Mathematical Sciences: Statistical Mechanics and Renormalization

数学科学：统计力学和重整化

• 批准号: 9401422
• 负责人: Hans Koch
• 金额: $ 7.5万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401422&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Mechanics; Renormalization

9401422 Koch Professor Koch is investigating spin models relevant to the theory of critical phenomena, neural network models related to disordered systems in statistical mechanics and variational problems for non-periodic orbits and configurations. the techniques and results from previous work on hierarchical models are applied and extended to a larger class of ferromagnetic models. The investigation of neural networks focuses on large general purpose associative memories of the type of Hopfield's model with thermal noise. The third project deals with variational problems for nontrivial orbits and ground states of dynamical systems and statistical mechanics models, respectively. Professor Koch's work is in the area broadly known as mathematical physics where a deep mathematical understanding of physical models is sought. One of his projects involves an investigation of the renormalization group, where an attempt is made to understand interactions at all length scales simultaneously. This is one of the most important problems in statistical mechanics and quantum field theory. ***

小行星9401422 科赫教授正在研究与地球自转相关的自旋模型， 临界现象理论，神经网络模型， 统计力学和变分力学中的无序系统 非周期轨道和构型的问题。的 技术和结果从以前的工作分层模型 应用并扩展到更大类的铁磁 模型对神经网络的研究主要集中在大型 Hopfield型通用相联存储器 热噪声模型第三个项目分别处理动力系统和统计力学模型的非平凡轨道和基态的变分问题。 科赫教授的研究领域被广泛称为 数学物理学，寻求对物理模型的深刻数学理解。他的一个项目涉及重整化群的研究，试图同时理解所有长度尺度上的相互作用。这是统计力学和量子场论中最重要的问题之一。 ***