A New Transport Equation for Single-Time Green′s Functions in an Arbitrary Quantum System. General Formalism

Abstract

Using new renormalization methods for nonequilibium real-time Green′s functions a set of exact self-consistent non-linear transport equations is derived for all one-particle distribution functions occurring in an arbitrary inhomogeneous multi-component quantum many-body system. In order to develop the theory for a general initial state even if the particle number is not conserved, a new generalization of Wick′s theorem is presented. The transport equation is given as a systematic perturbation expansion in the coupling parameter around a generalized Boltzmann and Enskog equation, whereby the non-locality of scattering processes, arbitrarily strong driving forces, collisional broadening effects, and energy renormalizations due to Hartree-Fock potentials are incorporated. Grand canonical, as well as canonical, ensembles can be treated, which makes the theory applicable to macroscopic, as well as mesoscopic, systems. The theory is also well suited for the calculation of transport coefficients in linear or non-linear response theory and can describe quantum interference effects like localization phenomena in disordered systems. Furthermore, it is shown that the diagonal singularity property of van Hove is equivalent to (quasi-)momentum conservation and the validity of the Zwanzig inversion method of classical kinetic theory is proven for an arbitrary quantum many-body system. A generalized Kadanoff-Baym ansatz is derived for systems without particle number conservation.