Mathematical Sciences: Some Problems in Statistical Mechanics

数学科学：统计力学的一些问题

• 批准号: 9100455
• 负责人: Joseph Conlon
• 金额: $ 12.85万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100455&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Statistical

The principal investigator will continue his studies of various problems in statistical mechanics. In particular, he will study the Heisenberg model for ferromagnetism, in order to show that at low temperature the free energy of this model approximates the free energy of a perfect Bose gas. He will also work on models of high density classical gases with short-range interaction and on ground state energies of many-body Coulomb systems. The basic aim of statistical mechanics is to obtain the large scale thermodynamic behavior of a many-particle system from a knowledge of the microscopic interactions between the particles. The principal investigator will validate several approximate theories concerning gases that have applicability to phenomena involving superfluidity and superconductivity.

首席研究员将继续研究统计力学中的各种问题。 特别是，他将研究铁磁性的海森堡模型，以证明该模型在低温下的自由能接近完美玻色气体的自由能。 他还将研究具有短程相互作用的高密度经典气体模型以及多体库仑系统的基态能量。 统计力学的基本目标是通过了解粒子之间的微观相互作用来获得多粒子系统的大规模热力学行为。 首席研究员将验证几种有关气体的近似理论，这些理论适用于涉及超流性和超导性的现象。