Delocalization, Localization, and other Phenomena in Disordered Systems

无序系统中的离域、定域和其他现象加州大学欧文分校Abel Klein这项研究的主题是研究无序系统中的离域、定域和其他现象。随机薛定谔算符的主要公开问题是离域；扩张态的存在。研究随机薛定谔算子的离域化是本方案的主要目的。这个提议的一个主要目的是证明随机薛定谔算符中的动态离域，使用基于输运的金属-绝缘体转变的新方法，而不是PI和Germinet引入的光谱性质。在量子力学中，随机薛定谔算符描述了电子在含有杂质的晶体中的运动。将杂质模拟为随机介质(或材料)。虽然纯材料可能是导体，但杂质会改变材料的导电性能。在杂质产生局域态的能量下，材料表现为绝缘体，而在扩展(离域)态的能量下，材料表现为导体。掺杂半导体给出了含有杂质的材料的例子，它们在电子领域有许多应用。这项研究将进一步加深对这类材料由于杂质的加入而引起的导电性质变化的理解。

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.