Quantum transport equations for vibrating isotopically disordered crystals

A transport equation approach is developed for the linear response of the electron-phonon system in a vibrating isotopically disordered crystal to a frequency dependent electric field. The smallness of the mutual differences of the various masses is taken into account to derive a microscopic set of equations for the phonon and electron distribution functions. Applying an appropriate averaging technique, we obtain a set of equations from which the relevant macroscopic transport equation and hence physical quantities, such as the electrical conductivity, may be derived.