Chaos in Quantum Dynamics: An Overview

  • Giulio Casati
Part of the NATO ASI Series book series (NSSB, volume 212)

Abstract

We discuss the quantum behaviour of systems which exhibit deterministic chaos in the classical limit. To this end we first examine the motion of a rotator under an external time-periodic δ-like perturbation. When the perturbation is strong enough, the classical motion is chaotic and diffusive while the quantum excitation remains strongly localized. A similar phenomenon takes place in the more physical problem of an hydrogen atom irradiated by a linearly polarized microwave field. In this latter case however, there exists a critical value of the microwave field intensity above which localization is destroyed and strong quantum excitation takes place. Numerical computations confirm the above theoretical predictions which also agree with the experimental results so far available.

Keywords

Wave Packet Chaotic Motion Microwave Field Anderson Localization Classical Motion 
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.
    For a clear and readable discussion see; Moser J., 1968, Memoirs Am. Math. Soc., No 81.Google Scholar
  2. 2.
    Chirikov B.V., 1979, Phys. Rep. 52 263.MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Ford J, Walker G.H., 1969, Phys. Rev. 188 416.MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Henon H., Heiles C, 1964, Astron. J. 69 73.MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Ford J., Physics Today, April 1983.Google Scholar
  6. 6.
    Casati G., Guarneri I. and Vivaldi F., 1983, Phys. Rev. Lett. 51 727.MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Percival I.C., 1973, J. Phys. B L. 229.Google Scholar
  8. 8.
    Proceedings of the II International Conference on Quantum Chaos, eds. T.H. Seligman and H. Nishioka, Lectures Notes, Physics Vol. 263.Google Scholar
  9. 9.
    G. Casati, B.V. Chirikov, F.M. Izrailev, J. Ford in “Stochastic Behaviour in Classical and Quantum Hamiltonian Systems”, Como, June 1977, Lectures Notes in Physics, Springer 93. (1979), 334.MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    G. Casati, J. Ford. I. Guarneri, F. Vivaldi Phys. Rev. A 34 (1986) 1413.ADSCrossRefGoogle Scholar
  11. 11.
    B.V. Chirikov, F.M. Izrailev, and D.L. Shepelyansky, (1981) Sov. Sci. Rev. Sec. C 2, 209.MathSciNetMATHGoogle Scholar
  12. 12.
    G.P. Brivio, G. Casati, L. Perotti, I. Guarneri, Physica D 33 (1988) 51.MathSciNetADSCrossRefMATHGoogle Scholar
  13. 13.
    S. Fishman, D.R. Grempel and R.E. Prange, 1982, Phys. Rev. Lett. 12, 509.MathSciNetADSCrossRefGoogle Scholar
  14. S. Fishman, D.R. Grempel and R.E. Prange, 1984. Phys. Rev. A 22. 1639.Google Scholar
  15. 14.
    J.E. Bayfield, P.M. Koch, Phys. Rev. Lett. 33. (1974) 258.ADSCrossRefGoogle Scholar
  16. 15.
    J.C. Leopold, I.C. Percival, Phys. Rev. Lett. 41 (1978) 944.ADSCrossRefGoogle Scholar
  17. 16.
    G. Casati, I. Guarneri and D.L. Shepelyansky, Phys. Rev. A 36 (1987) 3501.ADSCrossRefGoogle Scholar
  18. 17.
    G. Casati, I. Guarneri, D. Shepelyansky, J.E.E.E. J. of Quantum Electr. 24 (1988) 1420.ADSCrossRefGoogle Scholar
  19. 18.
    G. Casati, B.V. Chirikov, I. Guarneri, D.L. Shepelyansky, Physics Report 154 (1987). 77.Google Scholar
  20. 19.
    G. Casati. B.V. Chirikov, D.L. Shepelyansky, Phys. Rev. Lett. 53 (1984) 2525.ADSCrossRefGoogle Scholar
  21. 20.
    R.V. Jensen, Phys. Rev. A 30 (1984) 386.ADSCrossRefGoogle Scholar
  22. 21.
    K. van Leeuwen, G. v. Oppen, S. Renwick, J. Bowlin, P. Koch, R. Jensen, O. Rath, D. Richards, G. Leopold, Phys. Rev. Lett. 55 (1985) 2231.ADSCrossRefGoogle Scholar
  23. 22.
    R. Blumel, U. Smilansky, Phys. Rev. Lett. 58 (1987) 2531.ADSCrossRefGoogle Scholar
  24. 23.
    P. Koch, private communication.Google Scholar
  25. 24.
    J.E. Bayfield, G. Casati, I. Guarneri, D.V. Sokol: “Localization of classically chaotic diffusion for Hydrogen Atoms in Microwave Fields”. Preprint.Google Scholar
  26. 25.
    E.J. Galvey, B.E. Sauer, L. doorman, P.M. Koch, D. Richards; “Microwave lonization of H Atoms; Breakdown of Classical Dynamics for High Frequencies”. Preprint.Google Scholar
  27. 26.
    R. Blumel, R. Graham, L. Sirko, U. Smilansky, H. Walther, K. Yamada; “Microwave excitation of Rydberg atoms in the presence of noise”, Preprint.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Giulio Casati
    • 1
  1. 1.Dipartimento di FisicaUniversita’ di MilanoMilanoItaly

Personalised recommendations