, Volume 41, Issue 1, pp L75–L81

Symmetry breaking in quantum chaotic systems

  • Akhilesh Pandey
  • Ramakrishna Ramaswamy
  • Pragya Shukla
Rapid Communication


We show, using semiclassical methods, that as a symmetry is broken, the transition between universality classes for the spectral correlations of quantum chaotic systems is governed by the same parametrization as in the theory of random matrices. The theory is quantitatively verified for the kicked rotor quantum map. We also provide an explicit substantiation of the random matrix hypothesis, namely that in the symmetry-adapted basis the symmetry-violating operator is random.


Quantum chaos symmetry breaking intermediate ensembles 


05.45 03.65 24.60 


  1. [1]
    M L Mehta,Random matrices, (Academic Press, New York) (1990)Google Scholar
  2. [2]
    F Haake,Quantum signatures of chaos, (Springer, Berlin 1991)MATHGoogle Scholar
  3. [3]
    F J Dyson,J. Math. Phys. (N. Y.) 3, 1191 (1962)MATHCrossRefADSMathSciNetGoogle Scholar
  4. [4]
    A Pandey,Ann. Phys. (N.Y.) 134, 110 (1981)CrossRefADSGoogle Scholar
  5. [5]
    J B French, V K B Kota, A Pandey and S Tomsovic,Ann. Phys. (N. Y.) 181, 198, 235 (1988)CrossRefADSGoogle Scholar
  6. [6]
    A Pandey and M L Mehta,Commun. Math. Phys. 87, 449 (1983)MATHCrossRefADSMathSciNetGoogle Scholar
  7. [6a]
    M L Mehta and A Pandey,J. Phys. A16, 2655, L601 (1983)ADSMathSciNetGoogle Scholar
  8. [7]
    A Pandey and P Shukla,J. Phys. A24, 3907 (1991)ADSMathSciNetGoogle Scholar
  9. [8]
    T Guhr and H A Widenmüller,Ann. Phys. (N. Y.) 199, 412 (1991)CrossRefGoogle Scholar
  10. [9]
    G E Mitchell, E G Bilpuch, P M Endt and J F Shriner Jr.,Phys. Rev. Lett.,61, 1473 (1988)CrossRefADSGoogle Scholar
  11. [10]
    N Rosenzweig and C E Porter,Phys. Rev.,120, 1648 (1960)CrossRefADSGoogle Scholar
  12. [11]
    M V Berry and M Robnik,J. Phys.,A19 649 (1986)ADSMathSciNetGoogle Scholar
  13. [12]
    O Bohigas, M J Giannoni and C Schmit, inQuantum chaos and statistical nuclear physics, Eds T H Seligman and H Nishioka (Springer, Berlin, 1986), p 18Google Scholar
  14. [13]
    A M O de Almeida, inQuantum chaos, Eds H Cerdeira, R Ramaswamy, G Casati and M Gutzwiller, (World Scientific, Singapore, 1990)Google Scholar
  15. [14]
    N Dupuis and G Montambaux,Phys. Rev.,B43, 4390 (1991)Google Scholar
  16. [15]
    G Lenz and F Haake,Phys. Rev. Lett.,67, 1 (1991)MATHCrossRefADSMathSciNetGoogle Scholar
  17. [16]
    G Casati and L Molinari,Prog. Theor. Phys. Suppl.,98, 287 (1989)CrossRefADSMathSciNetGoogle Scholar
  18. [17]
    F M Izrailev,Phys. Rev. Lett.,56, 541 (1986)CrossRefADSGoogle Scholar
  19. [18]
    G Casati, L Molinari and F Izrailev,Phys. Rev. Lett.,64, 1851 (1990)MATHCrossRefADSMathSciNetGoogle Scholar
  20. [19]
    M Tabor,Physica,D6, 195 (1983)ADSMathSciNetGoogle Scholar
  21. [20]
    M C Gutzwiller,J. Math. Phys. (N. Y.) 12, 343 (1971)CrossRefADSGoogle Scholar
  22. [21]
    J Hannay and A M O de Almeida,J. Phys. A17, 3429 (1984)ADSGoogle Scholar
  23. [22]
    M V Berry,Proc. R. Soc. (London) A400, 299 (1985)ADSMathSciNetGoogle Scholar
  24. [23]
    P Shukla and A Pandey, (in preparation)Google Scholar

Copyright information

© the Indian Academy of Sciences 1993

Authors and Affiliations

  • Akhilesh Pandey
    • 1
  • Ramakrishna Ramaswamy
    • 1
  • Pragya Shukla
    • 1
  1. 1.School of Physical SciencesJawaharlal Nehru UniversityNew DelhiIndia

Personalised recommendations