The Quantum Mechanical Many-Body Problem and Statistical Mechanics

量子力学多体问题与统计力学

• 批准号: 9820650
• 负责人: Elliott Lieb
• 金额: $ 38.5万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-06-15 至 2003-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9820650&HistoricalAwards=false
• 关键词: Quantum; Mechanical; Many; Body; Problem

The work that will be done under this award addresses fundamental problems in the physics and mathematics of many-body systems. There will be three main areas: (1) the development of a non-perturbative quantum electrodynamics that can deal properly with the bound states of atomic and condensed matter physics; (2) a continuation of the progress made recently to understand rigorously the ground states of low density Bose gases, especially the condensation phenomenon, which is a subject of much current experimental interest; (3) the study of the Hubbard model, which is now considered one of the cornerstones of correlated electron phenomena. Additionally, some topics in pure mathematics and partial differential equations will be addressed.

该奖项将致力于解决多体系统物理学和数学中的基本问题。 主要有三个方面：（1）发展一种非微扰的量子电动力学，它能恰当地处理原子和凝聚态物理的束缚态;（2）继续最近在严格理解低密度玻色气体基态，特别是凝聚现象方面所取得的进展，这是目前实验上很感兴趣的一个课题;（3）研究Hubbard模型，它现在被认为是关联电子现象的基石之一。 此外，一些纯数学和偏微分方程的主题将得到解决。