This award provides support for the participation of Professor Abel Klein of the University of California, Irvine in a program of cooperative research with Professor J. Fernando Perez of the University of Sao Paulo, Brazil. The research will deal with extensions to our knowledge of random Schrodinger operators, a topic of relevance to the quantum-mechanical description of matter, and in particular to the motion of electrons in disordered systems. This project builds on the research of Prof. Klein currently supported by the Division of Mathematical Sciences of NSF. At first the Anderson model for the motion of quantum- mechanical particles on imperfect lattices will be extended to two and three dimensions. Such an extension would facilitate the description of both conduction and optical properties of quantum-mechanical systems. Subsequently, the Wegner model for such motion--an alternative to Anderson's, which can also describe extended states--will be used to investigate the properties of such states in disordered systems. The collaboration between Professors Klein and Perez, which is already of some six years' duration, has led to numerous joint publications in the field of mathematical physics, and the research now proposed should benefit all physicists and engineers who are seeking to understand the phenomena of conduction in very small systems.
