Non-Equilibrium Green's Functions (Negf) And Quantum Kinetic Theory : Detailed mathematical exposition and applications to phonons, electrons and disordered systems

In this work we show that Non-equilibrium Green's Function Perturbation Theory (NEGF) is really the overarching perturbative transport theory. It is developed in 3 directions: Landauer-like theory, kinetic theory and Green-Kubo linear response theory. This work generalizes the 2 directions of Landauer-like theory and the kinetic theory. Firstly, NEGF is used to derive phonon-phonon Hedin-like functional derivative equations which generates conserving self energy approximations for phonon-phonon interaction. Secondly, for the Landauer-like theory, using the perturbation expansion, we obtain anharmonic corrections to the ballistic energy current and to the noise associated to the energy current. Along a seperate line, we incooperate high mass disorder into the ballistic energy current formula. The coherent potential approximation (CPA) is found to be compatible with the ballistic energy current expression. Lastly, for the kinetic theory, Wigner coordinates + gradient expansion easily allow the derivation of phonon-phonon correlation corrections to kinetic equations. The main feature of this work is the extremely detailed mathematical explanations.