Quantum transport theory

Abstract

Quantum transport theory applied to mesoscopic structures is one of the most active fields within theoretical solid state physics. As the sample size diminishes, screening may become less effective and consequently the interactions between the system’s constituents increase in importance and it is necessary to provide a good description of the various interaction mechanisms. A point in case are one-dimensional systems (quantum wires): there electron-electron interactions may lead to a behaviour, which is qualitatively different from the standard Fermi liquid picture (Luttinger liquids). Further, the system is often far from equilibrium and it is thus necessary to develop a quantum many-body theory valid for nonequilibrium situations. Many different theoretical approaches have been developed for this purpose and a number of them are reviewed in other chapters of this book. In this chapter, two approaches will be outlined: the Kubo formula and the nonequilibrium Green’s function technique. We shall illustrate these two methods in terms of two physical examples: in the case of the Kubo formula we introduce and analyse in detail the phenomenon of Coulomb drag, while the nonequilibrium Green’s function technique will be applied to the case where a small, possibly strongly interacting mesoscopic region is coupled to noninteracting leads. The study of these two examples is motivated by the steady flow of new experimental data which challenges our ability to understand and interpret these measurements.