Skip to main content
SpringerLink
Log in
Book cover

Modern trends in Superconductivity and Superfluidity pp 117–149Cite as

Quantum Hydrodynamics of the P-Wave Superfluids with the Symmetry of 3He-A

  • Chapter
  • First Online:

  • 1999 Accesses

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

Abstract

In the present chapter we derive the equations of orbital hydrodynamics and analyze the spectrum of collective excitations for bosonic and fermionic p-wave triplet superfluids with the symmetry of A-phase.

This is a preview of subscription content, 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

Learn about institutional subscriptions

References

  1. Andreev, A.F., Kagan, M.Yu.: JETP 66, 594 (1987)

    Google Scholar 

  2. Kagan, M.Yu., Efremov, D.V.: JLTP 158, 749 (2010)

    Article  ADS  Google Scholar 

  3. Kagan, M.Yu., Efremov, D.V.: JETP 110, 426 (2010)

    Article  Google Scholar 

  4. Balatskii, A.V., Volovik, G.E., Konyshev, V.A.: JETP 63, 1194 (1986)

    Google Scholar 

  5. Volovik, G.E.: JETP Lett. 43, 428 (1986)

    Google Scholar 

  6. Volovik, G.E.: JETP Lett. 42, 363 (1985)

    ADS  Google Scholar 

  7. Volovik, G.E., Mineev, V.P.: JETP 56, 579 (1976)

    Google Scholar 

  8. Volovik, G.E., Mineev, V.P.: JETP 71, 1129 (1976)

    Google Scholar 

  9. Combescot, R., Dombre, T.: Phys. Rev. B 33, 79 (1986)

    Article  ADS  Google Scholar 

  10. Combescot, R., Dombre, T.: Phys. Rev. B 28, 5140 (1983)

    Article  ADS  Google Scholar 

  11. Volkov, D.V., Akulov, V.P.: JETP Lett. 16, 438 (1972)

    ADS  Google Scholar 

  12. Kee H.-Y., Raghavan A., Maki K.: arXiv:0711.0929 (2007)

    Google Scholar 

  13. Roy, R., Kallin, C.: Phys. Rev. B 77, 174513 (2008)

    Article  ADS  Google Scholar 

  14. Ivanov, D.A.: Phys. Rev. Lett. 89, 208 (2001)

    Google Scholar 

  15. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A.: Nature 438, 197 (2005)

    Article  ADS  Google Scholar 

  16. Tajima, N., Sugawara, S., Tamura, M., Kato, R., Nishio, Y., Kajita, K.: Europhys. Lett. 80, 47002 (2007)

    Article  ADS  Google Scholar 

  17. Vollhardt, D., Wölfle, P.: The superfluid phases of Helium 3. Taylor and Francis, London (1990)

    Google Scholar 

  18. Landau, L.D., Lifshitz, E.M.: Electrodynamics of Continuous Media. Pergamon Press, New York (1984)

    Google Scholar 

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

    Google Scholar 

  20. Lifshitz, E.M., Pitaevskii, L.P.: Statistical Physics. Pergamon Press, New York (1988). Part II

    Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  22. Cooper, L.N.: Phys. Rev. 104, 1189 (1956)

