Disorder Effects and Critical Behavior in Statistical Mechanics and in Quantum Systems

统计力学和量子系统中的无序效应和关键行为

• 批准号: 9214654
• 负责人: Michael Aizenman
• 金额: $ 25.2万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9214654&HistoricalAwards=false
• 关键词: Disorder; Effects; Critical; Behavior; Statistical

This project will carry out basic research in mathematical physics on topics in the area of statistical mechanics and quantum mechanics with emphasis on the effects of quenched disorder and critical phenomena. The topics to be studied include: spectral properties of operators with extensive disorder with the aim of providing a non- perturbative derivation of localization in higher-than-one dimensional systems; properties of quantum spin systems using random-walk techniques from classical spin models in the path integral representation of the quantum propagators; proofs of universality in the critical behavior for a variety of models.

该项目将在数学物理学上进行有关统计力学领域和量子力学领域的主题的基础研究，重点是淬火障碍和关键现象的影响。 要研究的主题包括：具有广泛疾病的操作员的光谱特性，目的是在高于较高的维度系统中提供非扰动的定位衍生物；量子自旋系统的性质使用来自量子传播器的路径积分表示中的经典自旋模型的随机步行技术；各种模型的临界行为的普遍性证明。