Skip to main content

Level Clustering

  • Chapter
  • First Online:
Quantum Signatures of Chaos

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 54))

  • 2740 Accesses

Abstract

Here I propose to cosnsider classical autonomous systems with f degrees of freedom and 2 f pairs of canonical variables p i , q i . We shall meet with invariant tori, caustics, and Maslov indices and proceed to the semiclassical torus quantization à la Einstein, Brillouin and Keller (EBK) and its modern variant, a periodic-orbit theory.

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 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
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. I.C. Percival: Adv. Chem: Phys. 36, 1 (1977)

    Article  Google Scholar 

  2. M. Brack, R.K. Bhaduri: Semiclassical Physics (Addison-Wesley, Reading, MA, 1997)

    Google Scholar 

  3. V.P. Maslov: Théorie des Perturbations et Méthodes Asymptotiques (Dunod, Paris, 1972)

    MATH  Google Scholar 

  4. V.P. Maslov, M.V. Fedoriuk: Semiclassical Approximation in Quantum Mechanics (Reidel, Boston, 1981)

    Google Scholar 

  5. J.B. Delos: Adv. Chem. Phys. 65, 161 (1986)

    Article  Google Scholar 

  6. J.-P. Eckmann, R. Sénéor: Arch. Rational Mech. Anal. 61, 153 (1976)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. R.G. Littlejohn, J.m. Robbins: Phys. Rev. A 36, 2953 (1987)

    MathSciNet  ADS  Google Scholar 

  8. N. Rosenzweig, C.E. Porter: Phys. Rev. 120, 1698 (1960)

    Article  ADS  Google Scholar 

  9. M.V. Berry, M. Robnik: J. Phys. A: Math. Gen. 17, 2413 (1984)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. M.V. Berry, M. Tabor: Proc. R. Soc. Lond. A349, 101 (1976)

    MathSciNet  ADS  Google Scholar 

  11. M.V. Berry, M. Tabor: Proc. R. Soc. Lond. A356, 375 (1977)

    ADS  Google Scholar 

  12. E.B. Bogomolny, U. Gerland, C. Schmit: Phys. Rev. E59, R1315 (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fritz Haake .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Haake, F. (2010). Level Clustering. In: Quantum Signatures of Chaos. Springer Series in Synergetics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05428-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-05428-0_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05427-3

  • Online ISBN: 978-3-642-05428-0

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics