Abstract
A semimicroscopic kinetic theory of the dilute solutions of3He in superfluid4He is presented. The theory considers only phonon and3He quasiparticle excitations and is therefore applicable at temperatures of up to about 0.6 K. The model underlying the theory utilizes a modified Landau-Pomeranchuck3He energy spectrum and a second-order momentum expansion for the effective3He quasiparticle interaction. In addition, it accounts for the effective phonon-3He quasiparticle interaction, to first order in the phonon momentum, by using a renormalized concentration-dependent sound velocity. The simplicity of the model enables the derivation of both a complete equilibrium theory and a complete set of equations of motion for the solutions. The resulting expressions for the thermodynamic properties and the macroscopic currents appearing in the equations of motion represent a useful parametrization of these quantities in terms of the parameters of the model. It is shown that the macroscopic currents can be written in a form which seems to have a simple physical interpretation. As expected, it is found that at local equilibrium the expressions for the currents reduce correctly to the respective phenomenological expressions.
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References
K. W. Taconis and R. de Bruyn Ouboter, inProgress in Low Temperature Physics, C. J. Gorter, ed. (North-Holland, Amsterdam, 1964), Vol. IV, p. 38.
J. C. Wheatly,Am. J. Phys. 36, 181 (1968).
J. C. Wheatly, inProgress in Low Temperature Physics, C. J. Gorter, ed. (North-Holland, Amsterdam, 1970), Vol. VI, p. 77.
C. Ebner and D. O. Edwards,Phys. Reports 2C, 77 (1971).
W. R. Abel, R. T. Johnson, J. C. Wheatly, and W. Zimmermann,Phys. Rev. Letters 18, 737 (1967).
I. M. Khalatnikov,Zh. Eksperim. i. Teor. Fiz. 23, 265 (1952).
I. M. Khalatnikov and N. V. Zharkov,Soviet Phys.—JEPT 5, 905 (1957).
G. Baym, inMathematical Methods in Solid State and Superfluid Theory, Scottish Universities' Summer School 1967, R. C. Clark and G. H. Derrick, eds. (Plenum Press, New York, 1968), p. 121.
G. Baym and C. Ebner,Phys. Rev. 164, 235 (1967).
G. Baym and W. F. Saam,Phys. Rev. 171, 172 (1968).
G. Baym, W. F. Saam, and C. Ebner,Phys. Rev. 173, 306 (1968).
See, for example, S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases, 2nd ed. (Cambridge University Press, London, 1952).
Y. Disatnik and H. Brucker,J. Low Temp. Phys. 7, 501 (1972).
L. D. Landau,J. Phys. USSR 5, 71 (1941).
N. R. Brubaker, D. O. Edwards, R. E. Sarwinski, P. Seligmann, and R. E. Sherlock,Phys. Rev. Letters 25, 714 (1970).
L. D. Landau and I. Pomeranchuck,Dokl. Akad. Nauk SSSR 59, 669 (1948).
L. D. Landau and I. M. Khalatnikov,Zh. Eksperim. i Teor. Fiz. 19, 637 (1949).
I. M. Khalatnikov, inContemporary Physics Trieste Symposium 1968 (International Atomic Energy Agency, Vienna, 1969), Vol. I, p. 71.
L. D. Landau,Zh. Eksperim. i Teor. Fiz. 30, 1058 (1956) [English transl.,Soviet Phys.—JETP 3, 920 (1957)].
See, for example, H. B. Callen,Thermodynamics (John Wiley and Sons, New York, 1966), p. 48.
Y. Disatnik and R. Meyuhas, to be published.
See, for example, L. D. Landau and E. M. Lifshitz,Fluid Mechanics (Pergamon Press, Oxford, 1963), p. 187.
I. M. Khalatnikov,An Introduction to the Theory of Superfluidity (W. A. Benjamin, New York, 1965), pp. 113–119.
Ibid.,, p. 153.
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Disatnik, Y., Yaniv, A. A kinetic theory of the dilute solutions of3He in superfluid4He. I. Thermodynamics and equations of motion. J Low Temp Phys 10, 595–620 (1973). https://doi.org/10.1007/BF00655455
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DOI: https://doi.org/10.1007/BF00655455