Rev. Lett. 80, 137.CrossRefGoogle Scholar
  30. 30.
    P. W. Anderson (1958). Phys. Rev. 109, 1492.CrossRefGoogle Scholar
  31. 31.
    M. Kohmoto, L. P. Kadanoff, and C. Tang (1983). Phys. Rev. Lett. 50, 1870.CrossRefGoogle Scholar
  32. 32.
    S. Ostlund, R. Pandit, D. Rand, H. J. Schellnhuber, and E. D. Siggia (1983). Phys. Rev. Lett. 50, 1873.CrossRefGoogle Scholar
  33. 33.
    M. Wilkinson and R. J. Kay (1996). Phys. Rev. Lett. 76, 1896.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Karsten Kruse
    • 1
  • Roland Ketzmerick
    • 1
  • Theo Geisel
    • 1
  1. 1.Max-Planck-Institut für Strömungsforschung und Fakultät Physik der Universität GöttingenGöttingenGermany

Personalised recommendations