Mathematical Sciences: Mathematical Problems in Statistical Mechanics and Condensed Matter Physics

数学科学：统计力学和凝聚态物理中的数学问题

• 批准号: 9104487
• 负责人: Jennifer Chayes
• 金额: $ 8.53万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1995-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104487&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Statistical; Mechanics

The principal investigator will address mathematical questions in several different branches of statistical mechanics and condensed matter physics. First, she will investigate both equilibrium and non-equilibrium properties of some simple classical systems. Second, she will study collective phenomena in some rather simple quantum systems, including both quantum spin models and systems of particles with anomalous statistics. All the questions she will address concern the behavior of systems with a large number of degrees of freedom, usually infinite. The mathematical methods to be developed to study these systems are rooted in probability theory and analysis, but also make use of dynamical systems, differential equations, group theory and numerical methods.

主要研究者将解决数学问题， 统计力学几个不同分支中的问题 和凝聚态物理学。 首先，她将调查 一些简单的平衡和非平衡性质 经典系统 其次，她将研究集体现象 在一些相当简单的量子系统中， 自旋模型和具有反常统计的粒子系统。 她将讨论的所有问题都涉及 具有大量自由度的系统，通常 无限的。 数学方法要发展到研究 这些系统植根于概率论和分析，但 还利用动力系统，微分方程，群 理论和数值方法。