Delocalization, Localization, and other Phenomena in Disordered Systems

无序系统中的离域、局域化和其他现象

• 批准号: 0457474
• 负责人: Abel Klein
• 金额: $ 33.3万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0457474&HistoricalAwards=false
• 关键词: Delocalization; Localization; other; Phenomena; Disordered

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.

无序系统中的离域、定域和其他现象Abel Klein加州大学欧文分校摘要本研究计划的主题是研究无序系统中的离域、定域和其他现象。随机薛定谔算子的主要开放问题是离域性，扩展态的存在性。随机薛定谔算子的离域性研究是本文的主要目标。 这个建议的一个主要目标是证明动态离域随机薛定谔算子，使用新的方法来传输的基础上，而不是由PI和Germinet介绍的光谱特性的金属-绝缘体过渡。 此外，还将研究与局域化和线性响应理论有关的问题。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。 杂质被建模为随机介质（或材料）。 虽然纯材料可以是导体，但杂质会改变材料的导电特性。 在杂质产生局域态的区域中的能量下，材料表现为绝缘体，而在具有扩展（离域）态的能量下，材料表现为导体。 掺杂半导体是含杂质材料的一个例子，它在电子学中有许多应用。 这项研究将进一步了解杂质的加入对材料导电性能的影响。