Coupling of non-equilibrium Green’s function and Wigner function approaches

We propose a coupling scheme, where the advantages of the coherent Greenpsilas function formalism are combined with the ability of the Wigner formalism to account for phase-breaking processes of interaction with phonons and other lattice imperfections. The Greenpsilas function formalism is used to calculate the coherent Wigner function which provides the initial condition in an equation, from which corrections due to phonon interactions can be calculated. A variety of possible approaches to the obtained equation are considered, and the case where the initial condition is small is investigated numerically.