Skip to main content
SpringerLink
Log in

Hydrodynamics of Rotating Superfluids with Quantized Vortices

  • Chapter
  • First Online:
Modern trends in Superconductivity and Superfluidity

Part of the book series: Lecture Notes in Physics ((LNP,volume 874))

  • 2053 Accesses

Abstract

While many forthcoming Chapters of the present manuscript deal with the microscopical models for the description of Quantum Gases, Fluids and Solids, as well as strongly correlated electron systems, the first four Chapters are devoted to a purely phenomenological (macroscopic) description of hydrodynamic phenomena in anisotropic and inhomogeneous superfluids and superconductors.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Landau, L.D., Lifshitz, E.M.: Fluid Mechanics, vol. 6 (Course of Theoretical Physics). Butterworth-Heinemann, Oxford (1987)

    Google Scholar 

  2. Landau, L.D.: J. Phys. (USSR) 5, 71 (1941)

    Google Scholar 

  3. Landau, L.D.: Phys. Rev. 75, 884–885 (1949)

    Google Scholar 

  4. Kapitza, P.L.: J. Phys. (USSR) 5, 59 (1941)

    Google Scholar 

  5. Kapitza, P.L.: Phys. Rev. 60, 354–355 (1941)

    Google Scholar 

  6. Landau, L.D., Lifshitz, E.M.: Quantum Mechanics. Non-Relativistic Theory. Pergamon Press, New York (1977)

    Google Scholar 

  7. Landau, L.D., Lifshitz, E.M.: Statistical Physics, Part I. Butterworth-Heinemann, Oxford (1999)

    Google Scholar 

  8. Allen, J.F., Misner, A.D.: Nature 141, 75(1938)

    Google Scholar 

  9. Allen, J.F., Misner, A.D.: Proc. Roy. Soc. A 172, 467 (1939)

    Google Scholar 

  10. Tisza, L.: Nature 141, 913 (1938)

    Google Scholar 

  11. Tisza, L.: Compt. Rend. 207, 1035, 1186 (1938)

    Google Scholar 

  12. Tisza, L.: J. Phys. Rad. 1, 164, 350 (1940)

    Google Scholar 

  13. Tisza, L.: Phys. Rev. 72, 838–854 (1947)

    Google Scholar 

  14. Khalatnikov, I.M.: An Introduction to the Theory of Superfluidity. Perseus Publishing, Cambridge (2000)

    Google Scholar 

  15. Bekarevich, I.L., Khalatnikov, I.M.: JETP 13, 643 (1962)

    Google Scholar 

  16. Putterman, S.J.: Superfluid Hydrodynamics (North-Holland series in low temperature physics). North-Holland, New York (1974). (and the reference therein)

    Google Scholar 

  17. Andronikashvili, E.L., Mamaladze, Y.G.: Rev. Mod. Phys. 38, 567–625 (1966)

    Google Scholar 

  18. Andronikashvili, E.L.: JETP 18, 424 (1948)

    Google Scholar 

  19. Feynman, R.P.: Progr. Low Temp. Phys. 1, Chap. 2, 17–53 (1955)

    Google Scholar 

  20. Onsager, L.: Nuovo Cimento 6(Suppl. 2), 249 (1949)

    Google Scholar 

  21. Feynman, R.P.: Statistical Mechanics: A Set of Lectures (Advanced Books Classics). Westview Press, Boulder (1998)

    Google Scholar 

  22. Tilley, D.R., Tilley, J.: Superfluidity and Superconductivity (Graduate Student Series in Physics). Institute of Physics Publishing, Bristol (1990)

    Google Scholar 

  23. Lifshitz, E.M., Pitaevskii, L.P.: Statistical Physics, Part 2. Pergamon, New York (1980)

    Google Scholar 

  24. Abrikosov, A.A.: JETP 5, 1174–1183 (1957)

    Google Scholar 

  25. Schrieffer, J.R.: Theory of Superconductivity. Benjamin, New York (1964)

    Google Scholar 

  26. Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. 108, 1175–1204 (1957)

