Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Quantum chaos

Nature volume 355, pages 311–318 (1992)Cite this article

Abstract

What are the special properties of strongly perturbed quantum systems when the corresponding classical mechanical systems exhibit chaotic behaviour? This is the central question of quantum chaos. Theoretical and experimental studies of highly excited atoms in strong magnetic fields and intense microwave fields have revealed surprising new physical phenomena with far-reaching applications.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Similar content being viewed by others

References

  1. May, R. M. Nature 261, 459–467 (1976).

    Article  ADS  CAS  Google Scholar 

  2. Dynamical Chaos (eds Berry, M. V., Percival, I. C. & Weiss, N. O.) (The Royal Society, London, 1987).

  3. The Ubiquity of Chaos (ed. Krasner, S.) (American Association for the Advancement of Science, Washington DC, 1990).

  4. Jensen, R. V. Am. Scient. 75, 168–181 (March 1987); Encyclopedia of Modern Physics, 69–96 (Academic, New York, 1990).

    Google Scholar 

  5. Ford, J. in The New Physics (ed. Davies, P. C. W.) 348–371 (Cambridge University Press, 1986).

    Google Scholar 

  6. Gleick, J. Chaos: Making a New Science (Viking, New York, 1987).

    MATH  Google Scholar 

  7. Goldstein, H. Classical Mechanics (Addison-Wesley, Reading, Massachusetts, 1980).

    MATH  Google Scholar 

  8. Lichtenberg, A. J. & Lieberman, M. A. Regular and Stochastic Motion (Springer, New York, 1983).

    Book  Google Scholar 

  9. Wisdom, J. Nature 315, 731–733 (1985).

    Article  ADS  Google Scholar 

  10. Poincaré, H. Les Methodes Nouvelles de la Mechanique Celeste (Gauthier-Villars, Paris, 1892). (reprinted) vol. 3, section 297 (Dover, New York, 1957).

    Google Scholar 

  11. Delos, J. B., Knudson, S. K. & Noid, D. W. Phys. Rev. A28, 7–21 (1983).

    Article  ADS  CAS  Google Scholar 

  12. Bohr, N. Kgl. Danske Vid. Selsk. Skr., nat-math. Afd. 8. Raekke IV.1, 1–3 (1918); (reprinted) in Sources of Quantum Mechanics (ed. van der Wærden, B. L.) 95–137 (Dover, New York, 1967).

    Google Scholar 

  13. Berry, M. V. Proc. R. Soc. Lond. A412, 183–198 (1987).

    Article  ADS  Google Scholar 

  14. Chirikov, B. V., Israilev, F. M. & Shepelyansky, D. L. Physica D33, 77–88 (1988).

    MathSciNet  CAS  Google Scholar 

  15. Chaos and Quantum Physics (eds Giannoni, M.-J., Voros, A. & Zinn-Justin, J.) (Elsevier, London, 1991).

  16. Holle, A., Wiebush, G., Main, J., Friedrich, H. & Welge, K. H. Phys. Rev. Lett. 56, 2594–2597 (1986).

    Article  ADS  CAS  Google Scholar 

  17. Holle, A. et al. Z. Phys. D5, 279–285 (1987).

    CAS  Google Scholar 

  18. Main, J., Wiebush, G., Holle, A. & Welge, K. H. Phys. Rev. Lett. 57, 2789–2792 (1986).

    Article  ADS  CAS  Google Scholar 

  19. Holle, A., Main, J., Wiebush, G., Rottke, H. & Welge, K. H. Phys. Rev. Lett. 61, 161–164 (1988).

    Article  ADS  CAS  Google Scholar 

  20. Welch, G. R., Kash, M. M., Iu, C., Hsu, L. & Kleppner, D. Phys. Rev. Lett. 62, 893–896 (1989).

    Article  ADS  CAS  Google Scholar 

  21. Iu, C., Welch, G. R., Kash, M. M., Hsu, L. & Kleppner, D. Phys. Rev. Lett. 63, 1133–1136 (1989).

    Article  ADS  CAS  Google Scholar 

  22. Iu, C., Welch, G. R., Kash, M. M., Kleppner, D., Delande, D. & Gay, J.-C. Phys. Rev. Lett. 66, 145–148 (1991).

    Article  ADS  CAS  Google Scholar 

  23. Bayfield, J. E. & Koch, P. M. Phys. Rev. Lett. 33, 258–261 (1974).

    Article  ADS  CAS  Google Scholar 

  24. Bayfield, J. E., Casati, G., Guarneri, I. & Sokol, D. W. Phys. Rev. Lett. 63, 364–367 (1989).

    Article  ADS  CAS  Google Scholar 

  25. van Leeuwen, K. A. H. et al. Phys. Rev. Lett. 55, 2231–2234 (1985).

