The Quantum Mechanical Many-Body Problems and Mathematical Analysis

量子力学多体问题与数学分析

• 批准号: 9513072
• 负责人: Elliott Lieb
• 金额: $ 36.65万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-02-01 至 2000-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9513072&HistoricalAwards=false
• 关键词: Quantum; Mechanical; Many; Body; Problems

9513072 Lieb This research is devoted to various aspects of many- body theory in quantum mechanics, to certain aspects of field theory and differential equations, and to some problems in pure mathematics. These various topics have grown out of a body of research over several decades and the underlying unity is that solutions in the various problem areas shed light on each other. There are four major areas. One is the study of geometric symmetry breaking in such models as Ginzburg- Landau vortices and Skyrmions. The question of symmetry breaking is a crucial one in modern physics. The second concerns electron correlations in many-body systems which, currently, is a central topic in areas such as superconductivity. The third concern centers around the structure of atoms and molecules. The earlier work in these areas, notably the problem of permanent dominance for matrices and the question of the continuity or lack of it for Steiner symmetrization of functions, which is a useful tool in quantum mechanics and analysis. ***

9513072 Lieb这项研究致力于量子力学中多体理论的各个方面，场论和微分方程的某些方面，以及纯数学中的一些问题。这些不同的主题是在几十年的研究中发展出来的，其根本的统一是各种问题领域的解决方案相互揭示。主要有四个方面。一个是研究金兹堡-朗道涡旋和Skyrmions等模型中的几何对称性破缺。对称性破缺问题是现代物理学中的一个关键问题。第二个涉及多体系统中的电子关联，目前，这是超导等领域的一个中心话题。第三个担忧集中在原子和分子结构上。这些领域的早期工作，特别是矩阵的永久支配问题和函数的Steiner对称化的连续性或缺乏问题，是量子力学和分析中的有用工具。***