Journal of Low Temperature Physics

, Volume 32, Issue 5–6, pp 789–801 | Cite as

Canonical equations of hydrodynamics of quantum liquids

  • I. M. Khalatnikov
  • V. V. Lebedev
Article

A method of constructing canonical equations for quantum liquids is proposed. For superfluid 4He the forms of the Hamiltonian equations of hydrodynamics and conservation laws are obtained. The kinetic terms in the equations of hydrodynamics are written out. The set of equations obtained is valid up to the λ point. For anisotropic quantum liquid 3He-A canonical equations both for spin and orbital hydrodynamics are found with the spin and orbital moments taken into account. The forms of the laws of the conservation of momentum, angular momentum, mass, and energy are obtained. The kinetic terms in the equations of hydrodynamics are considered, and both the dissipative and reactive coefficients are classified. A transfer equation for the order parameter near the A transition point is proposed with the dissipative term taken into account.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. M. Khalatnikov, Zh. Eksp. Teor. Fiz. 23, 169 (1952).Google Scholar
  2. 2.
    V. L. Pokrovsky and I. M. Khalatnikov, Zh. Eksp. Teor. Fiz. Pis'ma 23, 653 (1976).Google Scholar
  3. 3.
    V. L. Pokrovsky and I. M. Khalatnikov, Zh. Eksp. Teor. Fiz. 71, 1974, (1976).Google Scholar
  4. 4.
    I. M. Khalatnikov and V. V. Lebedev, Zh. Eksp. Teor. Fiz. Pis'ma 25, 377 (1977).Google Scholar
  5. 5.
    I. M. Khalatnikov and V. V. Lebedev, Phys. Lett. 61A, 319 (1977).Google Scholar
  6. 6.
    V. V. Lebedev and I. M. Khalatnikov, Zh. Eksp. Teor. Fiz. 73, 1537 (1977).Google Scholar
  7. 7.
    I. M. Khalatnikov, Theory of Superfluidity (Nauka, Moscow, 1971), Ch. Y.Google Scholar
  8. 8.
    L. P. Pitaevsky, Zh. Eksp. Teor. Fiz. 35, 408 (1958).Google Scholar
  9. 9.
    I. M. Khalatnikov, Zh. Eksp. Teor. Fiz. 57, 489 (1969).Google Scholar
  10. 10.
    A. Z. Patashinsky and V. L. Pokrovsky, Fluctuation Theory of Phase Transitions (Nauka, Moscow, 1975), Ch. Y.Google Scholar
  11. 11.
    P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).Google Scholar
  12. 12.
    A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975).Google Scholar
  13. 13.
    G. E. Volovick and V. P. Mineev, Zh. Eksp. Teor. Fiz. 71, 1129 (1976).Google Scholar
  14. 14.
    A. J. Leggett and S. Takagi, Phys. Rev. Lett. 36, 1379 (1976).Google Scholar
  15. 15.
    M. C. Cross, J. Low Temp. Phys. 26, 165 (1977).Google Scholar
  16. 16.
    T. L. Ho, Orbital Hydrostatics and Hydrodynamics of He3-A, Preprint (1977).Google Scholar
  17. 17.
    G. E. Volovick, The Hydrodynamics of Superfluid 3He and Other Systems with Broken Symmetry, Preprint (1977).Google Scholar
  18. 18.
    R. Graham and H. Pleiner, Phys. Rev. Lett. 34, 792 (1975).Google Scholar
  19. 19.
    R. Graham, Phys. Rev. Lett. 33, 1431 (1974).Google Scholar
  20. 20.
    Ch. R. Hu and W. M. Saslow, Phys. Rev. Lett. 38, 605 (1977).Google Scholar
  21. 21.
    M. Liu, Phys. Rev. Lett. 35, 1577 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • I. M. Khalatnikov
    • 1
  • V. V. Lebedev
    • 1
  1. 1.L. D. Landau Institute for Theoretical Physics, Academy of Sciences of the USSRMoscowUSSR

Personalised recommendations