    Article  ADS  CAS  Google Scholar 

  26. Galvez, E. J., Sauer, B. E., Moorman, L., Koch, P. M. & Richards, D. Phys. Rev. Lett. 61, 2011–2014 (1988).

    Article  ADS  CAS  Google Scholar 

  27. Koch, P. M. in The Ubiquity of Chaos (ed. Krasner, S.) 75–97 (American Association for the Advancement of Science, Washington DC, 1990).

    Google Scholar 

  28. Friedrich, H. & Wintgen, D. Phys. Rep. 183, 37–79 (1989).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  29. Hasegawa, H., Robnik, M. & Wunner, G. Progr. theor. Phys. 98, 198–286 (1989).

    Article  Google Scholar 

  30. Delande, D. in Chaos and Quantum Physics (eds Giannoni, M.-J., Voros, A. & Zinn-Justin, J.) (Elsevier, London, 1991).

    MATH  Google Scholar 

  31. Jensen, R. V. Phys. Rev. A30, 386–397 (1984).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  32. Quantum Chaos and Statistical Nuclear Physics (eds Seligman, T. H. & Nishioka, H.) (Springer, New York, 1986).

    Google Scholar 

  33. Jensen, R. V., Susskind, S. M. & Sanders, M. M. Phys. Rep. 201, 1–56 (1991).

    Article  ADS  CAS  Google Scholar 

  34. Blümel, R. & Smilansky, U. Z. Phys. D6, 83–105 (1987).

    Google Scholar 

  35. Casati, G., Chirikov, B. V. & Shepelyansky, D. L. Phys. Rev. Lett. 53, 2525–2528 (1984).

    Article  ADS  CAS  Google Scholar 

  36. Casati, G., Guarneri, I. & Shepelyansky, D. L. IEEE J. Quant. Electron. 24, 1420–1444 (1988).

    Article  ADS  CAS  Google Scholar 

  37. Chirikov, B. V. in Chaos and Quantum Physics (eds Giannoni, M.-J., Voros, A. & Zinn-Justin, J.) (Elsevier, London, 1991).

    MATH  Google Scholar 

  38. Heller, E. J. Phys. Rev. Lett. 53, 1515–1518 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  39. Zeeman, P. Phil. Mag. Ser. 5 43, 226–239 (1897).

    Article  Google Scholar 

  40. Schiff, L. I. Quantum Mechanics, 283–288 (McGraw-Hill, New York, 1955).

    Google Scholar 

  41. Garstang, R. H. Rep. Prog. Phys. 40, 105–154 (1977).

    Article  ADS  CAS  Google Scholar 

  42. Pericval, I. C. Adv. chem. Phys. 36, 1–62 (1977).

    Google Scholar 

  43. Zaslavsky, G. M. Phys. Rep. 80, 157–250 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  44. Einstein, A. Ver. Deut. Phys. Ger. 19, 82–92 (1917).

    Google Scholar 

  45. Garton, W. R. S. & Tompkins, F. S. Astrophys. J. 158, 839–845 (1969).

    Article  ADS  Google Scholar 

  46. Du, M. L. & Delos, J. B. Phys. Rev. A38, 1896–1912 (1988).

    Article  ADS  CAS  Google Scholar 

  47. Macdonald, J. & Kaufman, A. Phys. Rev. Lett. 42, 1189–1191 (1979).

    Article  ADS  Google Scholar 

  48. Waterland, R. L., Yuan, J.-M., Martens, C. C., Gillilan, R. E. & Reinhardt, W. P. Phys. Rev. Lett. 61, 2733–2736 (1988).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  49. Wintgen, D. & Hönig, A. Phys. Rev. Lett. 63, 1467–1470 (1989).