    Google Scholar 

  27. Baym, G., Chandler, E.: J. Low. Temp. Phys. 50, 57–87 (1983)

    Google Scholar 

  28. Baym, G.: Phys. Rev. B 51, 11697–11703 (1995)

    Google Scholar 

  29. Baym, G.: Phys. Rev. A 69, 043618 (2004)

    Google Scholar 

  30. Gifford, S.A., Baym, G.: Phys. Rev. A 70, 033602 (2004)

    Google Scholar 

  31. Andreev, A.F., Kagan, M.Yu.: JETP 59, 318 (1984)

    Google Scholar 

  32. Tkachenko, V.K.: JETP 22, 1282 (1965)

    Google Scholar 

  33. Tkachenko, V.K.: JETP 23, 1049 (1966)

    Google Scholar 

  34. Tkachenko, V.K.: JETP 29, 245 (1969)

    Google Scholar 

  35. Thomson W. (Lord Kelvin).: Phil. Mag. 10, 155–168 (1880)

    Google Scholar 

  36. Hall, E.: Proc. Roy. Soc. A 245, 546–561 (1958)

    Google Scholar 

  37. Hall, E., Vinen, W.F.: Proc. Roy. Soc. A 238, 215–234 (1956)

    Google Scholar 

  38. Hall, E.: Adv. Phys. 9, 89–146 (1960)

    Google Scholar 

  39. Sonin, E.B.: Rev. Mod. Phys. 59, 87–155 (1987)

    Google Scholar 

  40. Sonin, E.B.: Doctoral Dissertation. Lebedev Physical Institute, Moscow (1981)

    Google Scholar 

  41. Iordanskii, S.V.: JETP 22, 160 (1960)

    Google Scholar 

  42. Lebedev, V.V., Khalatnikov, I.M.: JETP 48, 1167 (1978)

    Google Scholar 

  43. Dzyaloshinskii, I.E., Volovik, G.E.: Ann. Phys. 125, 67–97 (1980)

    Google Scholar 

  44. Gurevich, V.L.: Transport in Phonon Systems (Modern Problems in Condensed Matter Sciences). Elsevier Science Ltd., Oxford, 1988, Kinetics of Phonon Systems, Moscow, Nauka, 1980

    Google Scholar 

  45. Vollhardt, D., Wölfle, P.: The Superfluid Phases of Helium 3. Taylor and Francis, London (1990)

    Google Scholar 

  46. Leggett, A.J.: Rev. Mod. Phys. 47, 331–414 (1975)

    Google Scholar 

  47. Zwierlein, M.W., Abo-Shaeer, J.R., Schirotzek, A., Schunck, C.H., Ketterle, W.:Nature 435, 1047–1051 (2005)

    Google Scholar 

  48. Williams, M.R., Fetter, A.L.: Phys. Rev. B 16, 4846–4852 (1977)

    Google Scholar 

  49. Fetter, A.L.: Phys. Rev. 162, 143–153 (1967)

    Google Scholar 

  50. Fetter, A.L.: Rev. Mod. Phys. 81, 647–691 (2009)

    Google Scholar 

  51. Matvienko, S.I., Kovrizhin, D., Ouvry, S., Shlyapnikov, G.V.: Phys. Rev. A 80, 063621 (2009)

    Google Scholar 

  52. Matvienko, S.I., Shlyapnikov, G.V.: Phys. Rev. A 83, 033604 (2011)

    Google Scholar 

  53. Cooper, N.R., Wilkins, N.K., Gunn, J.M.F.: Phys. Rev. Lett. 87, 120405 (2001)

    Google Scholar 

  54. Cooper, N.R.: Adv. Phys. 57, 539–616 (2008)

    Google Scholar 

  55. Cooper, N.R., Komineas, S., Read, N.: Phys. Rev. A 70, 033604 (2004)

    Google Scholar 

  56. Rezayi, E.H., Haldane, F.D.M.: Phys. Rev. B 50, 17199–17207 (1994)

    Google Scholar 

  57. Rezayi, E.H., Haldane, F.D.M., Yang, K.: Phys. Rev. Lett. 83, 1219–1222 (1999)

    Google Scholar 

  58. Bretin, V., Stock, S., Seurin, Y., Dalibard, J.: Phys. Rev. Lett. 92, 050403 (2004)

    Google Scholar 

  59. Madison, K.W., Chevy, F., Wohlleben, W., Dalibard, J.: Phys. Rev. Lett. 84, 806–809 (2000)

    Google Scholar 

  60. Chevy, F., Madison, K.W., Dalibard, J.: Phys. Rev. Lett. 85, 2223–2227 (2000)

    Google Scholar 

  61. Madison, K.W., Chevy, F., Bretin, V., Dalibard, J.: Phys. Rev. Lett. 86, 4443–4446 (2001)

    Google Scholar 

  62. Ho, T.-L.: Phys. Rev. Lett. 87, 060403 (2001)

    Google Scholar 

  63. Landau, L.D., Lifshitz, E.M.: Theory of Elasticity (Course of Theoretical Physics). Pergamon Press, Oxford (1959)

    Google Scholar 

  64. Lifshitz, E.M., Pitaevskii, L.P.: Physical Kinetics: Course of Theoretical Physics, vol. 10. Butterworth-Heinemann, Oxford (1981)

