Spectral and Transport Theory of Schrodinger Operators

薛定谔算子的谱与输运理论

• 批准号: 0300974
• 负责人: Svetlana Jitomirskaya
• 金额: $ 27.3万
• 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: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0300974&HistoricalAwards=false
• 关键词: Spectral; Transport; Theory; Schrodinger; Operators

PI: Svetlana Jitomirskaya, University of California, IrvineDMS-0300974*********************************************************************This project is centered around issues related to localization type effects for ergodic Schroedinger operators and the study of anomalous quantum transport in the quasiperiodic and Anderson model-type settings. It involves the continuing development of non-perturbative methods for theproofs of localization and other properties as well as studying phenomena that demonstrate the limitations of non-perturbative results. Another major goal is the development of methods to study anomalous quantum transport to be applied to both deterministic and random potentials.Our research concerns the anomalous spectral and diffusive properties of quasiperiodic and other deterministic and random structures. This is therefore research on the fundamental properties of disordered systems that serve as models of systems with impurities. Deterministic ergodic,particularly quasiperiodic, potentials are often used to model quasicrystals. Study of the spectral and quantum transport properties of the microscopic models is important to understand and interpret much of the experimental data on quasicrystals. Such understanding may lead to finding new materials with desired physical properties. Disordered systems are also used in modeling many other micro and macro effects: from quantum localization to earthquakes. The proposed topics include studying properties of both highly and weakly disordered systems of Quantum Mechanics that demonstrate certain anomalous behavior.

主要研究者：Svetlana Jitomirskaya，加州大学，IrvineDMS-0300974* 本项目主要研究各态历经薛定谔算符的局域化效应以及准周期和非周期量子系统中的反常量子输运，安德森模型类型设置。它涉及非微扰方法的持续发展，用于证明局部化和其他性质，以及研究证明非微扰结果的局限性的现象。我们的另一个主要目标是发展适用于确定性势和随机势的反常量子输运的研究方法，我们的研究涉及准周期和其他确定性和随机结构的反常光谱和扩散性质。因此，这是对作为杂质系统模型的无序系统的基本性质的研究。确定性遍历势，特别是准周期势常被用来模拟准晶。 微观模型的光谱和量子输运性质的研究对于理解和解释大量的准晶实验数据是非常重要的。这种理解可能会导致发现具有所需物理特性的新材料。 无序系统也被用于模拟许多其他微观和宏观效应：从量子局域化到地震。拟议的主题包括研究量子力学的高度和弱无序系统的性质，这些系统表现出某些异常行为。