Applications of Lie algebraic and phase space methods in quantum physics

李代数和相空间方法在量子物理中的应用

• 批准号: 249769-2012
• 负责人: deGuise, Hubert
• 金额: $ 1.46万
• 依托单位: Lakehead University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570724
• 关键词: Applications; Lie; algebraic; phase; space

Phase space methods in quantum mechanics have in common the objective of mapping quantum mechanical operators, defined in an abstract Hilbert space, to complex-valued functions in a classical phase space appropriate for the system under consideration. This proposal deals with applications of phase space methods to quantum systems with higher symmetries. The proposed applications include the extension of results already available for SU(3) to systems with SU(n) (and other) symmetries, a study of short time semiclassical dynamics of such systems focusing on squeezing as a short time effect, an investigation of so-called correspondence rules with possible applications to relaxation, and an investigation of phase operators for systems with higher symmetries using phase space methods as a starting point. The results of this work will be of use to physicists - theorists and experimentalists - in quantum optics with an interest in a better understanding some nonclassical properties of quantum states.

量子力学中的相空间方法 共同的目标是映射量子力学算子，定义在抽象的希尔伯特空间， 复值函数在一个经典的相空间适合的系统正在考虑。 这个建议涉及相空间方法的应用，以更高的对称性的量子系统。 建议的应用包括推广SU（3）的已有结果到SU（n）系统（和其他）对称性，对这种系统的短时半经典动力学的研究，重点是作为短时效应的压缩，对所谓的对应规则的研究及其在弛豫中的可能应用，并以相空间方法为出发点，对具有较高对称性的系统的相算符进行了研究。 这项工作的结果将是有用的物理学家-理论家和实验学家-在量子光学的兴趣，在更好地理解量子态的一些非经典性质。