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Excitations in Superfluid Helium

  • J. Ruvalds
Part of the NATO Advanced Study Institutes Series book series (volume 2)

Abstract

The elementary excitation spectrum of liquid helium has been the subject of intensive theoretical interest following the pioneering work of Landau in 1947 [1]. In order to explain the observed superfluid and thermodynamic properties of helium at very low temperatures, Landau proposed that the excitation spectrum of the liquid consists of phonon excitations at small momenta, free particle excitations at very large momenta, and roton excitations with an energy minimum Δ0 at intermediate momenta. The roton dispersion may be expressed in the form
$$ E\left( k \right) = {\Delta _{0}} + \frac{{{{\left( {k - {k_{0}}} \right)}^{2}}}}{{2\mu }};\;k \cong {k_{0}} $$
(1.1)
and the effective mass y, as well as the energy gap Δ0 and momentum k 0 may be obtained accurately from recent neutron scattering data. The existence of a roton energy gap is essential to understand the thermodynamic properties in the superfluid state. Furthermore, the possible frictionless flow of liquid helium at low velocities may be understood in terms of the excitation spectrum as suggested by Landau [1]. For example, the critical velocity v c = minE(k)/k, which is the upper limit for superfluid flow, corresponds to the kinematically allowed creation of an excitation in the superfluid.

