1 - Transport Properties of Spatially Inhomogeneous Quantum Systems From the First Principles

Abstract

First-principle theoretical tools of statistical mechanics include perturbation theory, projection operator methods and density functional theory (DFT) that form a fundamental basis of modern description of thermodynamic and transport properties in systems composed of three or more real or virtual quantum or classical particles. Among other technical advantages, the first two of these methods allow self-consistent prediction of the properties of such systems in terms of correlation functions and two-time temperature Green’s functions calculated analytically or numerically. Since its introduction in physics, perturbation theory remains the only rigorous and self-consistent method of those three available, although it encounters technical difficulties when applied to strongly spatially inhomogeneous systems, such as fluid flows at interfaces, or non-equilibrium processes in small and low-dimensional systems, such as molecules, quantum dots and wires, and thin films. Density functional theory experiences fundamental difficulties due to its non-variational nature already in the equilibrium system case, and its applications to non-equilibrium systems have not been rigorously justified. This chapter overviews a recent Green’s function (GF) - based fundamental theory of strongly spatially inhomogeneous quantum systems, and a self-consistent and explicit projection operator method to calculate GFs developed by Yu. A. Tserkovnikov in collaboration with D. N. Zubarev. This method of GF calculations is the only first-principle approach applicable to systems of any nature and dimensionality without fundamental restrictions. At the same time, as any projection operator method, this method is not closed in a sense discussed below, and thus currently undergoes further development.