Generating functional for a nonequilibrium system of electrons and phonons

Closed expression and integral equation for generating functional (GF) of nonequilibrium system of electrons and phonons are obtained. The closed, non Marcoffian equation of motion for quasiequilibrium GF which contains both exact system of kinetic equations and equation for lattice displacement, is derived.
Expressions for collision integrals for one-particle density matrices are obtained in the second order of the perturbation theory with respect to the interaction strength. The improved collision integrals are constructed, which take into account such high order effects as finite width of electron-phonon transitions due to nonperturbational energy conservation breaking and screening of electron-phonon interaction caused by indirect electron-electron interaction through phonon field.