    Article  MATH  ADS  Google Scholar 

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

    MATH  Google Scholar 

  24. Landau L.D., Lifshitz E.M.: Fluid Mechanics. Butterworth-Heinemann (1987)

    Google Scholar 

  25. Khalatnikov, I.M.: An Introduction to the Theory of Superfluidity. Perseus Books Group, New York (1989)

    Google Scholar 

  26. Berestetskii V.B., Lifshitz E.M., Pitaevskii L.P.: Quantum Electrodynamics. Butterworth-Heinemann (1982)

    Google Scholar 

  27. Bethe, H.A., Salpeter, E.E.: Quantum Mechanics of One and Two Electron Atoms. Springer, Berlin (1957)

    Book  MATH  Google Scholar 

  28. Ward, J.C.: Phys. Rev. 78, 182 (1950)

    Article  MATH  ADS  Google Scholar 

  29. Volovik, G.E.: The Universe in Helium Droplet. Oxford University Press, Oxford (2002)

    Google Scholar 

  30. Volovik, G.E.: Exotic Properties of Superfluid 3He. World Scientific, Singapore (1992)

    Book  Google Scholar 

  31. Leggett, A.J.: Modern Trends in the Theory of Condensed Matter Physics, p. 14. Springer, Berlin (1980)

    Google Scholar 

  32. Nozieres, P., Schmitt-Rink, S.: JLTP 59, 195 (1985)

    Article  ADS  Google Scholar 

  33. Ticknor, C., Regal, C.A., Jin, D.S., Bohn, J.L.: Phys. Rev. A 69, 042712 (2004)

    Article  ADS  Google Scholar 

  34. Regal, C.A., Ticknor, C., Bohn, J.L., Jin, D.S.: Phys. Rev. Lett. 90, 053201 (2003)

    Article  ADS  Google Scholar 

  35. Schunck, C.H., Zwierlin, M.W., Stan, C.A., Raupach, S.M.F., Ketterle, W., Simoni, A., Tiesinga, E., Williams, C.J., Julienne, P.S.: Phys. Rev. A 71, 045601 (2005)

    Article  ADS  Google Scholar 

  36. de Gennes, P.G.: The Physics of Liquid Crystals. Oxford University Press, London (1974)

    Google Scholar 

  37. de Gennes, P.G.: Phys. Lett. A 44, 271 (1973)

    Article  ADS  Google Scholar 

  38. de Gennes, P.G.: Superconductivity of Metals and Alloys. Benjamin, New York (1966)

    MATH  Google Scholar 

  39. Mermin, N.D., Ho, T.L.: Phys. Rev. Lett. 36, 594 (1977)

    Article  ADS  Google Scholar 

  40. Putterman, S.J.: Superfluid Hydrodynamics. North-Holland Publishing Company, New York (1974)

    Google Scholar 

  41. Vaks, V.G., Galitskii, V.M., Larkin, A.I.: JETP 15, 914 (1962)

    MATH  Google Scholar 

  42. Stone M., Anduaga I.: Ann. Phys. (Weinheim), 323, 2 (2008)

    Google Scholar 

  43. Stone M., Gaitan F.: Ann. Phys. (Weinheim), 178, 89 (1987)

    Google Scholar 

  44. Stone, M.: Phys. Rev. B 54, 13222 (1996)

    Article  ADS  Google Scholar 

  45. Stone, M.: Physica B 280, 117 (2000)

    Article  ADS  Google Scholar 

  46. Stone, M., Roy, R.: Phys. Rev. B 69, 184511 (2004)

    Article  ADS  Google Scholar 

  47. Gaitan, F.: Phys. Lett. A 151, 551 (1990)

    Article  ADS  Google Scholar 

  48. Mermin, N.D., Muzikar, P.: Phys. Rev. B 21, 980 (1980)

    Article  ADS  Google Scholar 

  49. Leggett A.J.: Private communication

    Google Scholar 

  50. Andreev, A.F., Marchenko, V.I.: Sov. Phys. Uspekhi 23, 21 (1977)

    Article  ADS  Google Scholar 

  51. Tsvelik A.M.: Quantum Field Theory in Condensed Matter Physics. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  52. Berezin, F.A.: The Method of Second Quantization. Academic Press, New York and London (1966)

    MATH  Google Scholar 

  53. Slavnov A., Faddeev L.: Gauge Fields: An Introduction to Quantum Theory. Westview Press (1993)

    Google Scholar 

  54. Feynmann, R.P., Hibbs, A.: Quantum Mechanics and Path Integrals. McGraw-Hill Companies, New York (1965)

    Google Scholar 

  55. Feynmann, R.P.: The Feynman Lectures on Physics, Addison Wesley Longman (1970)

    Google Scholar 

  56. Popov, V.N.: Functional Integrals in Quantum Field Theory and Statistical Physics. Kluwer, Dordrecht (1983)

    Book  MATH  Google Scholar 

  57. Alonso, V., Popov, V.I.: JETP 46, 760 (1977)

    ADS  Google Scholar 

  58. Bogoliubov N.N, Shirkov D.V.: Introduction to the theory of quantized fields. Wiley, New York (1980)

    Google Scholar 

  59. Bjorken J.D., Drell S.D.: Relativistic Quantum Mechanics and Relativistic Quantum Fields. McGraw-Hill, New York (1964)

