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

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.