Keywords

Excitation Spectrum Liquid Helium Final State Interaction Superfluid Helium Raman Data 
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.
    Landau, L.D. (1941). J. Phys. USSR, 5, 71;Google Scholar
  2. 1a.
    Landau, L.D. (1947). J. Phys. USSR, 11, 91.Google Scholar
  3. 2.
    Bogoliubov, N.N. (1947). J. Phys., 11, 23.Google Scholar
  4. 3.
    Feynman, R.P. (1954). Phys. Rev., 94, 262;MATHCrossRefADSGoogle Scholar
  5. 3.
    Feynman, R.P. and Cohen, M. (1956). Phys. Rev. 102, 1189.MATHCrossRefADSGoogle Scholar
  6. 4.
    Lee, T.D., Huang, K. and Yang, C.N. (1957). Phys. Rev., 106, 1135.MathSciNetMATHCrossRefADSGoogle Scholar
  7. 5.
    Brueckner, K.A. and Sawada, K. (1957). Phys. Rev., 106, 117.CrossRefADSGoogle Scholar
  8. 6.
    Beliaev, S.T. (1958). Sov. Phys. JETP, 7, 289, 299.MathSciNetGoogle Scholar
  9. 7.
    Hugenholtz, N. and Pines, D. (1959). Phys. Rev., 116, 489.MathSciNetMATHCrossRefADSGoogle Scholar
  10. 8.
    Gavoret, J. and Nozières, P. (1964). Ann. Phys., 28, 349.CrossRefADSGoogle Scholar
  11. 9.
    Feenberg, E. (1969). Theory of Quantum Fluids, (Academic Press, New York), and references cited therein.Google Scholar
  12. 10.
    See for example: Woods, A.D.B. and Cowley, R.A. (1970). Can. J. Phys., 49, 177, and references cited therein.Google Scholar
  13. 11.
    Ruvalds, J. and Zawadowski, A. (1970). Phys. Rev. Lett., 25, 333;CrossRefADSGoogle Scholar
  14. 11a.
    Zawadowski, A., Ruvalds, J. and Solana, J. (1972). Phys. Rev., A5, 399.ADSGoogle Scholar
  15. 12.
    Iwamoto, F. (1970). Prog. Theor. Phys. (Kyoto), 44, 1135.CrossRefADSGoogle Scholar
  16. 13.
    Greytak, T.J. and Yan, James, (1969). Phys. Rev. Lett., 22, 987.CrossRefADSGoogle Scholar
  17. 14.
    Greytak, T.J., Woerner, J., Yan, J. and Benjamin, R. (1970). Phys. Rev. Lett., 25, 1547.CrossRefADSGoogle Scholar
  18. 15.
    Yau, J. and Stephen, M. (1971).Google Scholar
  19. 15a.
    Yau, J. and Stephen, M. (1971). Phys. Rev. Lett., 27, 482;CrossRefADSGoogle Scholar
  20. 15a.
    Fomin, I.A. (1971). Sov. Phys. JETP, 33, 637;ADSGoogle Scholar
  21. 15b.
    Solana, J., Celli, V., Ruvalds, J., Tüttö, I. and Zawadowski, A. (1972). Phys. Rev, A6, 1665;ADSGoogle Scholar
  22. 15c.
    Nagai, K., Nojima, K. and Hatano, A. (1972). Prog. Theor. Phys. (Kyoto), 46, 355.CrossRefADSGoogle Scholar
  23. 16.
    Ruvalds, J. (1972). Phys. Rev. Lett., 27, 1769;CrossRefADSGoogle Scholar
  24. 16a.
    Nagai, K. (1973). Prog. Theor. Phys., 49, 46;MathSciNetCrossRefADSGoogle Scholar
  25. 16b.
    Tüttö, I. (1973). J. Low Temp. Phys., 11, 77;CrossRefADSGoogle Scholar
  26. 16c.
    Kebukawa, T. (1973). Prog. Theor. Phys., 49, 388.Google Scholar
  27. 17.
    Bogoliubov, N.N. and Zubarev, D.N. (1955). Sov. Phys. JETP, 1, 83.Google Scholar
  28. 18.
    Sunakawa, S., Yoki-o, Y. and Nakatani, H. (1962). Prog. Theor. Phys., 27, 589, 600;CrossRefADSGoogle Scholar
  29. 18a.
    Sunakawa, S., Yoki-o, Y. and Nakatani, H. (1962). Prog. Theor. Phys., 28, 127.MATHCrossRefADSGoogle Scholar
  30. 19.
    Sunakawa, S., Yamasaki, S. and Kebukawa, T. (1969). Prog. Theor. Phys., 41, 919;CrossRefADSGoogle Scholar
  31. 19a.
    Kebukawa, T., Yamasaki, S. and Sunakawa, S. (1970). Prog. Theor. Phys., 44, 565.CrossRefADSGoogle Scholar
  32. 20.
    Rajagopal, A.K., Bagchi, A. and Ruvalds, J. Phys. Rev. (to be published).Google Scholar
  33. 21.
    For a recent review of the low temperature properties of He3-He4 mixtures see, for example: Ebner, C. and Edwards, D.O. (1971). Phys. Rep., 1, 77.CrossRefADSGoogle Scholar
  34. 22.
    Stephen, M.J. (1969). Phys. Rev., 187, 279.CrossRefADSGoogle Scholar
  35. 23.
    Cohen, M.H. and Ruvalds, J. (1969). Phys. Rev. Lett., 23, 1378.CrossRefADSGoogle Scholar
  36. 24.
    Bagchi, A. and Ruvalds, J. (To be published).Google Scholar
  37. 25.
    Bardeen, J., Cooper, L.N. and Schrieffer, J.R. (1957). Phys. Rev., 106, 162;MathSciNetCrossRefADSGoogle Scholar
  38. 25a.
    Bardeen, J., Cooper, L.N. and Schrieffer, J.R. (1957). Phys. Rev., 108, 1175.MathSciNetMATHCrossRefADSGoogle Scholar
  39. 26.
    Fermi, E. (1931). Z. Phys., 71, 250.CrossRefADSGoogle Scholar
  40. 27.
    Silberglitt, R. and Brooks Harris, A. (1968). Phys. Rev., 174, 640.CrossRefADSGoogle Scholar
  41. 28.
    Scott, J.F. (1968). Phys. Rev. Lett., 21, 907.CrossRefADSGoogle Scholar
  42. 29.
    Ruvalds, J. and Zawadowski, A. (1970). Phys. Rev., B2, 1172.ADSGoogle Scholar
  43. 30.
    Pitayevski, L.P. (1959). Zh. Eksp. Teor. Piz., 36, 1168.Google Scholar
