Dynamic theory of deformable solids with quasiparticle excitations in the presence of electromagnetic fields

A full self-consistent set of equations is deduced to describe the kinetics and dynamics of charged quasiparticles (electrons, holes, etc.) with arbit rary dispersion law in crystalline solids subjected to time-varying deforma tions. The set proposed unifies the nonlinear elasticity theory equation, a Boltzmann kinetic equation for quasiparticle excitations, and Maxwell's eq uations supplemented by the constitute relations. The kinetic equation used is valid for the whole Brillouin zone. It is compatible with the requireme nt for periodicity in k space and contains an essential new term compared t o the traditional form of the Boltzmann equation. The theory is exact in th e frame of the quasiparticle approach and can be applied to metals and semi conductors, as well as to other crystalline solids including quantum crysta ls and low-dimensional lattice structures. Instructive examples concerning the form of the Fokker-Plank equation as well as the pinning of effective m agnetic induction lines in deformable metals are considered.