Skip to main content

Linear Chaos

  • Conference paper
Nonlinearity with Disorder

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 67))

Abstract

The controversial phenomenon of quantum (wave) chaos is reviewed using a simple analogy with classical linear waves in cavities. Estimates for the main statistical properties of wave dynamics are evaluated and discussed. The transient nature of wave chaos is emphasized and explained in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A Lichtenberg and M. Lieberman, Regular and StochasticMotion, Springer, 1983

    Google Scholar 

  2. G.M. Zaslaysky, Chaos in Dynamic Systems, Harwood, New Jork, 1985.

    Google Scholar 

  3. Ya.G. Sinai, Usp. Mat. Nauk, 25, N 2 (1970) 141.

    MATH  MathSciNet  Google Scholar 

  4. L.A Bunimovich, Zh. Eksper. Teor. Fiz., 89 (1985) 1452.

    Google Scholar 

  5. V.I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics, Benjamin, 1968.

    Google Scholar 

  6. J. Wersinger, E. Ott, and J. Finn, Phys. Fluids, 21 (1978) 2263.

    Article  ADS  Google Scholar 

  7. I. Kornfeld, S. Fomin and Ya. Sinai, Ergodic Theory, Springer, 1982.

    Google Scholar 

  8. S.S. Abdullaev, G.M. Zaslaysky, 7h. Exper. Teor. Fiz., 80 (1981) 524; 85 (1983) 1573; 87 (1984) 763.

    Google Scholar 

  9. AV. Chigarev, Yu. V. Chigarev, Akustich. 7h., 24 (1978) 765.

    Google Scholar 

  10. P. Seba. Phys. Rev. Lett., 64 (1990) 1855.

    Google Scholar 

  11. B.V. Chirikov, F.M. Izrailev and D.L. Shepelyansky, Soy. Sci. Rev. 2 (1981) 209

    MATH  MathSciNet  Google Scholar 

  12. B.V. Chirikov, F.M. Izrailev and D.L. Shepelyansky, Physica, 33 (1988) 77.

    Article  MATH  MathSciNet  Google Scholar 

  13. B.V. Chirikov, Time-Dependent Quantum Systems, Proc. Les Houches Summer School on Chaos and Quantum Physics, Elsevier, 1990.

    Google Scholar 

  14. A.I. Shnirelman, Usp. Mat. Nauk, 29, N6 (1974) 181; On the Asymptotic Properties of Eigenfunctions in the Regions of Chaotic Motion, Addendum to the book: V.F. Lasutkin. The KAM Theory and Asymptotics of Spectrum of Elliptic Operators, Springer, 1990.

    Google Scholar 

  15. D.L. Shepelyansky, Physica, D 8 (1983) 208

    Article  ADS  Google Scholar 

  16. G. Casati, B.V. Chirikov, I. Guarneri, and D.L. Shepelyansky, Phys. Rev. Lett., 56 (1986) 2437.

    Google Scholar 

  17. G.P. Berman and G.M. Zaslaysky, Physica, 91 (1978) 450.

    Article  MathSciNet  Google Scholar 

  18. K. Nakamura, A. Bishop, and A. Shudo, Phys. Rev., 39 (1989) 422.

    Google Scholar 

  19. S.S. Abdullaev, Zh. Tekhn. Fiz., 51 (1981) 697.

    Google Scholar 

  20. F. Rannou, Astron. Astroph., 31 (1974) 289

    MATH  ADS  Google Scholar 

  21. F. Rannou, Y. Levy. Phys. Lett., A 88 (1982) 1

    Article  MathSciNet  Google Scholar 

  22. F. Rannou, J. McCauley, Ibid., 115 (1986) 433.

    Google Scholar 

  23. B.V. Chirikov, Wiss. Z., 24 (1975) 215.

    Google Scholar 

  24. M. Gell-Mann and J. Hartle, Quantum Mechanics in the Light of Quantum Cosmology. Proc. 3rd. Intern. Symp. on The Foundations of Quantum Mechanics in the Light of New Technology, Tokyo. 1989.

    Google Scholar 

  25. F.M. Izrailev, Phys. Lett., 125 (1987) 250.

    Article  MathSciNet  Google Scholar 

  26. E. Heller, Phys. Rev. Lett., 53 (1984) 1515.

    Article  ADS  MathSciNet  Google Scholar 

  27. R. Jensen et al., Phys. Rev. Lett., 63 (1989) 2771.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chirikov, B.V. (1992). Linear Chaos. In: Abdullaev, F., Bishop, A.R., Pnevmatikos, S. (eds) Nonlinearity with Disorder. Springer Proceedings in Physics, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84774-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-84774-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84776-9

  • Online ISBN: 978-3-642-84774-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics