Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Quantum Signatures of Chaos

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

  • 1157 Accesses

Abstract

As is by now well known there are two radically different types of motion in classical Hamiltonian mechanics: the regular motion of integrable systems and the chaotic motion of nonintegrable systems.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    The classical limit of a periodically driven spin was realized by Waldner [1]; much later came the first realization of the quantum version in Jessen’s group [2].

  2. 2.

    Chaotic scattering and graphs make for equally interesting applications of unitary random matrices.

References

  1. F. Waldner, D.R. Barberis, H. Yamazaki, Phys. Rev. A 31, 420 (1985)

    Article  ADS  Google Scholar 

  2. S. Chaudhury, A. Smith, B.E. Anderson, S. Ghose, P.S. Jessen, Nature 461, 768 (2009)

    Article  ADS  Google Scholar 

  3. A. Peres: Quantum Theory: Concepts and Methods (Kluwer Academic, New York, 1995)

    MATH  Google Scholar 

  4. M.V. Berry, M. Tabor, Proc. R. Soc. Lond. A 356, 375 (1977)

    Article  ADS  Google Scholar 

  5. G.M. Zaslavskii, N.N. Filonenko, Sov. Phys. JETP 8, 317 (1974)

    ADS  Google Scholar 

  6. M.V. Berry, M. Tabor, Proc. R. Soc. Lond. A 349, 101 (1976)

    Article  ADS  Google Scholar 

  7. M.V. Berry, Les Houches Session XXXVI 1981, in Chaotic Behavior of Deterministic Systems, ed. by G. Iooss, R.H. Helleman, R. Stora (North-Holland, Amsterdam, 1983)

    Google Scholar 

  8. O. Bohigas, R. Haq, A. Pandey, Nuclear Data for Science and Technology, ed. by K. Böckhoff (Reidel, Dordrecht, 1983)

    Google Scholar 

  9. G. Bohigas, M.-J. Giannoni, Mathematical Andrandom Computational Methods in Nuclear Physics. Lecture Notes in Physics, vol. 209 (Springer, Berlin/Heidelberg, 1984)

    Google Scholar 

  10. O. Bohigas, M.J. Giannoni, C. Schmit, Phys. Rev. Lett. 52, 1 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  11. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, P.S.M. Wong, Rev. Mod. Phys. 53, 385 (1981)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. H.S. Camarda, P.D. Georgopulos, Phys. Rev. Lett. 50, 492 (1983)

    Article  ADS  Google Scholar 

  14. M.R. Schroeder, J. Audio Eng. Soc. 35, 307 (1987)

    Google Scholar 

  15. H.J. Stöckmann, J. Stein, Phys. Rev. Lett. 64, 2215 (1990)

    Article  ADS  Google Scholar 

  16. H. Alt, H.-D. Gräf, H.L. Harney, R. Hofferbert, H. Lengeler, A. Richter, P. Schart, H.A. Weidenmüller, Phys. Rev. Lett. 74, 62 (1995)

    Article  ADS  Google Scholar 

  17. H. Alt, H.-D. Gräf, R. Hofferbert, C. Rangacharyulu, H. Rehfeld, A. Richter, P. Schart, A. Wirzba, Phys. Rev. E 54, 2303 (1996)

    Article  ADS  Google Scholar 

  18. T. Zimmermann, H. Köppel, L.S. Cederbaum, C. Persch, W. Demtröder, Phys. Rev. Lett. 61, 3 (1988); G. Persch, E. Mehdizadeh, W. Demtröder, T. Zimmermann, L.S. Cederbaum: Ber. Bunsenges. Phys. Chem. 92, 312 (1988)