    Article  ADS  CAS  Google Scholar 

  50. Sirdhar, S. Phys. Rev. Lett. 67, 785–788 (1991).

    Article  ADS  Google Scholar 

  51. Gutzwiller, M. Chaos In Classical and Quantum Mechanics (Springer, New York, 1990).

    Book  Google Scholar 

  52. Feynman, R. P. & Hibbs, A. R. Quantum Mechanics and Path-Integrals (McGraw-Hill, New York, 1965).

    MATH  Google Scholar 

  53. Ezra, G. S., Richter, K., Tanner, G. & Wintgen, D. J. Phys. B24, L413–420 (1991).

    ADS  CAS  Google Scholar 

  54. Van Vleck, J. H. Phil. Mag. 44, 842–869 (1922).

    Article  CAS  Google Scholar 

  55. Einstein, A. Ann. Phys. 17, 132–148 (1905).

    Article  CAS  Google Scholar 

  56. Leopold, J. G. & Percival, I. C. Phys. Rev. Lett. 41, 944–947 (1978).

    Article  ADS  CAS  Google Scholar 

  57. Chirikov, B. V., Israilev, F. M. & Shepelyansky, D. L. Sov. Scient. Rev. C2, 209 (1981).

    Google Scholar 

  58. Jensen, R. V., Susskind, S. M. & Sanders, M. M. Phys. Rev. Lett. 62, 1476–1479 (1989).

    Article  ADS  CAS  Google Scholar 

  59. Leopold, J. G. & Richards, D. J. Phys. B22, 1931–1961 (1989).

    ADS  Google Scholar 

  60. Jensen, R. V., Sanders, M. M., Saraceno, M. & Sundaram, B. Phys. Rev. Lett. 63, 2771–2775 (1989).

    Article  ADS  CAS  Google Scholar 

  61. Alhassid, Y., Novoselsky, A. & Whelan, N. Phys Rev. Lett. 65, 2971–2974 (1990).

    Article  ADS  CAS  Google Scholar 

  62. Jensen, R. V. & Sundaram, B. Phys. Rev. Lett. 65, 1964 (1990).

    Article  ADS  CAS  Google Scholar 

  63. Smilansky, U. in Chaos and Quantum Physics (eds, Giannoni, M.-J., Voros, A. & Zinn-Justin, J.) (Elsevier Science, London, 1991).

    Google Scholar 

  64. Pollak, E. & Child, M. S. Chem. Phys. 60, 23 (1981).

    Article  CAS  Google Scholar 

  65. Thompson, T. C. & Truhlar, D. G. J. phys. Chem. 88, 210–214 (1984).

    Article  CAS  Google Scholar 

  66. Davis, M. J. J. phys. Chem. 92, 3124–3144 (1988).

    Article  CAS  Google Scholar 

  67. Gaspard, P. & Rice, S. J. chem. Phys. 90, 2225–2241; 2242–2254; 2255–2262 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  68. Doron, E., Smilansky, U. & Frenkel, A. Phys. Rev. Lett. 65, 3072–3075 (1990).

    Article  ADS  CAS  Google Scholar 

  69. Jalabert, R. A., Baranger, H. U. & Stone, A. D. Phys. Rev. Lett. 65, 2442–2445 (1990).

    Article  ADS  CAS  Google Scholar 

  70. Kliner, D. A. V., Rinnen, K.-D. & Zare, R. N. Chem. Phys. Lett. 166, 107–111 (1990).

    Article  ADS  CAS  Google Scholar 

  71. Lee, P. A., Stone, A. D. & Fukuyama, H. Phys. Rev. B35, 1039–1070 (1987).

    Article  ADS  CAS  Google Scholar 

  72. Frautschi, S. C. Nuovo Cimento A12, 133–161 (1972).

    Article  ADS  CAS  Google Scholar 

  73. Politzer, H. D. Phys. Rep. C14, 129–180 (1974).

    Article  ADS  Google Scholar 

  74. Delande, D. thesis, Univ, Pierre and Marie Curie, Paris (1988).

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Wesleyan University, Middletown, Connecticut, 06457, USA

    Roderick V. Jensen

Authors
  1. Roderick V. Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jensen, R. Quantum chaos. Nature 355, 311–318 (1992). https://doi.org/10.1038/355311a0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/355311a0

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing