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.
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References
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.
P. G. de Gennes, Phys. Lett. 44A, 271 (1973).
R. Graham, Phys. Rev. Lett. 33, 1431 (1974).
R. Graham and H. Pleiner, Phys. Rev. Lett. 34, 792 (1975).
M. Liu, Phys. Rev. B 13, 4174 (1976).
C. R. Hu and W. M. Saslow, Phys. Rev. Lett. 38, 605 (1977).
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.
D. Lhuillier, J. Phys. (Paris) Lett. 38, 121 (1977).
V. V. Lebedev and I. M. Khalatnikov, Sov. Phys.—JETP 46, 808 (1977).
I. M. Khalatnikov and V. V. Lebedev, Phys. Lett. 61A, 319; J. Low Temp. Phys. 32, 789 (1978).
H. E. Halland J. R. Hook, J. Phys. C 10, L91 (1977).
J. R. Hook and H. E. Hall, J. Phys. C 12, 783 (1979).
M. Liu and M. C. Cross, Phys. Rev. Lett. 43, 296 (1979).
P. Wölfle, Phys. Lett. 47A, 224 (1974).
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.
M. C. Cross, J. Low Temp. Phys. 21, 525 (1975).
A. J. Leggett and S. Takagi, Phys. Rev. Lett. 36, 1379 (1979); Ann. Phys. (N. Y.) 110, 353 (1978); Erratum 112, 485 (1978).
C. J. Pethick and H. Smith, Phys. Rev. Lett. 37, 226 (1976).
M. Combescot and R. Combescot, Phys. Rev. Lett. 37, 388 (1976).
M. Ishikawa, Prog. Theor. Phys. 52, 1 (1977).
G. E. Volovik and V. P. Mineev, Sov. Phys.—JETP 44, 591 (1977).
M. C. Cross, J. Low Temp. Phys. 26, 165 (1977).
N. V. Kopnin, Sov. Phys.—JETP 47, 804 (1978).
R. Combescot, preprint (unpublished).
K. Nagai, J. Low Temp. Phys. 36, 485 (1979).
J. Hara and K. Nagai, J. Low Temp. Phys. 34, 351 (1979).
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).
A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975).
P. W. Anderson and P. Morel, Phys. Rev. 123, 1911 (1961).
P. W. Anderson and W. F. Brinkman, Phys. Rev. Lett. 30, 1108 (1973).
P. Wölfle, J. Low Temp. Phys. 22, 157 (1976).
L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1965).
A. A. Abrikosov and I. M. Khalatnikov, Rep. Prog. Phys. 22, 329 (1959).
J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972), Chap. 5.
P. Bhattacharrya, C. J. Pethick, and H. Smith, Phys. Rev. B 15, 3367 (1977).
P. Wölfle, J. Low Temp. Phys. 26, 659 (1977).
R. Combescot and T. Dombre, preprint.
K. Nagai, to be published.
H. Brand, M. Dörfle, and R. Graham, Ann. Phys. (N.Y.) 119, 434 (1979).
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Nagai, K. Theory of orbital dynamics of the A phase of superfluid 3He. II. Orbital hydrodynamic equations. J Low Temp Phys 38, 677–705 (1980). https://doi.org/10.1007/BF00115497
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DOI: https://doi.org/10.1007/BF00115497