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.

Ergodic Sc​​hroedinger Operators的光谱特性提议的研究S.Vetlana Jitomirskaya这个项目是研究ergodic Sc​​hroedinger操作员的光谱和定位类型效应，并研究Quasiperiodic and-erserson和Erersers-ersers-ersers-ersers-ersers-ersers-ersers-anders-ersers-anders-anders-erserson-anders-anders-andersers-type-type-type-type-type-type-type-type-typepe-typepe-typepe。还计划研究与恒定和/或随机磁场中Bloch电子有关的几种模型。 该项目涉及持续开发非扰动方法，以证明本地化和其他相关特性以及对绝对连续频谱的研究。其他重要的目标是研究与准二级操作员的cantor光谱有关的问题，它的发生，普遍性和缩放特性以及平滑（而不是分析）方法的发展。拟议的研究调查了Quasiperiodic和其他确定性和随机结构和其他确定性和随机结构的异常光谱和异常性。这是关于无序系统的基本特性的基础研究，该系统是具有杂质系统模型的模型。准碘操作员为整数量子霍尔效应，实验准晶体和量子混乱理论提供了中心或重要模型。严格理论的发展有望有助于对所有三种现象的理解，尤其是可能导致找到具有所需物理特性的新材料。 无序系统还用于建模许多其他微观和宏观效应：从量子定位到地震。拟议的主题包括研究表现出某些异常行为的高度和弱小的量子力学系统的特性。