Skip to main content

Temperature Dependence of S(Q, ω) for Liquid 4He

  • Conference paper

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 79))

Abstract

It was most appropriate to hold this symposium in a year when two very important helium anniversaries were celebrated — the 40th anniversary of LANDAU’S [1] now famous phonon-roton dispersion relation for the elementary excitations in superfluid 4He (see Fig. 1), and the 30th anniversary of the first experimental observation, using neutron scattering techniques, of rotons by PALEVSKY et al. [2]. Their measurements and others [3–6] which quickly followed, all stimulated by the suggestion of COHEN and FEYNMAN [7] that neutron scattering could be used to directly determine the helium dispersion relation, confirmed that the form proposed by Landau was indeed correct.

This is a preview of subscription content, log in via an institution.

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Landau: J. Phys. USSR 11, 91 (1947). Even earlier [J. Phys. USSR 5, 71 (1941)], Landau had postulated the existence of rotons but at that time he envisaged them as forming a separate b5anch of excitations with energy-momentum dispersion relation e = A + p /21; where µ is an effective m5ss. In 1947 he changed the roton dispersion relation to e = A + (p - pa) /211 and connected the phonons (e = cp, where c is the velocity of sound) and rotons to form the continuous dispersion relation shown as an inset in Fig. 1

    Google Scholar 

  2. H. Palevsky, K. Otnes, K.E. Larsson, R. Pauli, R. Stedman: Phys. Rev. 108, 1346 (1957)

    Article  ADS  Google Scholar 

  3. J.L. Yarnell, G.P. Arnold, P.J. Bendt, E.C. Kerr: Phys. Rev. Lett. 1, 9 (1958) and Phys. Rev. 113, 1379 (1959)

    Google Scholar 

  4. H. Palevsky, K. Otnes, K.E. Larsson: Phys. Rev. 112, 11 (1958)

    Article  ADS  Google Scholar 

  5. D.G. Henshaw: Phys. Rev. Lett. 1, 127 (1958)

    Article  ADS  Google Scholar 

  6. K.E. Larsson, K. Otnes: Ark. Fys. 15, 49 (1959)

    Google Scholar 

  7. M. Cohen, R.P. Feynman: Phys. Rev. 107, 13 (1957)

    Article  MATH  ADS  Google Scholar 

  8. A.D.B. Woods, R.A. Cowley: Rep. Prog. Phys. 36, 1135 (1973)

    Article  ADS  Google Scholar 

  9. D.L. Price: In The Physics of Liquid and Solid Helium, Part II, ed. by K.H. Bennemann, J.B. Ketterson ( Wiley, New York 1978 ) p. 675

    Google Scholar 

  10. R.A. Cowley: In Quantum Liquids, ed. by J. Ruvalds, T. Regge ( North-Holland, Amsterdam 1978 ) p. 27

    Google Scholar 

  11. H.R. Glyde: In Condensed Matter Research Using Neutrons, ed. by S.W. Lovesey, R. Scherm ( Plenum, New York 1984 ) p. 95

    Google Scholar 

  12. E.C. Svensson, V.F. Sears: In Frontiers of Neutron Scattering, ed. by R.J. Birgeneau, D.E. Moncton, A. Zeilinger (North-Holland, Amsterdam 1986) p.126 [Reprinted from Physics 137B, 126 (1986)]

    Google Scholar 

  13. H.R. Clyde, E.C. Svensson: In Neutron Scattering, ed. by D.L. Price, K. Skold, Methods of Exp. Phys., Vol. 23, Part B ( Academic Press, New York 1987 ) p. 303

    Google Scholar 

  14. R.J. Donnelly, J.A. Donnelly, R.N. Hills: J. Low Temp. Phys. 44, 471 (1981)

    Article  ADS  Google Scholar 

  15. A.D.B. Woods, E.C. Svensson: Phys. Rev. Lett. 41, 974 (1978)

    Article  ADS  Google Scholar 

  16. B.N. Brockhouse: In Inelastic Scattering of Neutrons in Solids and Liquids ( International Atomic Energy Agency, Vienna 1961 ) p. 113

    Google Scholar 

  17. E.C. Svensson, R. Scherm, A.D.B. Woods: J. de Phys. 39, C6–211 (1978)

    Google Scholar 

  18. E.C. Svensson, W.G. Stirling, E. Talbot, H.R. Clyde: In Proc. 18th Int. Conf. on Low Temperature Physics, Jpn. J. Appl. Phys. 26 (Suppl. 26–3), 33 (1987)

    Google Scholar 

  19. E.F. Talbot, H.R. Glyde, W.G. Stirling, E.C. Svensson: Phys. Rev. B 38, 11229 (1988)

    Article  ADS  Google Scholar 

  20. E.C. Svensson, P. Martel, V.F. Sears, A.D.B. Woods: Can. J. Phys. 54, 2178 (1976)

    Article  ADS  Google Scholar 

  21. R.A. Cowley, A.D.B. Woods: Can. J. Phys. 49, 177 (1971)

    Article  ADS  Google Scholar 

  22. P. Martel, E.C. Svensson, A.D.B. Woods, V.F. Sears, R.A. Cowley: J. Low Temp. Phys. 23, 285 (1976)

    Article  ADS  Google Scholar 

  23. D.G. Henshaw, A.D.B. Woods: In Proc. VIIth Int. Conf. on Low Temperature Physics, ed. by G.M. Graham, A.C. Hollis Hallett ( Univ. of Toronto Press, Toronto 1961 ) p. 539

    Google Scholar 

  24. D.G. Henshaw, A.D.B. Woods: Phys. Rev. 121, 1266 (1961)

    Article  ADS  Google Scholar 

  25. A.D.B. Woods: Phys. Rev. Lett. 14, 355 1965 )

    Article  ADS  Google Scholar 

  26. W. Dietrich, E.H. Graf, C.H. Huang, L. Passell: Phys. Rev. A 5, 1377 (1972)

    Article  ADS  Google Scholar 

  27. N.M. Blagoveshchenskii, E.B. Dokukin: Sov. Phys. JETP Lett. 28, 363 (1978)

    ADS  Google Scholar 

  28. J.A. Tarvin, L. Passell: Phys. Rev. B 19, 1458 (1979)

    Article  ADS  Google Scholar 

  29. F. Mezei: Phys. Rev. Lett. 44, 1601 (1980)

    Article  ADS  Google Scholar 

  30. F. Mezei, W.G. Stirling: In 75th Jubilee Conf. on Helium-4, ed. by J.G.M. Armitage ( World Scientific, Singapore 1983 ) p. 111

    Google Scholar 

  31. R. Golub, C. Jewell, P. Ageron, W. Mampe, B. Heckel, I. Kilvington: Z. Phys. B 51, 187 (1983)

    Article  ADS  Google Scholar 

  32. L.D. Landau, I.M. Khalatnikov: Zh. Eksp. Teor. Fiz. 19, 637 (1949)

    Google Scholar 

  33. P.J. Bendt, R.D. Cowan, J.L. Yarnell: Phys. Rev. 113, 1386 (1959)

    Article  ADS  Google Scholar 

  34. J.S. Brooks, R.J. Donnelly: J. Phys. Chem. Ref. Data 6, 51 (1977)

    Article  ADS  Google Scholar 

  35. A.D.B. Woods, E.C. Svensson, P. Martel: In Neutron Inelastic Scattering 1972 ( International Atomic Energy Agency, Vienna 1972 ) p. 359

    Google Scholar 

  36. A.D.B. Woods, E.C. Svensson, P. Martel: Phys. Lett. 43A, 223 (1973)

    Article  Google Scholar 

  37. E.H. Graf, V.J. Minkiewicz, H. Bjerrum Miller, L. Passell: Phys. Rev. A 10, 1748 (1974)

    Article  ADS  Google Scholar 

  38. B.A. Dasannacharya, A. Kollmar, T. Springer: Phys. Lett. 55A, 337 (1976)

    Article  Google Scholar 

  39. A.D.B. Woods, E.C. Svensson, P. Martel: Can. J. Phys. 56, 302 (1978)

    Article  ADS  Google Scholar 

  40. A. Miller, D. Pines, P. Nozieres: Phys. Rev. 127, 14522 1962 )

    Google Scholar 

  41. J. Maynard: Phys. Rev. B 14, 3868 (1976)

    Article  ADS  Google Scholar 

  42. A.D.B. Woods, E.C. Svensson: Unpublished work based on the study reported in [15]

    Google Scholar 

  43. V.P. Mineev: Sov. Phys. JETP Lett. 32, 489 (1980)

    ADS  Google Scholar 

  44. K. Bedell, D. Pines, I. Fomin: J. Low Temp. Phys. 48, 417 (1982)

    Article  ADS  Google Scholar 

  45. K. Bedell, D. Pines, A. Zawadowski: Phys. Rev. B 29, 102 (1984)

    Article  ADS  Google Scholar 

  46. E.C. Svensson, V.F. Sears, A.D.B. Woods, P. Martel: Phys. Rev. B 21, 3638 (1980) and V.F. Sears, E.C. Svensson, A.D.B. Woods, P. Martel: Atomic Energy of Canada Limited Report No. AECL-6779 (1979)

    Article  ADS  Google Scholar 

  47. E.C. Svensson, V.F. Sears, A. Griffin: Phys. Rev. B 23 4493 (1981)

    Article  ADS  Google Scholar 

  48. E.C. Svensson, A.F. Murray, Physica 108B, 1317 (19813

    Google Scholar 

  49. T.J. Greytak, J. Yan: In Proc. 12th It Conf. on Low Temperature Physics, ed. by E. Kanda ( Keigaku Publ. Co., Tokyo 1971 ) p. 89

    Google Scholar 

  50. A.D.B. Woods, P.A. Hilton, R. Scherm, W.G. Stirling: J. Phys. C 10, L45 (1977)

    Article  ADS  Google Scholar 

  51. A. Griffin: Phys. Rev. B 19, 5946 (1979), Phys. Lett. 71A, 237 (1979) and J. Low Temp. Phys. 44, 441 (1981)

    Google Scholar 

  52. A. Griffin, E. Talbot: Phys. Rev. B 24, 5075 (1981)

    Article  ADS  Google Scholar 

  53. E. Talbot, A. Griffin: Ann. Phys. (N.T.) 151, 71 (1983)

    Article  ADS  Google Scholar 

  54. E. Talbot, A. Griffin: Phys. Rev. B 29 2531 (1984)

    Article  ADS  Google Scholar 

  55. K. Yamada: Prog. Theor. Phys. 63, 715 (1980) and K. Ishikawa, K. Yamada: These proceedings

    Article  ADS  Google Scholar 

  56. A. Griffin: Can. J. Phys. 65, 1368 (1987) and these proceedings

    Article  ADS  Google Scholar 

  57. S.H. Payne, A. Griffin: Phys. Rev. B 32, 7199 (1985)

    Article  ADS  Google Scholar 

  58. A. Griffin, S.H. Payne: J. Low Temp. Phys. 64, 155 (1986)

    Article  ADS  Google Scholar 

  59. H.J. Maris: Rev. Mod. Phys. 49, 341 (1977)

    Article  ADS  Google Scholar 

  60. W.G. Stirling: In 75th Jubilee Conf. on Helium-4, ed. by J.G.M. Armitage ( World Scientific, Singapore 1983 ) p. 109

    Google Scholar 

  61. E.C. Svensson, D.C. Tennant: In Proc. 18th Int. Conf. on Low Temperature Physics, Jpn. J. Appl. Phys. 26 (Suppi. 26–3), 31 (1987)

    Google Scholar 

  62. V.K. Wong: Phys. Lett. 61A, 454 (1977)

    Article  Google Scholar 

  63. F.H. Wirth, R.B. Hallock: Phys. Rev. B 35, 89 (1987)

    Article  ADS  Google Scholar 

  64. K. Ohbayashi, M. Udagawa: Phys. Rev. B 31, 1324 (1985)

    Article  ADS  Google Scholar 

  65. M. Udagawa, H. Nakamura, M. Murakami, K. Ohbayashi: Phys. Rev. B 34, 1563 (1986)

    Article  ADS  Google Scholar 

  66. M. Udagawa, T. Imada, K. Ohbayashi: J. Phys. C 20, 1063 (1987)

    Article  ADS  Google Scholar 

  67. K. Ohbayashi, M. Udagawa, M. Watabe: Can. J. Phys. 65, 1571 (1987) and M. Udagawa, M. Watabe, K. Ohbayashi: These proceedings

    Article  ADS  Google Scholar 

  68. K. Ohbayashi: Private communication and these proceedings

    Google Scholar 

  69. J. Ruvalds: Phys. Rev. Lett. 27, 1769 (1971)

    Article  ADS  Google Scholar 

  70. W.G. Stirling: In Proc. 2nd Int. Conf. on Phonon Physics, ed. by J. Kollar, N. Kroo, N. Menyhard, T. Siklos ( World Scientific, Singapore 1985 ) p. 829

    Google Scholar 

  71. H.W. Jackson: Phys. Rev. A 4, 2386 (1971) and 8, 1529 (1973)

    Article  ADS  Google Scholar 

  72. F. Iwamoto, K. Nagai, K. Nojima: In Proc. 12th Int. Conf. on Low Temperature Physics, ed. by E. Kanda ( Keigaku Publ. Co., Tokyo 1971 ) p. 189

    Google Scholar 

  73. W. Götze, M. Lucke: Phys. Rev. B 13, 3825 (1976)

    Article  ADS  Google Scholar 

  74. E. Manousakis, V.R. Pandharipande: Phys. Rev. B 33, 150 (1986) and E. Manousakis: Ph.D. Thesis, Univ. of Illinois at Urbana Champaign, 1985

    Article  ADS  Google Scholar 

  75. K. Fukushima, N. Koyama, T. Sugiyama: Prog. Theor. Phys. 61, 367 (1979)

    Article  ADS  Google Scholar 

  76. K. Fukushima, F. Iseki: Phys. Rev. B 38, 4448 (1988) and these proceedings.

    Article  ADS  Google Scholar 

  77. W.G. Stirling: Private communication

    Google Scholar 

  78. K. Sköld, C.A. Pelizzari: Phil. Trans. R. Soc. Lond. B 290, 605 (1980)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin, Heidelberg

About this paper

Cite this paper

Svensson, E.C. (1989). Temperature Dependence of S(Q, ω) for Liquid 4He. In: Ohbayashi, K., Watabe, M. (eds) Elementary Excitations in Quantum Fluids. Springer Series in Solid-State Sciences, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83428-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83428-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83430-1

  • Online ISBN: 978-3-642-83428-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics