Long and short time quantum dynamics: I. Between Green's functions and transport equations

This paper summarizes the present views on construction of the electron quantum transport equations based on the Non-Equilibrium Green's Functions approach. The basic tool is the so-called Ansatz decoupling; one Ansatz family stems from the original Kadanoff-Baym Ansatz and is suitable for extending the quasi-particle picture of the Landau theory out of equilibrium. The other family based on the Generalized KB Ansatz is appropriate for short time transients. The physical and formal context of the Ansatzes is analyzed; the most important question explored is the status of the Reconstruction Theorems, reducing a full description of a non-equilibrium system to a dynamic theory in terms of one-particle quantities. A comparison is made between the Time Dependent Density Functional Theory and the properly renormalized NGF formalism. There is a close relationship between both formalisms. The Reconstruction Theorems form a general basis for obtaining improved quantum transport equations.