Mathematical Sciences: Block Travel Grant for Conference on the State of Matter

数学科学：物质状态会议的全额旅行补助金

• 批准号: 9201934
• 负责人: Mary Beth Ruskai
• 金额: $ 1.23万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201934&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Block; Travel; Grant

During the past two decades there has been considerable progress in the understanding of the nature of matter through the rigorous mathematical analysis of models which describe different states of matter. The more notable developments include (1) a thorough analysis of Thomas-Fermi and related semi-classical models for atomic and molecular systems, (2) analysis of the stability of matter, (3) verification of the correct asymptotes of the ground state of energy of atoms up to certain orders, (4) proof of the finiteness of the maximum excess charge of atomic and molecular systems, estimates on the maximum excess charge, and proofs of asymptotic neutrality, (5) proofs of the existence of the thermodynamic limit for Coulomb systems, (6) analysis of models in quantum and statistical mechanics, (7) analysis of such quantum phenomena as the quantum Hall effect and the formation of Cooper pairs, and (8) proof of the existence of the hydrodynamic limit of Boltzmann's equation for interacting particle systems. This project will support a block travel grant to the Conference on the State of Matter to be held in Copenhagen, Denmark from July 30 to August 1, 1992. The conference will provide an opportunity for newer mathematicians and scientists to learn about developments at the leading edge of this branch of mathematical physics.

在过去的二十年中，通过对描述物质不同状态的模型进行严格的数学分析，在理解物质的本质方面取得了相当大的进展。更值得注意的发展包括：(1)对原子和分子系统的托马斯-费米模型和相关的半经典模型进行了彻底的分析，(2)对物质稳定性的分析，(3)验证了原子能量基态的正确渐近线，直到某些阶，(4)证明了原子和分子系统的最大多余电荷的有限性，(5)库仑系统热力学极限存在的证明；(6)量子力学和统计力学模型的分析；(7)量子霍尔效应和库珀对形成等量子现象的分析；(8)证明了相互作用粒子系统玻尔兹曼方程流体动力极限的存在性。这个项目将支助将于1992年7月30日至8月1日在丹麦哥本哈根举行的关于物质状况的会议的一笔旅行补助金。会议将为新数学家和科学家提供一个机会，了解数学物理这一分支的前沿发展。