NONEQUILIBRIUM PHONONS IN INSULATING CRYSTALS: DERIVATION OF A QUANTUM MECHANICAL BOLTZMANN EQUATION FOR COUPLED ELECTRON PHONON SYSTEMS.

A quantum-mechanical phonon Boltzmann equation for a weakly coupled electron-phonon system is derived from the von Neumann equation using the Kelly-Argyres projection operator formalism. The phonon distribution is described by one particle Wigner operators. The relevant part of the statistical operator is identified with the phonons, the irrelevant part with the electrons, which show no own dynamics. Starting with a specific electron-phonon interaction the formalism leads to transport equations for acoustic phonons in insulating crystals. The results are compared with the ones given by the 'quasidiffusion' and 'spectral-spatial diffusion' models often used.