U.S.-Brazil Cooperative Research: Theory of Disordered Systems

美国-巴西合作研究：无序系统理论

• 批准号: 9016926
• 负责人: Abel Klein
• 金额: $ 0.86万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1993-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9016926&HistoricalAwards=false
• 关键词: U.S.; Brazil; Cooperative; Research; Theory

This award will support research on the mathematics of disordered systems to be conducted by Abel Klein of the University of California at Irvine in cooperation with J. Fernando Perez and Henrique von Dreifus from the University of Sao Paulo, Brazil. They will investigate phenomena in two types of disordered systems: quantum spin systems with disorder and random Schrodinger operators. Quantum spin systems with random parameters have been introduced to study the effect of impurities in several physical systems. Examples of such systems are given by quantum X - Y, Heisenberg and Ising models in the presence of a random transverse field. These models are related to superfluidity and superconductivity. The study of disordered quantum systems that exhibit zero- temperature transitions is a new and exciting area of research in Mathematical Physics. In such models, one has to treat the combined effects of randomness and quantum fluctuations. Such combination has hardly been studied in the Physics literature or in Mathematical Physics. Such study is a long range goal of this research proposal.

该奖项将支持数学研究， 由阿贝尔·克莱因（Abel Klein）进行的无序系统 加州大学欧文分校与J. 大学的费尔南多·佩雷斯和亨里克·冯·德雷富斯 位于巴西的圣保罗。 他们将调查 两种无序系统：量子自旋系统， 无序和随机薛定谔算子。 量子自旋 随机参数系统被引入研究 杂质在几个物理系统中的影响。 这种系统的例子由量子X-Y，海森堡， 和伊辛模型在存在随机横截面 领域 这些模型与超流性有关， 超导性 对无序量子系统的研究， 温度转换是一个新的和令人兴奋的领域， 研究数学物理。 在这样的模型中，必须 把随机性和量子性的综合效应 波动 这样的结合几乎没有被研究过， 物理学文献或数学物理学中。 此类研究 是本研究计划的长远目标。