Spectral Fluctuations and Chaotic Motion

  • Oriol Bohigas
  • Marie-Joya Giannoni
  • Charles Schmit
Part of the NATO ASI Series book series (NSSB, volume 130)


It has been known since the early days of nuclear physics the existence of fine structure resonances to which are associated very long lifetimes (~ six orders of magnitude larger than the time it takes to a nucleon to traverse the nucleus). These compound nucleus resonances have been systematically studied at neutron threshold (~6 MeV excitation energy). It has been clear that a “microscopic” (a one by one) study of them was neither possible nor suitable but that an adequate goal was to attain a statistical description. One can distinguish two kinds of properties in a statistical description, global and local ones. An example of the first is the average density ρav(E) of resonances or quasi-bound levels as a function of excitation energy E. Local spectral properties or spectral fluctuations are connected with the statistical description and characterization of the departures of the microscopic level density ρ(E), a sum of spikes — ρ(E)=∑ δ (E−Ei)-, from its average ρav(E). The average density ρav(E) depends on specific nuclear properties alike size, shell effects, pairing, etc., and although theories of nuclear level densities are successful at a semiquantitative level, a detailed agreement between theory and experiment is still lacking. In several respects the situation is quite different concerning spectral fluctuations. First, level fluctuations do not depend, for a given nucleus.


Chaotic Motion Riemann Zeta Function Random Matrix Theory Chaotic Regime Fluctuation Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Be-83]
    M.V. BERRY, in Chaotic Behaviouz oA Detezministic Systems,Les Houches Summer School Lectures XXXVI, R.H.G. Helleman and G. Joos (Eds.), North-Holland, Amsterdam 1983, p. 171.Google Scholar
  2. [Be-84]
    M.V. BERRY in Chaotic Behavioz in Quantum Systems,G. Casati (ed. ), Plenum, 1984.Google Scholar
  3. [BFF-81]
    T.A. BRODY, J. FLORES, J.B. FRENCH, P.A. MELLO,A. PANDEY and S.S.M. WONG, Rev.Mod.Phys. 53 (1981) 385.Google Scholar
  4. [BG-84]
    O. BOHIGAS and M.J. GIANNONI, in Mathematical and Com-putational Methods in Nucleaz Physics, J.S. Dehesa et al. (eds.), Lecture Notes in Physics 209, Springer Verlag, 1984,p. 1.Google Scholar
  5. [BGS-84a]
    O. BOHIGAS, M.J. GIANNONI and C. SCHMIT, Phys.Rev.Lett. 52 (1984) 1.CrossRefGoogle Scholar
  6. BGS-84b] O. BOHIGAS,M.J. GIANNONI and C. SCHMIT, J.Physique Lett. 45 (1984) L-1015.Google Scholar
  7. [BHP-83]
    O. BOHIGAS, R.U. HAQ and A. PANDEY, in Nucteaz Data Science and Technology, K.H. Böckhoff (ed.), Reidel, Dordrecht, 1983, p. 809.Google Scholar
  8. [BHP-84]
    O. BOHIGAS, R.U. HAQ and A. PANDEY, preprint, 1984. [BR-84] M.V. BERRY and M. ROBNIK, J.Phys. A17 (1984) 2413.Google Scholar
  9. [BT-77]
    M.V. BERRY and M. TABOR, Proc.Roy.Soc.Lond. A356 (1977) 375.CrossRefGoogle Scholar
  10. [CG-83]
    H.S. CAMARDA and P.D. GEORGOPULOS, Phys.Rev.Lett. 50 (1983) 492.CrossRefGoogle Scholar
  11. [Ga-85]
    J.C. GAY in Photo physics and Photochemistzy in the Vacuum Ultzaviolet, S.P. Mc Glynn et al. (eds.), Reidel, 1985, p. 631.Google Scholar
  12. [Gu-83]
    M.C. GUTZWILLER, Physica 7D (1983) 341.Google Scholar
  13. [HKC-83]
    E. HALLER, H. KOPPEL and L.S. CEDERBAUM, Chem.Phys. Lett. 101 (1983) 215.CrossRefGoogle Scholar
  14. [HKC-84]
    E. HALLER, H. KOPPEL and L.S. CEDERBAUM, Phys.Rev. Lett. 52 (1984) 1665.Google Scholar
  15. [HMY-81]
    F.T. HIOE, E.W. MONTROLL and M. YAMAWAKI, in Pe2bpecttves in Statisttcaf Physics, H.J. Raveche (ed.), North-Holland, 1981, p. 295.Google Scholar
  16. [HPB-82]
    R.U. HAQ, A. PANDEY and O. BOHIGAS, Phys.Rev.Lett. 48 (1982) 1086.CrossRefGoogle Scholar
  17. [IY-84]
    T. ISHIKAWA and T. YUKAWA, preprint 1984.Google Scholar
  18. [KKK-84]
    R. KUBO, A. KAWABATA and S. KOBAYASHI, Ann.Rev. Mater.Sci. 14 (1984) 49.CrossRefGoogle Scholar
  19. [MD-83]
    S.W. Mc DONALD, Ph.D. Thesis, University of California,Berkeley, 1983, unpublished.Google Scholar
  20. [MK-79]
    S.W. Mc DONALD and A.N. KAUFMAN, Phys.Rev.Lett. 42 (1979) 1189.Google Scholar
  21. [Mo-74]
    H.L. MONTGOMERY, Proc. of Int. Congr. of Mathematicians,Vancouver, 1974.Google Scholar
  22. [Od-84]
    A. ODLYZKO, private communication, 1984.Google Scholar
  23. [Or-74]
    D.S. ORNSTEIN, E’cgodic Theory, Randomness, and DynamdcaQ Systems, New Haven and London, Yale University Press, 1974.Google Scholar
  24. [Pa-79]
    A. PANDEY, Ann.Phys. 119 (1979) 170.CrossRefGoogle Scholar
  25. [Pe-83]
    P. PECHUKAS, Phys.Rev.Lett. 51 (1983) 943.CrossRefGoogle Scholar
  26. [Ro-84]
    M. ROBNIK, J. Phys. A17 (1984) 1049.Google Scholar
  27. [Ro-85]
    M. ROBNIK, in Photophysies and Photochemistry in the Vacuum Wtzav-iokt, S.P. Mc Glynn et al. (eds.), Reidel, 1985, p. 579.Google Scholar
  28. [S’c-54]
    M. SCHRÖDER, Acustica, 4 (1954) 456.Google Scholar
  29. [SG-84]
    M. SHAPIRO and G. GOELMAN, Phys. Rev. Lett. 53 (1984) 1714.Google Scholar
  30. [SVZ-84]
    T.H. SELIGMAN, J.J.M. VERBAARSCHOT and M.R. ZIRNBAUER, Phys.Rev.Lett. 53 (1984) 215.CrossRefGoogle Scholar
  31. Sw-84] W.J. SWIATECKI, in Theo’et.ica1 Appzoaches oÇ Heavy ionReaction Mechanisms, M. Martinot, C. Ngô and F. Lepage (eds.), Nucl.Phys. A428 (1984) p.199c.Google Scholar
  32. We-84] H.A. WEIDENMÜLLER, these Proceedings.Google Scholar
  33. [Za-77]
    D. ZAGIER, The Math.Intelligencer 0 (1977) 7.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Oriol Bohigas
    • 1
  • Marie-Joya Giannoni
    • 1
  • Charles Schmit
    • 1
  1. 1.Division de Physique ThéoriqueInstitut de Physique NucléaireOrsay CedexFrance

Personalised recommendations