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

在过去的二十年里，通过对描述不同物质状态的模型进行严格的数学分析，人们在理解物质的本质方面取得了长足的进步。更值得注意的进展包括：(1)彻底分析了托马斯-费米和有关原子分子系统的半经典模型，(2)分析了物质的稳定性，(3)验证了某些阶以下原子能量基态的正确渐近线，(4)证明了原子和分子系统最大超额电荷的有限性，最大超额电荷的估计和渐近中性的证明，(5)库仑系统热力学极限存在的证明，(6)量子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，以及(8)相互作用粒子系统玻尔兹曼方程流体极限存在性的证明。该项目将支助将于1992年7月30日至8月1日在丹麦哥本哈根举行的国情咨文会议的整笔旅费。这次会议将为新的数学家和科学家提供一个机会，了解这一数学物理分支的前沿发展。

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.