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In this thesis I deal with two effects which are related to the Quantum Hall systems. In Chapter 2 I study the Coulomb magneto-drag, particularly concentrating on the question of the so-called anomalous drag recently observed experimentally. The observed sign reversal of the drag signal poses an intriguing task for theoretical investigations. Chapter 3 is an attempt to predict possible a Jahn-Teller effect in Si inverse layers. There I consider the interplay between the valley splitting, the electron-phonon and electron-electron interactions in these systems and their effect on the ground state and low-lying skyrmionic excitations.
Scanning tunneling miscoscopy is one of the most powerful spectroscopic tools for single-electron excitations. We show that the conductance fluctuations, or noise in the conductance, of a tunneling current into an interacting electron system is dominated by density-density and spin-spin correlations. This allows one to probe two-particle properties (susceptibilities) and collective excitations by standard experimental tunneling methods. We demonstrate this theoretically, using a novel many-body calculation for the multi-center Kondo problem, including both direct and indirect exchange between magnetic atoms. An example of the two-particle correlations around a single magnetic adatom in the Kondo regime, as would be viewed by a scanning tunneling microscope, is given. The spatial dependance of the charge and spin correlations, includi...
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