Mathematical Sciences: Exact Results in Statistical Mechanics

数学科学：统计力学的精确结果

• 批准号: 9105661
• 负责人: Sheldon Goldstein
• 金额: $ 6.15万
• 依托单位: Rutgers University New Brunswick
• 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: 1991-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9105661&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Exact; Results; Statistical

In this project the principal investigator will look into a fundamental problem of importance in statistical mechanics today, namely establishing connections between microscopic phenomena and macroscopic phenomena. More specifically, he will try to understand the relationship between microscopic laws that describe the interactions of many particles and macroscopic observables such as temperature that characterize the bulk properties of a phenomenon, in the context of quantum mechanics. Part of the difficulty here lies in the fact that physicists cannot agree about what the microscopic laws are for the quantum mechanical formalism. The principal investigator will attempt to establish such laws and then examine their phenomenological consequences in a rigorous fashion. An easily describable and observable phenomenon such as the temperature of your morning cup of coffee is what physicists and applied mathematicians call a "macroscopic" or bulk property of the coffee, that is, it is a measurable quantity that describes how hot or cold the liquid is, based upon some conventional scale. The temperature however is actually governed by the collective behavior of the many molecules and atoms that are in ceaseless motion inside of the cup and that are governed by the "microscopic" laws of interaction. In this proposal the principal investigator will examine the relationship between microscopic and macroscopic effects in the context of quantum mechanics, the ultimate theory of matter.

在这个项目中，首席研究员将研究当今统计力学中一个重要的基本问题，即建立微观现象和宏观现象之间的联系。 更具体地说，他将尝试在量子力学的背景下理解描述许多粒子相互作用的微观定律与表征现象整体特性的宏观可观测值（例如温度）之间的关系。 这里的部分困难在于，物理学家无法就量子力学形式主义的微观定律达成一致。 主要研究者将尝试建立这样的法则，然后以严格的方式检验它们的现象学后果。 一种容易描述和观察到的现象，例如早上喝咖啡的温度，被物理学家和应用数学家称为咖啡的“宏观”或整体属性，也就是说，它是一个可测量的量，基于某种传统的尺度来描述液体的热度或冷度。 然而，温度实际上是由许多分子和原子的集体行为决定的，这些分子和原子在杯子内不断运动，并受到相互作用的“微观”定律的控制。 在这项提案中，首席研究员将在物质的终极理论——量子力学的背景下研究微观和宏观效应之间的关系。