DERIVATION OF TRANSPORT EQUATIONS FOR ANHARMONIC LATTICES

Non-equilibrium properties of dielectric crystals are described using a Green function approach which represents transport phenomena by correlation functions of the equilibrium system. The equation which is equivalent to a Boltzmann equation for phonons is the integral equation for the vertex part corrections. Including all irreducible diagrams quadratic in the cubic and linear in the quartic anharmonicities the vertex part equation is reduced to a form which could be used as a starting point for numerical studies of microscopic models. The vertex part is also used to express the space and time variation of the phonon density and the frequency change of the phonons in response to an external displacement field. We also relate the integral equation for the vertex part to a form of the transport equation which is used in Landau's theory of quantum liquids. © 1969 Springer-Verlag.