Journal of Low Temperature Physics

, Volume 38, Issue 5–6, pp 677–705 | Cite as

Theory of orbital dynamics of the A phase of superfluid 3He. II. Orbital hydrodynamic equations

  • K. Nagai
Article
Received:

Orbital hydrodynamic equations in 3He-A are derived microscopically in the hydrodynamic regime near the transition temperature. Transport coefficients as well as reactive coefficients are evaluated as rigorously as possible. The expression for the time derivative of the phase of the order parameter is shown to contain l · rot Ν n with the Yosida function as a coefficient. It is shown that when the supercurrent is given by the usual definition which includes only the first-order space derivative of the order parameter, the stress tensor becomes antisymmetric and there is an additional contribution to the local angular momentum density of dynamical origin. The stress tensor can be made symmetric by changing the definition of the supercurrent.

Keywords

Transition Temperature Angular Momentum Stress Tensor Magnetic Material Time Derivative 
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References

  1. 1.
    W. F. Brinkman and M. C. Cross, in Progress in Low Temperature Physics, D. F. Brewer, ed. (North-Holland, Amsterdam, 1978), Vol. VIIA, Chap. 2.Google Scholar
  2. 2.
    P. G. de Gennes, Phys. Lett. 44A, 271 (1973).Google Scholar
  3. 3.
    R. Graham, Phys. Rev. Lett. 33, 1431 (1974).Google Scholar
  4. 4.
    R. Graham and H. Pleiner, Phys. Rev. Lett. 34, 792 (1975).Google Scholar
  5. 5.
    M. Liu, Phys. Rev. B 13, 4174 (1976).Google Scholar
  6. 6.
    C. R. Hu and W. M. Saslow, Phys. Rev. Lett. 38, 605 (1977).Google Scholar
  7. 7.
    T. L. Ho, in Quantum Fluids and Solids, S. B. Trickey, E. D. Adams, and J. W. Dufty, eds. (Plenum, New York, 1977), p. 97.Google Scholar
  8. 8.
    D. Lhuillier, J. Phys. (Paris) Lett. 38, 121 (1977).Google Scholar
  9. 9.
    V. V. Lebedev and I. M. Khalatnikov, Sov. Phys.—JETP 46, 808 (1977).Google Scholar
  10. 10.
    I. M. Khalatnikov and V. V. Lebedev, Phys. Lett. 61A, 319; J. Low Temp. Phys. 32, 789 (1978).Google Scholar
  11. 11.
    H. E. Halland J. R. Hook, J. Phys. C 10, L91 (1977).Google Scholar
  12. 12.
    J. R. Hook and H. E. Hall, J. Phys. C 12, 783 (1979).Google Scholar
  13. 13.
    M. Liu and M. C. Cross, Phys. Rev. Lett. 43, 296 (1979).Google Scholar
  14. 14.
    P. Wölfle, Phys. Lett. 47A, 224 (1974).Google Scholar
  15. 15.
    M. C. Cross and P. W. Anderson, in Proceedings Of LT14, M. Krusius and M. Vuorio, eds. (North-Holland, Amsterdam, 1975), Vol. 1, p. 29.Google Scholar
  16. 16.
    M. C. Cross, J. Low Temp. Phys. 21, 525 (1975).Google Scholar
  17. 17.
    A. J. Leggett and S. Takagi, Phys. Rev. Lett. 36, 1379 (1979); Ann. Phys. (N. Y.) 110, 353 (1978); Erratum 112, 485 (1978).Google Scholar
  18. 18.
    C. J. Pethick and H. Smith, Phys. Rev. Lett. 37, 226 (1976).Google Scholar
  19. 19.
    M. Combescot and R. Combescot, Phys. Rev. Lett. 37, 388 (1976).Google Scholar
  20. 20.
    M. Ishikawa, Prog. Theor. Phys. 52, 1 (1977).Google Scholar
  21. 21.
    G. E. Volovik and V. P. Mineev, Sov. Phys.—JETP 44, 591 (1977).Google Scholar
  22. 22.
    M. C. Cross, J. Low Temp. Phys. 26, 165 (1977).Google Scholar
  23. 23.
    N. V. Kopnin, Sov. Phys.—JETP 47, 804 (1978).Google Scholar
  24. 24.
    R. Combescot, preprint (unpublished).Google Scholar
  25. 25.
    K. Nagai, J. Low Temp. Phys. 36, 485 (1979).Google Scholar
  26. 26.
    J. Hara and K. Nagai, J. Low Temp. Phys. 34, 351 (1979).Google Scholar
  27. 27.
    K. Nagai, in Lecture Notes in Physics, Proceedings of the 16th Winter School of Theoretical Physics (Karpacz, Poland, February 1979) (Springer Verlag, to be published).Google Scholar
  28. 28.
    A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975).Google Scholar
  29. 29.
    P. W. Anderson and P. Morel, Phys. Rev. 123, 1911 (1961).Google Scholar
  30. 30.
    P. W. Anderson and W. F. Brinkman, Phys. Rev. Lett. 30, 1108 (1973).Google Scholar
  31. 31.
    P. Wölfle, J. Low Temp. Phys. 22, 157 (1976).Google Scholar
  32. 32.
    L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1965).Google Scholar
  33. 33.
    A. A. Abrikosov and I. M. Khalatnikov, Rep. Prog. Phys. 22, 329 (1959).Google Scholar
  34. 34.
    J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972), Chap. 5.Google Scholar
  35. 35.
    P. Bhattacharrya, C. J. Pethick, and H. Smith, Phys. Rev. B 15, 3367 (1977).Google Scholar
  36. 36.
    P. Wölfle, J. Low Temp. Phys. 26, 659 (1977).Google Scholar
  37. 37.
    R. Combescot and T. Dombre, preprint.Google Scholar
  38. 38.
    K. Nagai, to be published.Google Scholar
  39. 39.
    H. Brand, M. Dörfle, and R. Graham, Ann. Phys. (N.Y.) 119, 434 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • K. Nagai
    • 1
  1. 1.Max-Planck-Institut für Physik und AstrophysikMunichWest Germany

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