Skip to main content

Abstract

We discuss two problems which relate to the foundations of the subject, and a third about asymptotic properties of spectral distributions. We give also a brief list of topics which should be further explored.

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. K. G. Wilson, Scientific American 241, 158 (August, 1979 ).

    Google Scholar 

  2. E. P. Wigner, in “Gatlinberg Conference on Neutron Physics”, ORNL Report #2309 (1957). This article is reprinted in: C.E. Porter (ed.), “Fluctuations”, Academic Press, N.Y., 1965.

    Google Scholar 

  3. L. D. Landau and Ya. Smorodinski, “Lectures on the Theory of the Atomic Nucleus”, (Consultants Bureau) N.Y., 1958; the relevant short section is reprinted in Porter2.

    Google Scholar 

  4. J. Von Neumann and E. P. Wigner, Phys. Zeitschr. 130 (1929) 467.

    Google Scholar 

  5. F. J. Dyson, J. Math. Phys. 3 (1962) 140; 3 (1962) 157: 3 (1962) 166; 3 (1962) 1191; 3. (1962) 1199; F. J. Dyson and M. L. Mehta, J. Math. Phys. 4 (1963) 701; M. L. Mehta and F. J. Dyson, J. Math Phys. 4 (1963) 713. These papers are reprinted in Porter2.

    Google Scholar 

  6. H. Camarda, H. I. Liou, F. Rahn, G. Hacken, M. Slagowitz, W. W. Havens, Jr., and J. Rainwater, in “Statistical Properties of Nuclei”, J. B. Garg, editor, Plenum Press, N.Y., 1972. See also later papers in Physical Review by this Columbia group.

    Google Scholar 

  7. E. G. Bilpuch, A. M. Lane, G. E. Mitchell and J. D. Moses, Phys. Reports 28 (1976) 145.

    Article  ADS  Google Scholar 

  8. M. L. Mehta, “Random Matrices and the Statistical Theory of Energy Levels”, Academic Press, N.Y., 1967; C. E. Porter in Porter2; E.P. Wigner, SIAM Review 9 (1967) 1;M.L. Mehta in Garg0; M. Carmeli, J. Stat. Phys. JLO (1974) 259; T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey and S. S. M. Wong, to be published; J. B. French in Proceedings of the 1979 Michigan Summer School, to be published.

    Google Scholar 

  9. A. Pandey, Ann. Phys. (N.Y.) 119 (1979) 170.

    Article  ADS  Google Scholar 

  10. J. B. French, Rev. Mex. Fis. 22 (1973) 221. Closely related “two-body random ensembles” (TBRE), which are intractable analytically, were introduced earlier and studied via Monte- Carlo calculations, by J. B. French and S. S. M. Wong, Phys. Lett. 33B (1970) 449, 35B. (1971) 5 and by O. Bohigas and J. Flores, Phys. Lett. 34JB (1971) 261, 35B (1971) 383.

    Google Scholar 

  11. K. K. Mon and J. B. French, Ann. Phys. (N.Y.) 95. (1975) 90.

    Article  MathSciNet  ADS  Google Scholar 

  12. J. B. French and A. Pandey, to be published.

    Google Scholar 

  13. J. B. French and S. S. M. Wong, unpublished.

    Google Scholar 

  14. F. J. Dyson, the third paper of the series, Eq. (75).

    Google Scholar 

  15. K. F. Ratcliff, Phys. Rev. C3 (1971) 117.

    Google Scholar 

  16. F. S. Chang and A. Zuker, Nucl. Phys. A198 (1972) 417.

    Article  Google Scholar 

  17. J. P. Draayer, private communication.

    Google Scholar 

  18. J. B. French, in “Isospin in Nuclear Physics,” D. H. Wilkinson, editor, North-Holland, Amsterdam, 1969.

    Google Scholar 

  19. K. Kar, Ph.D. Thesis, University of Rochester, 1979.

    Google Scholar 

  20. P. Mugambi, Ph.D. Thesis, University of Rochester, 1970; G. D. Lougheed and S. S. M. Wong, Nucl. Phys. A243 (1975) 215,: A246 (1975) 29.

    Google Scholar 

  21. C. Mahaux and H. A. Weidenmuller, Shell-Model Approach to Nuclear Reactions, North-Holland, Amsterdam, 1969.

    Google Scholar 

  22. A. Arima and F. Iachello, Ann. Phys. (N.Y.) 99 (1976) 253, 111 (1978) 201, 123 (1979) 468. Some results on spectral distributions for bosons are due to M. Nomura, Ann. Phys. (N.Y.) 91. (1975) 83; P. F. Bortignon, V. R. Manfredi and S. Spitz, Lett. Nuovo Cimento 23 (1978) 210; V. K. B. Kota, Jour, de Physique 40 (1979) L-579; V. K. B. Kota and V. Potbhare, in press.

    Google Scholar 

  23. J. P. Draayer, J. B. French and S. S. M. Wong, Ann. Phys. (N. Y.) 106. (1977) 472, 503.

    Article  Google Scholar 

  24. T. R. Halemane, Ph.D. Thesis, University of Rochester, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Plenum Press, New York

About this chapter

Cite this chapter

French, J.B. (1980). Special Topics in Spectral Distributions. In: Dalton, B.J., Grimes, S.M., Vary, J.P., Williams, S.A. (eds) Theory and Applications of Moment Methods in Many-Fermion Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3120-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3120-9_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3122-3

  • Online ISBN: 978-1-4613-3120-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics