Disordered and Strongly Correlated Condensed Matter Systems

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9400142 Fisher The presence of microscopic quenched disorder often changes qualitatively the macroscopic behavior of condensed matter systems. The effects of disorder are revealed even more dramatically at low temperatures when they dominate over thermal fluctuations. At low temperatures, though, it is often necessary to disentangle the subtle interplay between disorder and quantum fluctuations. Particularly challenging are those quantum systems in which the interactions are so strong that a simple description in terms of a reference non-interacting model are inappropriate. This theoretical research will focus on the behavior of such strongly correlated and disordered systems. In particular, the following problems will be studied: (1) Transport in interacting one- dimensional electron gases (Luttinger liquids) and edge states in the fractional quantum Hall effect; (2) The quantum phase transition between plateaus in disordered fractional and integer quantum Hall fluids and the closely related superconductor- insulator transition in disordered superconductors; (3) The crossovers to the two-dimensional thin film limit and non- equilibrium fluctuations and noise in the mixed state of the cuprate superconductors; (4) The mesoscopic superconductivity associated with small superconducting systems and with normal mesoscopic systems in contact with superconductors. %%% This theoretical research will focus on a number of related problems at the forefront of modern condensed matter physics. They all have the common theme of competition between physical disorder and disorder induced by the quantum nature of the systems being studied. While the primary focus is on fundamental condensed matter physics, the results have potential for a broad impact on materials. The systems to be studied include the new high temperature superconductors and the the two-dimensional electron gas (as found at semiconductor interfaces in strong magnetic fields). ***