Two-Fluid Transport Equations for Lattices

A Green's-function approach is developed to derive in lowest order of the anharmonic interaction the transport equations for a pure Bravais lattice. The motion of the anisotropic elastic continuum is coupled to the distribution function for the quasiparticle gas. Summing the most divergent terms contributing to the hydrodynamical singularities of the self-energy kernel by means of a decoupling procedure for the hierarchy of retarded Green's functions, we obtain a Boltzmann equation. The results are the simplest approximation for the two-fluid equations describing nonequilibrium phenomena of the lattice.