Wigner function for open systems with electron-phonon interaction

The Wigner-function (WF) formalism is used to analyze the quantum dynamics of charge carriers in presence of electron-phonon (e-p) interaction in open mesoscopic systems making use of the perturbation theory with the external fields incorporated into the unperturbed Hamiltonian. Proper boundary conditions have been chosen and the transport phenomenon inside the device is treated in such a way that boundary conditions at finite positions are kept unaltered, even though the basis of extended scattering states is used.