Mathematical Sciences: Research in the Theory of Disordered Systems (Mathematical Sciences)

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Professor Klein is the leader of a strong group of mathematical physicists at University of California at Irvine. His recent work has been in the study of disordered systems. This is the study of properties of materials in the presence of impurities. For example, the motion of electrons in a crystal with impurities is described quantum mechanically by a random potential. The most striking and exceedingly important development with wide technological implications, is the remarkable change in conductivity of the material due to impurities. The science of composite materials, especially semiconductors, is undergoing a major evolution in this regard. The mathematical study of disordered systems, from many perspectives, is especially important, as instabilities often interfere with the natural physical intuition. In this proposal, Professor Klein will continue his productive study of random Schrodinger operators and spin glasses, with particular emphasis on the weak disorder limit and the properties of the density of states for random Schrodinger operators.