  44. 30a.
    Pitayevski, L.P. (1959). Sov. Phys. JETP, 9, 830;Google Scholar
  45. 30b.
    Pitayevski, L.P. (1966). Usp. Fiz. Nauk, 88, 409.Google Scholar
  46. 30c.
    Pitayevski, L.P. (1966). Sov. Phys. Usp., 9, 197.ADSGoogle Scholar
  47. 31.
    Miller, A., Pines, D. and Nozières, P. (1962). Phys. Rev., 127, 1452.MATHCrossRefADSGoogle Scholar
  48. 32.
    Woods, A.D.B., Svensson, E.C. and Martel, P. (Preprint).Google Scholar
  49. 33.
    Kebukawa, T., Yamasaki, S. and Sunakawa, S. (1973). Prog. Theor. Phys., 49, 1802.CrossRefADSGoogle Scholar
  50. 34.
    Schneider, T. and Enz, C.P. (1971). Phys. Rev. Lett., 27, 1186.CrossRefADSGoogle Scholar
  51. 35.
    Celli, V. and Ruvalds, J. (1972). Phys. Rev. Lett., 28, 539.CrossRefADSGoogle Scholar
  52. 36.
    Landau, L.D. and Khalatnikov, I.M. (1967). In Collected Papers of L.D. Landau, (ed. D. Ter Haar), (Gordon and Breach, New York), pp. 494, 511;Google Scholar
  53. 36a.
    Khalatnikov, I.M. (1965). Theory of Superfluidity, (Benjamin, New York).Google Scholar
  54. 37.
    Yau, J. and Stephen, M. (1971). Phys. Rev. Lett., 27, 482;CrossRefADSGoogle Scholar
  55. 37a.
    Fomin, I.A. (1971). Sov. Phys. JETP, 33, 637;ADSGoogle Scholar
  56. 37b.
    Solana, J., Celli, V., Ruvalds, J., Tüttö, I. and Zawadowski, A. (1972). Phys. Rev., A6, 1665;ADSGoogle Scholar
  57. 37c.
    Nagai, K., Nojima, K. and Hatano, A. (1972). Prog. Theor. Phys. (Kyoto), 46, 355.CrossRefADSGoogle Scholar
  58. 38.
    Ruvalds, J. (1972). Phys. Rev. Lett., 27, 1769;CrossRefADSGoogle Scholar
  59. 38a.
    Nagai, K. (1973). Prog. Theor. Phys., 49, 46;MathSciNetCrossRefADSGoogle Scholar
  60. 38b.
    Tüttö, I. (1973). J. Low Temp. Phys., 11, 77;CrossRefADSGoogle Scholar
  61. 38c.
    Kebukawa, T. (1973). Prog. Theor. Phys., 49, 388.CrossRefADSGoogle Scholar
  62. 39.
    Landau, L.D. and Pomeranchuk, I. Ya. (1948). Cokl. Akad. Nauk. SSR, 59, 669.Google Scholar
  63. 40.
    See for example: Pines, D. and Nozières, P. (1966). The Theory of Quantum Fluids, (W.A. Benjamin, New York), p. 109.Google Scholar
  64. 41.
    Bowley, R.M. (1973). J. Low Temp. Phys., 10, 481.CrossRefADSGoogle Scholar
  65. 42.
    Baym, G. (1967). Phys. Rev. Lett., 18, 71.CrossRefADSGoogle Scholar
  66. 43.
    Emery, V.J. (1966). Phys. Rev., 148, 138.CrossRefADSGoogle Scholar
  67. 44.
    Bardeen, J., Baym, G. and Pines, D. (1966). Phys. Rev. Lett., 17, 372;CrossRefADSGoogle Scholar
  68. 44a.
    Bardeen, J., Baym, G. and Pines, D. (1967). Phys. Rev., 156, 207.CrossRefADSGoogle Scholar
  69. 45.
    McMillan, W.L. (1969). Phys. Rev., 182, 299.CrossRefADSGoogle Scholar
  70. 46.
    Khalatnikov, I.M. and Zharkov, V.N. (1957). Sov. Phys. JETP, 5, 905;Google Scholar
  71. 46a.
    Zharkov, V.N. (1958). Sov. Phys. JETP, 6, 714.ADSGoogle Scholar
  72. 47.
    Bartley, D.L., Robinson, J.E. and Wong, V.K. (1973). J. Low Temp. Phys., 12, 71.CrossRefADSGoogle Scholar
  73. 48.
    Bagchi, A. and Ruvalds, J. (1973). Phys. Rev. Google Scholar
  74. 49.
    Surko, CM. and Slusher, R.E. (1973). Phys. Rev. Lett., 30, 1111;CrossRefADSGoogle Scholar
  75. 49.
    Woerner, R.L., Rockwell, D.A. and Greytak, T.J. (1973). Phys. Rev. Lett., 30, 1114.CrossRefADSGoogle Scholar
  76. 50.
    Rowe, J.M., Price, D.L. and Ostrowski, G.E. (1973). Phys. Rev. Lett., 31, 510.CrossRefADSGoogle Scholar
  77. 51.
    Tan, H.T. and Woo, Chia-Wei. (1973). Phys. Rev. Lett., 30, 365.CrossRefADSGoogle Scholar
  78. 52.
    Wortis, M. (1963). Phys. Rev., 132, 85;MathSciNetCrossRefADSGoogle Scholar
  79. 52a.
    Janus, J. (1963). Phys. Rev. Lett., 11, 336.MathSciNetCrossRefADSGoogle Scholar
  80. 53.
    Ngai, K.L., Ruvalds, J. and Economou, E.N. (1973). Phys. Rev. Lett., 31, 166.CrossRefADSGoogle Scholar
  81. 54.
    Eselson, B.N., Kovdrya, Yu.Z. and Shikin, V.B. (1971). Zh. Eksp. Teor. Piz., 59, 64;Google Scholar
  82. 54a.
    Eselson, B.N., Kovdrya, Yu.Z. and Shikin, V.B. (1971). Sov. Phys. JETP, 32, 37;ADSGoogle Scholar
  83. 54b.
    Cyumin, N.E., Eselson, B.N., Rudavskii, E.Ya. and Serbin, I.A. (1969). Zh. Eksp. Teor. Fiz., 56, 747;Google Scholar
  84. 54c.
    Cyumin, N.E., Eselson, B.N., Rudavskii, E.Ya. and Serbin, I.A. (1969). Sov. Phys. JETP, 29, 406.ADSGoogle Scholar

Copyright information

© Plenum Press, London 1974

Authors and Affiliations

  • J. Ruvalds
    • 1
  1. 1.Physics DepartmentUniversity of VirginiaCharlottesvilleUSA

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