A kinetic theory of the dilute solutions of3He in superfluid4He. I. Thermodynamics and equations of motion

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.