Spectral Properties of Ergodic Schroedinger Operators

遍历薛定谔算子的谱性质

• 批准号: 0601081
• 负责人: Svetlana Jitomirskaya
• 金额: $ 26万
• 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: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0601081&HistoricalAwards=false
• 关键词: Spectral; Properties; Ergodic; Schroedinger; Operators

Spectral Properties of Ergodic Schroedinger OperatorsAbstract of Proposed ResearchSvetlana Jitomirskaya This project is to study spectra and localization type effects for ergodic Schroedinger operators and the study of anomalous absolutely continuous spectrum and anomalous quantum transport in the quasiperiodic and Anderson model-type settings. It is also planned to study several models related to Bloch electrons in constant and/or random magnetic fields. The project involves the continuing development of non-perturbative methods both for the proofs of localization and other related properties as well as for the study of absolutely continuous spectrum. Other important objectives are the study of issues related to Cantor spectra of quasiperiodic operators, it's occurrence, prevalence, and scaling properties, and the development of smooth (rather than analytic) methods.The proposed research investigates the anomalous spectral and diffusive properties of quasiperiodic and other deterministic and random structures. This is basic research on the fundamental properties of disordered systems that serve as models of systems with impurities. Quasiperiodic operators provide central or important models for integer quantum Hall effect, experimental quasicrystals, and quantum chaos theory. The development of the rigorous theory is expected to contribute to the understanding of all three phenomena, and in particular, 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.

遍历薛定谔算子的光谱性质拟议研究摘要Svetlana Jitomirskaya 该项目旨在研究遍历薛定谔算子的光谱和局域化效应，以及准周期和安德森模型类型设置中反常绝对连续光谱和反常量子输运的研究。还计划研究与恒定和/或随机磁场中的布洛赫电子相关的几种模型。 该项目涉及非微扰方法的持续开发，用于定位和其他相关属性的证明以及绝对连续谱的研究。其他重要目标是研究与准周期算子的康托谱相关的问题，它的出现、普遍性和标度特性，以及平滑（而不是解析）方法的开发。本研究调查了准周期算子的反常谱和扩散特性。其他确定性和随机结构。这是对作为含杂质系统模型的无序系统基本性质的基础研究。准周期算子为整数量子霍尔效应、实验准晶体和量子混沌理论提供了中心或重要的模型。严格理论的发展预计将有助于理解所有这三种现象，特别是可能导致寻找具有所需物理性质的新材料。 无序系统还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无序和弱无序系统的特性，这些系统表现出某些异常行为。