    Article  ADS  Google Scholar 

  19. H. Held, J. Schlichter, G. Raithel, H. Walther, Europhys. Lett. 43, 392 (1998)

    Article  ADS  Google Scholar 

  20. C. Ellegaard, T. Guhr, K. Lindemann, H.Q. Lorensen, J. Nygård, M. Oxborrow, Phys. Rev. Lett. 75, 1546 (1995)

    Article  ADS  Google Scholar 

  21. C. Ellegaard, T. Guhr, K. Lindemann, J. Nygård, M. Oxborrow, Phys. Rev. Lett. 77, 4918 (1996)

    Article  ADS  Google Scholar 

  22. A. Hoenig, D. Wintgen, Phys. Rev. A 39, 5642 (1989)

    Article  ADS  Google Scholar 

  23. M. Oxborrow, C. Ellegaard, Proceedings of the 3rd Experimental Chaos Conference, Edinburgh (1995)

    Google Scholar 

  24. S. Deus, P.M. Koch, L. Sirko, Phys. Rev. E 52, 1146 (1995)

    Article  ADS  Google Scholar 

  25. O. Legrand, C. Schmit, D. Sornette, Europhys. Lett. 18, 101 (1992)

    Article  ADS  Google Scholar 

  26. U. Stoffregen, J. Stein, H.-J. Stöckmann, M. Kuś, F. Haake, Phys. Rev. Lett. 74, 2666 (1995)

    Article  ADS  Google Scholar 

  27. P. So, S.M. Anlage, E. Ott, R.N. Oerter, Phys. Rev. Lett. 74, 2662 (1995)

    Article  ADS  Google Scholar 

  28. O. Hul, S. Bauch, P. Pakoñski, N. Savytskyy, K. Życzkowski, L. Sirko, Phys. Rev. E 69, 056205 (2004)

    Article  ADS  Google Scholar 

  29. C.H. Joyner, S. Müller, M. Sieber, Europhys. Lett. 107, 50004 (2014)

    Article  ADS  Google Scholar 

  30. A. Rehemanjiang, M. Allgaier, C.H. Joyner, S. Müller, M. Sieber, U. Kuhl, H.-Stöckmann, Phys. Rev. Lett. 107, 064101 (2016)

    Google Scholar 

  31. A. Rehemanjiang, M. Richter, U. Kuhl, H.-J. Stöckmann, Phys. Rev. E 97, 022204 (2018)

    Article  ADS  Google Scholar 

  32. T. Dittrich, R. Graham, Ann. Phys. 200, 363 (1990)

    Article  ADS  Google Scholar 

  33. M.L. Mehta, Random Matrices (Academic, New York, 1967); 2nd edition 1991; 3rd edition (Elsevier, 2004)

    Google Scholar 

  34. C.E. Porter (ed.), Statistical Theory of Spectra (Academic, New York 1965)

    Google Scholar 

  35. T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep. 299, 192 (1998)

    Article  ADS  Google Scholar 

  36. K. Efetov: Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, 1997)

    MATH  Google Scholar 

  37. S. Fishman, D.R. Grempel, R.E. Prange, Phys. Rev. Lett. 49, 509 (1982); Phys. Rev. A 29, 1639 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  38. J.H. Poincaré, Les Méthodes nouvelles de la mécanique céleste (Gauthier-Villard, Paris, 1899); (reed. A. Blanchard, Paris, 1987)

    Google Scholar 

  39. P. Pechukas, Phys. Rev. Lett. 51, 943 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  40. T. Yukawa, Phys. Rev. Lett. 54, 1883 (1985)

    Article  ADS  Google Scholar 

  41. T. Yukawa, Phys. Lett. A 116, 227 (1986)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Duisburg-Essen, Essen, Germany

    Fritz Haake

  2. School of Mathematical Science, University of Nottingham, Nottingham, UK

    Sven Gnutzmann

  3. Center for Theoretical Physics, Polish Academy of Sciences, Warszawa, Poland

    Marek Kuś

Authors
  1. Fritz Haake
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sven Gnutzmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marek Kuś
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Haake, F., Gnutzmann, S., Kuś, M. (2018). Introduction. In: Quantum Signatures of Chaos. Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-97580-1_1

Download citation

Publish with us

Policies and ethics

Search

Navigation