Quasiclassical approach to kinetic equations for superfluid 3hellum: General theory and application to the spin dynamics

Using the method of the quasiclassical Green function, we derive a set of kinetic equations which describe general nonequilibrium situations in the quasiclassical regime, i.e., when the external frequency and wave vector, ω and q are small compared to the atomic scale (ω ? μ, ∥ q ∥ ? pf. The equations consist of a Boltzmann equation for the quasiparticle distribution function, labeled by the energy and the direction of the momentum (particle representation), coupled to a time dependent Ginzburg-Landau equation for the order parameter. We discuss extensively the properties of these equations, and apply them to orbital and spin dynamics. Solving the Boltzmann equation in a well defined approximation, we are able to derive the expressions for the linewidths for all temperatures, with the correct identification of the phenomenological relaxation times. Furthermore, we discuss the connection between various relaxation times used in non-equilibrium situations, and we give a detailed comparison of the particle representation with the excitation representation which is used frequently in other work on non-equilibrium phenomena in superfluid ³He and in superconductors.