Mathematical Sciences: Itinerant Electron Systems and Quantum Mechanical Spin Systems

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Kennedy will study itinerant fermion and quantum spin systems. The nature of the ground state of one of the simplest itinerant fermion systems will be studied in detail. In particular he will investigate whether there is a 3-dimensional analog of the recent 2-dimensional result that for the neutral model in a certain range of densities the ions are always arranged in diagonal lines. He will also study the localization problem for a system of particles moving in a random potential. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.