    Google Scholar 

  65. Kamerlingh Onnes, H.: Proc. Roy. Acad. (Amsterdam), 13, 1903 (1911)

    Google Scholar 

  66. Kamerlingh Onnes, H.: Trans. Faraday Soc. 18, 145–174 (1922)

    Google Scholar 

  67. Shalnikov, A.I.: JETP 14, 753 (1962)

    Google Scholar 

  68. Pitaevskii, L.P.: JETP 13, 451 (1961)

    Google Scholar 

  69. Dalfovo, F., Giorgini, S., Pitaevskii, L.P., Stringari, S.: Rev. Mod. Phys. 71, 463–512 (1999)

    Google Scholar 

  70. Gross, E.P.: Nuovo Cimento 20, 454 (1961)

    Google Scholar 

  71. Gross, E.P.: J. Math. Phys. 4, 195 (1963)

    Google Scholar 

  72. Kim, E., Chan, M.H.W.: Nature 427, 225–227 (2004)

    Google Scholar 

  73. Kim, E., Chan, M.H.W.: Science 305, 1941–1944 (2004)

    Google Scholar 

  74. Andreev, A.F., Lifshitz, I.M.: JETP 56, 2057 (1969)

    Google Scholar 

  75. Leggett, A.J.: Phys. Rev. Lett. 25, 1543–1546 (1970)

    Google Scholar 

  76. Hugenholtz, N.M., Pines, D.: Phys. Rev. 116, 489–506 (1959)

    Google Scholar 

  77. Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields: Course of Theoretical Physics, vol. 2. Butterworth-Heinemann, Oxford (1980)

    Google Scholar 

  78. Volovik, G.E., Dotsenko, V.S.: JETP 51, 65–73 (1980)

    Google Scholar 

  79. Reatto, L.: Phys. Rev. 167, 191–202 (1968)

    Google Scholar 

  80. Kittel, C.: Quantum Theory of Solids. Wiley, New York (1963)

    Google Scholar 

  81. Kittel, C.: Introduction to Solid State Physics. Wiley, New York (1986)

    Google Scholar 

  82. Laughlin, R.B.: Rev. Mod. Phys. 71, 863–874 (1999)

    Google Scholar 

  83. Laughlin, R.B.: Phys. Rev. B 23, 5632–5633 (1981)

    Google Scholar 

  84. Laughlin, R.B.: Phys. Rev. Lett. 50, 1395–1398 (1983)

    Google Scholar 

  85. Laughlin, R.B.: Phys. Rev. B 27, 3383–3389 (1983). In: Prange, R.E., Girvin, S.M. (eds.) The Quantum Hall Effect, 2nd edn. Springer, New York (1990)

    Google Scholar 

  86. Packard, R.E.: XVI international conference on low temperature physics. Physica B+C 109, 110, 1474 (1982)

    Google Scholar 

  87. Yarmchuk, E.J., Gordon, M.J.V., Packard, R.E.: Phys. Rev. Lett. 43, 214–217 (1979)

    Google Scholar 

  88. Yarmchuk, E.J., Packard, R.E.: J. Low Temp. Phys. 46, 479 (1982)

    Google Scholar 

  89. Anderson, M.H., Ensher, J.R., Matthews, M.R., Wieman, C.E., Cornell, E.A.: Science 269, 198–201 (1995)

    Google Scholar 

  90. Bradley, C.C., Sackett, C.A., Tollett, J.J., Hulet, R.G.: Phys. Rev. Lett. 75, 1687–1690 (1995)

    Google Scholar 

  91. Davis, K.B., Mewes, M.-O., Andrews, M.R., van Druten, N.J., Durfee, D.S., Kurn, D.M., Ketterle, W.: Phys. Rev. Lett. 75, 3969–3973 (1995)

    Google Scholar 

  92. Abo-Shaeer, J.R., Raman, C., Vogels, J.M., Ketterle, W.: Science 292, 476–479 (2001)

    Google Scholar 

  93. Reut, L.S., Fisher, I.Z.: JETP 28, 375 (1969)

    Google Scholar 

  94. Abrikosov, A.A., Gor’kov, L.P., Dzyaloshinskii, I.E.: Quantum Field Theoretical Methods in Statistical Physics. Pergamon, New York (1965)

    Google Scholar 

  95. Keesom, W.H., Macwood, G.E.: Physica 5, 737 (1938)

    Google Scholar 

  96. Keesom, W.H., Keesom, A.P.: Physica 2, 557 (1935)

    Google Scholar 

  97. Keesom, W.H.: Helium. Elsevier, Amsterdam (1942)

    Google Scholar 

  98. Lee, T.D., Yang, C.N.: Phys. Rev. 105, 1119–1120 (1957)

    Google Scholar 

  99. Lee, T.D., Huang, K., Yang, C.N.: Phys. Rev. 106, 1135–1145 (1957)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Department, P.L Kapitza Institute for Physical Problems, Kosygin street 2, Moscow, Russia, 119334

    M. Yu. Kagan

Authors
  1. M. Yu. Kagan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Yu. Kagan .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Kagan, M.Y. (2013). Hydrodynamics of Rotating Superfluids with Quantized Vortices. In: Modern trends in Superconductivity and Superfluidity. Lecture Notes in Physics, vol 874. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6961-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-6961-8_1

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-6960-1

  • Online ISBN: 978-94-007-6961-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation