Mathematical Sciences: Random Quantum Systems

数学科学：随机量子系统

• 批准号: 9002357
• 负责人: James Howland
• 金额: $ 7.59万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002357&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Random; Quantum; Systems

This research will focus on three areas: 1) Stability and instability of quantum Hamiltonians with dense point and singular spectra; 2) Existence of absolutely continuous spectra of Schrodinger operators with random potential; and 3) Solutions of a commutator inequality which arose in connection with random Hamiltonians. This work is in the general area of mathematical physics. The problem examined by this researcher is to some extent a simple quantum analogue of the KAM problem in classical mechanics. Problems of this sort with time-periodic potentials are of considerable physical interest, particularly in connection with atoms in laser fields.

本研究将集中在三个方面：1）稳定性和 具有稠密点和奇异性量子哈密顿量的不稳定性 2）绝对连续谱的存在性 具有随机势的Schrodinger算子; 3） 一个换位子不等式， 汉密尔顿人 这项工作是在一般领域的数学物理。 这个研究人员所研究的问题在某种程度上是一个 经典KAM问题的简单量子模拟 力学 具有时间周期势的这类问题 有相当大的物理利益，特别是在连接 在激光场中的原子。