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Excitations in Superfluid 4He and the Dielectric Formalism

  • Allan Griffin
Part of the NATO ASI Series book series (NSSB, volume 257)

Abstract

Despite great efforts over many years, a truly microscopic understanding of the phonon-maxon-roton spectrum in superfluid 4He has continued to be elusive. High resolution neutron scattering studies1,2,3 of the lineshape exhibited by \(S(\vec{Q},\omega )\) have given vivid evidence of the completely different behaviour of the low Q phonon spectrum and the high Q maxon-roton spectrum as the temperature increases towards T λ. Recently, Glyde and the author have realized that recent experimental results gave the needed clues which were missing before. We have proposed a unified theory4 of the excitations in superfluid 4He which is firmly anchored in the existence of a Bose broken symmetry (see Sokol, these proceedings). We believe that a suitably parameterized version of this microscopic formulation will provide a natural starting point for detailed comparisons with the excitations observed in high resolution neutron scattering data. For further discussion of its experimental implications, we refer to the papers by Glyde and Svensson in these proceedings. The main goals of this article are to discuss the basic elements of the new picture, to review its historical development and relation to earlier ideas, and finally, to sketch how it might be brought into contact with the very successful phenomenological approach based on variational many body wavefunctions.

Keywords

Density Fluctuation Dynamic Structure Factor Zero Sound Dielectric Formalism Density Response Function 
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.

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References

  1. 1.
    A.D.B. Woods and E.C. Svensson, Phys. Rev. Letters 41, 974 (1978).ADSCrossRefGoogle Scholar
  2. 2.
    E.F. Talbot, H.R. Glyde, W.G. Stirling and E.C. Svensson, Phys. Rev. B38, 11 229 (1988).Google Scholar
  3. 3.
    W.G. Stirling and H.R. Glyde, Phys. Rev. B41, 4224 (1990).ADSCrossRefGoogle Scholar
  4. 4.
    H.R. Clyde and A. Griffin, Phys. Rev. Letters, 65, September 17 issue (1990).Google Scholar
  5. 5.
    N.N. Bogoliubov, J. Phys.(U.S.S.R.) 11, 23 (1947).Google Scholar
  6. 6.
    S.T. Beliaev, Sov. Phys. JETP 7, 289 (1958)Google Scholar
  7. S.T. Beliaev, [Zh. Eksp. Teor. Fiz. 34 417 (1958)].Google Scholar
  8. 7.
    N. Hugenholtz and D. Pines, Phys. Rev. 116, 489 (1959).MathSciNetADSMATHCrossRefGoogle Scholar
  9. 8.
    J. Gavoret and P. Nozières, Ann. Phys. (N.Y.) 28, 349 (1964).ADSCrossRefGoogle Scholar
  10. 9.
    P.C. Hohenberg and P.C. Martin, Ann. Phys. (N.Y.) 34, 291 (1965).ADSCrossRefGoogle Scholar
  11. 10.
    S.K. Ma and C.W. Woo, Phys. Rev. 159, 165 (1967).ADSCrossRefGoogle Scholar
  12. 11.
    P. Szépfalusy and I. Kondor, Ann. Phys. (N.Y.) 82, 1 (1974).ADSCrossRefGoogle Scholar
  13. 12.
    A. Griffin and T.H. Cheung, Phys. Rev. A7, 2086 (1973).ADSCrossRefGoogle Scholar
  14. 13.
    V. Wong and H. Gould, Ann. Phys. (N.Y.) 83, 252 (1974).ADSCrossRefGoogle Scholar
  15. 14.
    E. Talbot and A. Griffin, Ann. Phys. (N.Y.) 151, 71 (1983).ADSCrossRefGoogle Scholar
  16. 15.
    For a review, see A. Griffin, Can. Journ. Phys. 65, 1368 (1987).ADSCrossRefGoogle Scholar
  17. 16.
    A. Miller, D. Pines and P. Nozières, Phys. Rev. 127, 1452 (1962).ADSMATHCrossRefGoogle Scholar
  18. 17.
    D. Pines, in Quantum Fluids, ed by D.F. Brewer ( John Wiley, N.Y., 1966 ), p. 257.Google Scholar
  19. 18.
    A. Griffin and E. Talbot, Phys. Rev. B24, 5075 (1981).ADSCrossRefGoogle Scholar
  20. 19.
    A. Griffin and S. Payne, Journ. Low Temp. Phys. 64, 155 (1986).Google Scholar
  21. 20.
    For a review, see D. Pines, Can. Journ. Phys. 65, 1357 (1987).ADSCrossRefGoogle Scholar
  22. 21.
    H.R. Glyde and A. Griffin, in preparation.Google Scholar
  23. 22.
    A.D.B. Woods, Phys. Rev. Letters 14, 355 (1965).ADSCrossRefGoogle Scholar
  24. 23.
    L.D. Landau, J. Phys. (U.S.S.R.) 11, 91 (1947).Google Scholar
  25. 24.
    A. Griffin, Phys. Rev. B19, 5946 (1979).MathSciNetADSCrossRefGoogle Scholar
  26. 25.
    R.P. Feynman, Phys. Rev. 91, 1301 (1953)MathSciNetADSCrossRefGoogle Scholar
  27. R.P. Feynman, Phys. Rev. 94, 262 (1954).ADSMATHCrossRefGoogle Scholar
  28. 26.
    See, for example, W. Hsu, D. Pines and C.H. Aldrich, Phys. Rev. B32, 7179 (1985).ADSGoogle Scholar
  29. 27.
    E. Talbot and A. Griffin, Journ. Low Temp. Phys. 56, 141 (1984).Google Scholar
  30. 28.
    A. Zawadowski, J. Ruvalds and J. Solana, Phys. Rev. A5, 399 (1972).ADSCrossRefGoogle Scholar
  31. 29.
    W.G. Stirling, in Proc. 2nd International Conf. on Phonon Physics, ed. by J. Kollar, N. Kroo, N. Menyhard, T. Siklos ( World Scientific, Singapore, 1985 ), p. 829.Google Scholar
  32. 30.
    A. Griffin and E.C. Svensson, LT-19 Proceedings (Sussex), in Physica B165 + 166, 487 (1990).Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Allan Griffin
    • 1
  1. 1.Department of PhysicsUniversity of TorontoTorontoCanada

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