    Google Scholar 

  60. Landau, L.D., Lifshitz, E.M.: Quantum Mechanics: Nonrelativistic Theory, 3rd edn. Pergamon Press, Oxford (1977). (problem to paragraph 17, p. 52)

    Google Scholar 

  61. Cross, M.C.: JLTP 21, 525 (1975)

    Article  ADS  Google Scholar 

  62. Cross, M.C.: JLTP 26, 165 (1977)

    Article  ADS  Google Scholar 

  63. Nagai, K.: JLTP 38, 677 (1980)

    Article  ADS  Google Scholar 

  64. Dmitriev, V.V., Krasnikhin, D.A., Mulders, N., Zavjalov, V.V., Zmeev, D.E.: JETP Lett. 86, 594 (2007)

    Article  ADS  Google Scholar 

  65. Elbs, J., Bunkov, Yu.M, Collin, E., Godfrin, H., Volovik, G.E.: Phys. Rev. Lett. 100, 215304 (2008)

    Article  ADS  Google Scholar 

  66. Fomin, I.A.: JETP Lett. 88, 59 (2008)

    Article  ADS  Google Scholar 

  67. Fomin, I.A.: JETP Lett. 77, 240 (2003)

    Article  ADS  Google Scholar 

  68. Volovik, G.E.: JETP Lett. 61, 958 (1995)

    ADS  Google Scholar 

  69. Volovik, G.E.: JETP 75, 990 (1992)

    MathSciNet  Google Scholar 

  70. Thouless, D.J., Ao, P., Niu, Q.: Phys. Rev. Lett. 76, 3758 (1996)

    Article  ADS  Google Scholar 

  71. Kopnin, N.B., Salomaa, M.M.: Phys. Rev. B 44, 9667 (1991)

    Article  ADS  Google Scholar 

  72. Kopnin N.B.: Physica B 210, 267 (1995)

    Google Scholar 

  73. Kopnin, N.B., Soinen, P.S., Salomaa, M.M.: Phys. Rev. B 45, 5491 (1992)

    Article  ADS  Google Scholar 

  74. Vakaryuk, V., Leggett, A.J.: Phys. Rev. Lett. 103, 057003 (2009)

    Article  ADS  Google Scholar 

  75. Bevan, T.D.C., Mannien, A.J., Cook, J.B., Alles, H., Hook, J.R., Hall, H.E.: JLTP 109, 423 (1997)

    ADS  Google Scholar 

  76. Bevan, T.D.C., Mannien, A.J., Cook, J.B., Hook, J.R., Hall, H.E., Vachaspati, T., Volovik, G.E.: Nature 386, 689 (1997)

    Article  ADS  Google Scholar 

  77. Chubukov, A.V.: Phys. Rev. B 44, 12318 (1995)

    Article  ADS  Google Scholar 

  78. Chubukov A.V: Phys. Rev. B 52, R3840 (1995)

    Google Scholar 

  79. Abrikosov A.A, Gor’kov L.P.: JETP 12, 1243 (1961)

    Google Scholar 

  80. Larkin, A.I.: JETP 31, 784 (1970)

    ADS  Google Scholar 

  81. Volovik, G.E., Solov’ev, A., Yakovenko, V.M.: JETP Lett. 49, 65 (1989)

    Google Scholar 

  82. Read, N., Green, D.: Phys. Rev. B 61, 10267 (2000)

    Article  ADS  Google Scholar 

  83. Gurarie V., Radzihovsky L.: Ann. Phys. (Weinheim), 322, 2 (2007)

    Google Scholar 

  84. Cheng, C.H., Yip, S.K.: Phys. Rev. Lett. 95, 070404 (2005)

    Google Scholar 

  85. Klinkhamer, F.R., Volovik, G.E.: JETP Lett. 80, 343 (2004)

    Article  ADS  Google Scholar 

  86. Volovik, G.E.: JETP Lett. 90, 398 (2009)

    Article  ADS  Google Scholar 

  87. Volovik G.E.: JETP Lett., 90, 587 (2009) and references therein

    Google Scholar 

  88. Berry, M.V.: Proc. Roy. Soc. London A 392, 45 (1984)

    Article  MATH  ADS  Google Scholar 

  89. Leggett, A.J.: Rev. Mod. Phys. 47, 331 (1975)

    Article  ADS  Google Scholar 

  90. Bogoliubov, N.N.: JETP 34, 58 (1958)

    Google Scholar 

  91. Bogoliubov, N.N.: JETP 34, 73 (1958)

    Google Scholar 

  92. Bogoliubov, N.N., Tolmachev, N.N., Shirkov, D.V.: A New Method in the Theory of Superconductivity. Consultants Bureau, New York (1959)

