Open Access

Peter Schwab

• The article is arranged as follows: In chapter 2 we introduce the Green's function technique in the non-equilibrium (Keldysh) formulation, which is the main theoretical tool throughout this article. The chapter is rather formal and may be skipped by a reader who is not interested in technical details. Nevertheless we included the material as the general background on which the results presented in the subsequent chapters have been obtained. Following the literature we will demonstrate how a Boltzmann-like theory and the Drude conductivity are found within the Green's function formalism. In chapter 3 transport beyond the Drude-Boltzmann theory will be considered. By extending the formalism of chapter 2 contributions to the current density due to "maximally crossed diagrams" and due to the Coulomb interaction will be calculated. Chapter 4 will be devoted to some applications. The general expression for the current density of chapter 3 will be evaluated explicitly for differentThe article is arranged as follows: In chapter 2 we introduce the Green's function technique in the non-equilibrium (Keldysh) formulation, which is the main theoretical tool throughout this article. The chapter is rather formal and may be skipped by a reader who is not interested in technical details. Nevertheless we included the material as the general background on which the results presented in the subsequent chapters have been obtained. Following the literature we will demonstrate how a Boltzmann-like theory and the Drude conductivity are found within the Green's function formalism. In chapter 3 transport beyond the Drude-Boltzmann theory will be considered. By extending the formalism of chapter 2 contributions to the current density due to "maximally crossed diagrams" and due to the Coulomb interaction will be calculated. Chapter 4 will be devoted to some applications. The general expression for the current density of chapter 3 will be evaluated explicitly for different experimental setups. We will consider the nonlinear conductivity in films and wires. Furthermore we will investigate the question of whether the phase coherence time, which is a central quantity for weak localization, is also relevant for the Coulomb interaction corrections to the conductivity. In chapter 5 a rather different type of electron-electron interaction will be considered, namely electrons interacting via dynamical impurities. We will present results obtained for persistent currents in rings and discuss the relevance of dynamical defects for low temperature dephasing. The main focus of the article is on systems with diffusive electron motion. Interesting physics is, however, also found in other circumstances. In the last chapter of this article we will approach the vast field of transport through quantum dots. In particular we will investigate transport through a strongly interacting dot, where Kondo physics is relevant. After summarizing the established results for a quantum dot which is connected to two normal conducting leads, we will discuss the presently available results for a quantum dot which is connected to a normal and to a superconducting lead.…