Complete nonstationary density matrix of electron-phonon system in the functional integration representation

In the functional integral representation of the complete wave function of an electronphonon system describing its evolution from an arbitrary initial state, all integrations with respect to the phonon coordinates are performed and the displacements of the centers of the oscillations of the phonon modes are found. A nonstationary density matrix which depends on the electron and phonon coordinates is found for any mixed ensemble of electron-phonon systems.