Delocalization, Localization, and other Phenomena in Disordered Systems

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Delocalization, Localization and other Phenomena in Disordered SystemsAbel Klein University of California, Irvine AbstractThe subject of this research proposal is the study of delocalization, localization, and other phenomena in disordered systems. The main open problem in random Schrodinger operators is delocalization; the existence of extended states. The study of delocalization in random Schrodinger operators is the main goal of this proposal. A major objective of this proposal is to prove dynamical delocalization in random Schrodinger operators, using the new approach to the metal-insulator transition based on transport instead of spectral properties introduced by the PI and Germinet. In addition, questions related to localization and linear response theory will be investigated.In quantum mechanics, random Schrodinger operators describe the motion of an electron in a crystal with impurities. The impurities are modeled as a random media (or material). While the pure materials may be conductors, impurities change the conduction properties of materials. At energies in the region where impurities create localized states the material behaves as an insulator, while at energies with extended (delocalized) states the material behaves as a conductor. Examples of materials with impurities are given by doped semiconductors, which have many applications in electronics. The proposed research will further the understanding of the changes in the conduction properties of such materials caused by the addition of impurities.