Mathematical Analysis of Interacting Bose Gases

相互作用的玻色气体的数学分析

• 批准号: 0353181
• 负责人: Robert Seiringer
• 金额: $ 13.11万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0353181&HistoricalAwards=false
• 关键词: Mathematical; Analysis; Interacting; Bose; Gases

Mathematical Analysis of Interacting Bose Gases" by R. Seiringer The main focus of this project is the continuation of the author's research in the mathematical analysis of the low-temperature properties of an interacting Bose gas, with special attention on the phenomenon of Bose-Einstein condensation. Motivated by recent experimental breakthroughs in the treatment of dilute Bose gases, which led to Nobel prize awards in 2001, there has been a lot of progress in this field in the last few years. Partly in joint work with E.H. Lieb and J. Yngvason it was possible to rigorously prove the existence of Bose-Einstein condensation, superfluidity and other phenomena like one-dimensional behavior of trapped gases in highly elongated traps, starting from the basic Schroedinger equation. With the help of developing the necessary mathematical tools it was possible to gain considerable physical insight into these phenomena. There are a lot of open problems, however, that are planned to be addressed within this project. Among them are the proof of Bose-Einstein condensation for infinite (in contrast to trapped) systems, behavior of rotating systems and vortices, mixtures of Bose and Fermi gases, etc. These problems are interesting both from a mathematical and physical point of view, being of a complex nature that brings about the need for new mathematical ideas, and being closely related to properties of systems studied for the first time in current experiments which can be expected to yield further fascinating results within the near future. Progress in the mathematical analysis of these phenomena will certainly yield further insight into the complex physics that is going on in interacting bosonic systems at very low temperature. Other fields of research that the author would like to study within this project include the Pauli-Fierz model of non-relativistic Quantum Electro-dynamics, the Bessis-Moussa-Villani conjecture about traces of positive matrices, and classical models of Quark confinement.

R. Seiringer 的“相互作用玻色气体的数学分析” 该项目的主要重点是作者对相互作用玻色气体的低温特性的数学分析研究的延续，特别关注玻色-爱因斯坦凝聚现象。受最近稀玻色气体处理实验突破的推动，该领域获得了 2001 年诺贝尔奖。 在过去的几年里。部分与 E.H. 合作Lieb 和 J. Yngvason 从基本的薛定谔方程开始，可以严格证明玻色-爱因斯坦凝聚、超流性和其他现象的存在，例如高度细长陷阱中捕获气体的一维行为。在开发必要的数学工具的帮助下，可以获得对这些现象的大量物理洞察。有一个 然而，计划在该项目中解决许多未解决的问题。其中包括无限（与俘获）系统的玻色-爱因斯坦凝聚的证明、旋转系统和涡流的行为、玻色和费米气体的混合物等。这些问题从数学和物理的角度来看都很有趣，其性质复杂，需要新的数学思想，并且与所研究的系统的性质密切相关 在当前的实验中这是第一次，预计在不久的将来会产生更多令人兴奋的结果。对这些现象的数学分析的进展肯定会进一步深入了解极低温度下相互作用的玻色子系统中正在发生的复杂物理现象。作者希望在该项目中研究的其他研究领域包括非相对论量子电动力学的 Pauli-Fierz 模型、Bessis-Moussa-Villani 关于正矩阵迹的猜想和夸克禁闭的经典模型。