Quasiparticle kinetic equation in geometry of local base vectors

Abstract

Kinetic equations for quasiparticle excitations in ideal crystals, known from solid state physics, are generalized to the case of material bodies the crystal structure of which is distorted by the existence of continuously distributed defects. Distribution of defects is described by a field of local base vectors of a primitive crystal lattice. The form of conservation laws implied by such kinetic equations is discussed using the example of energy balance in a phonon system. It is shown that energy balance can be written either with respect to lattice connection or with respect to the Euclidean connection, having a vanishing source term in both cases. Transition from one version to another involves a redefinition of the heat flux vector.