Spin d~namics for arbitrarily polarized and very dilute solutions of 3He in liquid He are described. We began at a very fundamental level by deriving a kinetic equation for arbitrarily polarized dilute quantum systems based on a method due to Boercker and Dufty. This approach allows more controlled approximations than our previous derivation based on the Kadanoff-Baym technique. Our previous work is here generalized to include T-matrix interactions rather than the Born approximation. Spin hydrodynamic equations are derived. The general equations are valid for both Fermi and Bose systems. By use of a well-known phenomenological potential to describe the 3He-JHe Tmatrix we calculate longitudinal and transverse spin diffusion coefficients D_L and D/I and the identical-particle spin-rotation parameter ~t. We confirm that these two diffusion constants differ at low T with DI approaching a constant as T ~ O, and D H ~ lIT 2. Estimates of errors made by our approximations are considered in detail. Good agreement is found in comparison with data from both Cornell University and the University of Massachusetts. We find that the s-wave approximation is inadequate and that mean-field corrections are important. Comparison is also made between theory and the recent UMass viscosity measurements.

2014 Nous établissons une équation cinétique pour des systèmes dilués polarisés qui inclut les effets de dégénérescences par la méthode des fonctions de Green de Kadanoff et Baym. Combinée avec l'approximation de Born, cette équation se réduit à un résultat dû à Silin. Dans la limite de Boltzmann, notre résultat se réduit à l'équation de Lhuillier et Laloë, à laquelle s'ajoute un terme de dérive de champ moyen analogue à celui qui apparaît dans l'équation de Landau-Silin. Nous utilisons notre équation cinétique pour établir une expression pour le temps de relaxation de la diffusion de spin transverse 03C4~ pour un système de Fermi. Dans les limites de Boltzmann et de polarisation faible, 03C4~ se réduit à 03C4~, le temps de relaxation longitudinal. Toutefois, dans un système dégénéré fortement polarisé, 03C4~ peut être beaucoup plus petit que 03C4~.Abstract. 2014 A kinetic equation, which includes the effects of degeneracy, is derived for dilute, polarized systems by the Green's function method of Kadanoff and Baym. When the Born approximation is used for the self-energy, the equation reduces to a result due to Silin. In the Boltzmann limit our result is equivalent to the equation of Lhuillier and Laloë, with the addition of a mean-field drift term analogous to that appearing in the Landau-Silin equation. Our kinetic equation is used to derive an expression for the transverse spin-diffusion relaxation time, 03C4~, for a Fermi system. In the Boltzmann and low-polarization limits 03C4~ reduces to 03C4~, the longitudinal relaxation time. However, in a highly polarized degenerate system 03C4~ can be very much shorter than 03C4~.

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