    Google Scholar 

  93. Schwinger, J.: Phys. Rev. 82, 664 (1951)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  94. Schwinger, J.: Phys. Rev. 128, 2425 (1962)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  95. Schwinger J.: Particles, Sources and Fields, vol. 1,2. Addison Wesley, Reading (1970) and (1973)

    Google Scholar 

  96. Adler, S.: Phys. Rev. 177, 2426 (1969)

    Article  ADS  Google Scholar 

  97. Adler S: Lectures on Elementary Particles and Quantum Field Theory. In: Desser S., Grissaru M., Pendelton H. (ed.) Cambridge MIT (1970)

    Google Scholar 

  98. Adler, S., Dashen, R.: Current Algebras. Benjamin, New York (1968)

    MATH  Google Scholar 

  99. Itzykson C., Zuber Z.-B.: Quantum Field Theory, vol. 2. Dover Publications (2006)

    Google Scholar 

  100. Bell, J.S., Jackiw, R.: Nuovo Cimento, Series A 60, 47 (1969)

    Article  ADS  Google Scholar 

  101. Jackiw R.: Lectures on Current Algebra and its Applications. Princeton University Press (1972)

    Google Scholar 

  102. Bardeen, W.A.: Phys. Rev. 184, 1848 (1969)

    Article  ADS  Google Scholar 

  103. Williams, J.R., Goldhaber-Gordon, D.: Nat. Phys. 8, 778 (2012)

    Article  Google Scholar 

  104. Ivanov, D.A.: Phys. Rev. Lett. 86, 268 (2001)

    Article  ADS  Google Scholar 

  105. Gong, M., Tewari, S., Zhang, C.: Phys. Rev. Lett. 107, 195303 (2011)

    Article  ADS  Google Scholar 

  106. Gong, M., Chen, G., Jia, S., Zhang, C.: Phys. Rev. Lett. 109, 105302 (2012)

    Article  ADS  Google Scholar 

  107. Lutchyn, R.M., Sau, J.D., Das Sarma, S.: Phys. Rev. Lett. 105, 077001 (2010)

    Article  ADS  Google Scholar 

  108. Mourik, V., Zuo, K., Frolov, S.M., Plissard, S.R., Bakkers, E.P.A.M., Kouwenhoven, L.P.: Science 336, 1003 (2012)

    Article  ADS  Google Scholar 

  109. Oreg, Y., Refael, G., von Oppen, F.: Phys. Rev. Lett. 105, 177002 (2010)

    Article  ADS  Google Scholar 

  110. Brusov, P.N., Brusov, P.P.: Collective Excitations in Unconventional Superconductors and Superfluids. World Scientific, New Jersey (2010)

    Google Scholar 

  111. Brusov, P.N., Lomakov, M.V., Brusova, N.P.: Sov. Jour. Low. Temp. Phys. 21, 85 (1995)

    Google Scholar 

  112. Brusov, P.N., Lomakov, M.V.: JLTP 85, 91 (1991)

    Google Scholar 

  113. Haldane, F.D.M.: Phys. Lett. 93A, 464 (1983)

    Google Scholar 

  114. Haldane, F.D.M.: Phys. Rev. Lett. 50, 1153 (1993)

    Google Scholar 

  115. Josephson, B.D.: In Superconductivity, ed. Parks, R.D. M. Dekker, New York (1969)

    Google Scholar 

  116. Josephson, B.D.: Phys. Lett. 1, 251 (1962)

    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). Quantum Hydrodynamics of the P-Wave Superfluids with the Symmetry of 3He-A. 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_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-6961-8_4

  • 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