9529138 Kotliar This grant concerns those properties of a Fermi system that are not present in the weakly interacting-clean substances but that arise as a result of the strong interparticle interaction and/or lack of translational invariance. These properties are present in experiments on metal-insulator transitions. They are also critical to our understanding of heavy fermions, doped semiconductors, amorphous alloys and high temperature superconductors. Specifically, the project consists of three parts (a) Mott transition in orbitally degenerate systems, (b) a large dimension analysis of the interplay between localization and interaction and (c) Effect of quantum fluctuations in the melting of a vortex lattice. %%% Typically, magnets are insulating (Iron Cobalt and Nickel are very subtle exceptions) and superconductors are good metals at high temperatures (when they are not superconducting). Recent discoveries of high temperature superconductors show these materials to belong to a special class, where the normal state of a superconductor is not a very good metal and there is magnetism in similar compounds. The puzzling coexistence of magnetism and dirty metallic character and superconductivity is a complex and challenging theoretical problem. The present grant suggests a novel approach to the solution of this problem and possible understanding of the phenomena of high temperature superconductivity. ***
