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

Abstract

A full self-consistent set of equations is deduced to describe the kinetics and dynamics of charged quasiparticles (electrons, holes, etc.) with arbitrary dispersion law in crystalline solids subjected to time-varying deformations. The set proposed unifies the nonlinear elasticity theory equation, a Boltzmann kinetic equation for quasiparticle excitations, and Maxwell’s equations supplemented by the constitute relations. The kinetic equation used is valid for the whole Brillouin zone. It is compatible with the requirement for periodicity in k space and contains an essential new term compared to the traditional form of the Boltzmann equation. The theory is exact in the frame of the quasiparticle approach and can be applied to metals and semiconductors, as well as to other crystalline solids including quantum crystals and low-dimensional lattice structures. Instructive examples concerning the form of the Fokker-Plank equation as well as the pinning of effective magnetic induction lines in deformable metals are considered.