On transport theory of correlated mesoscopic systems

Sammanfattning: This thesis is about the theory of quantum transport through low dimensional correlated systems. Correlated systems are interacting many-particle systems where collective effects predominate over the individual properties of particles whereof they consist. Single particle approach to correlated systems would be essentially wrong. That is why many well developed theoretical tools appropriate for quantum transport theory of weakly correlated systems fail for strongly correlated ones. At present theory of transport in correlated systems is an intensively developing field. Last decade saw a significant progress in theoretical understanding of the Quantum Hall effect and the quasi 1-dimensional transport. Yet the influx of new puzzles and challenging questions does not seem to subside in a large measure due to the abundance of constantly updated experimental matherial. In this thesis we consider some aspects of the theory of quantum transport through low dimensional correlated systems such as quantum Hall fluids or quantum wires. We investigate the DC transport through both clean and dirty correlated systems. In the clean case we develop a generalization of the Landauer-Büttiker approach and use it for establishing non-renormalization of the DC conductance by a broad class of interparticle interactions. We also provide an explanation of the experiments of A. Yacoby et al., in which renormalization of the DC conductance of very clean quantum wires was observed. We approach dirty systems by considering the quantum impurity problem in the limit of weak electron-electron interactions. We suggest that the scaling behavior of the DC transport be governed by a two-parametric flow of the scattering matrix. Using perturbative renormalization group we derive the flow equations. We discuss experimental implications of obtained results.Last, we discuss tunneling spectroscopy of the quantum Hall edges. We present our interpretation of the tunneling I-V characteristics obtained in a recent experiment by M. Grayson et al