Applications of Many-Body Theory

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Research will be undertaken on a number of problems in electronic many-body theory, complexity and disordered systems. Topic to be studied include: high temperature superconductors and related problems such as the Hubbard model in one and two dimensions; disordered electronic and magnetic systems including breakdown of Fermi liquid behavior in quenched random systems; physics of complexity and problems of early evolution. %%% Electronic many-body theory as usually practiced has been challenged by phenomena such as high temperature superconductors in which usual /perturbative techniques haved been found lacking. The complex interactions in these materials between magnetism, disorder, superconductivity and metal-insulator transitions have led to the need for new paradigms. The research proposed here will address the fundamdental behavior of electrons in these highly usual systems. Addition work will be devoted to the application of spin glass models to pre-biotic evolution.