Phase Space Quantum Mechanics and the Quantum-Classical Relation

相空间量子力学和量子经典关系

• 批准号: RGPIN-2022-04225
• 负责人: Walton, Mark
• 金额: $ 1.75万
• 依托单位: University of Lethbridge
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762656
• 关键词: Phase; Space; Quantum; Mechanics; Classical

Phase-Space Quantum Mechanics and the Quantum-Classical Relation Quantum mechanics (QM) describes physics at short, "microscopic'' distances. Classical mechanics (CM) applies at macroscopic scales. Each works eminently well in its regime. The quantum-classical (QC) relation, however, is not well understood. For example, if one imagines moving from the microscopic to the macroscopic, QM does not morph into CM. Even worse, the so-called classical limit becomes singular, and it is difficult to understand how classical can emerge from quantum. I propose a research program aimed at understanding the QC relation better. Improved understanding would represent an advance in the foundations of physics. It would also be important for many experiments now being done and the technology being developed in the QC regime. My work uses phase space quantum mechanics (PSQM). It is the formulation of QM best suited to studying the QC relation. Both PSQM and CM live in phase space, for example, and neither uses operators. Hybrid QC systems point to problems. Many different systems exist in nature that appear to be composed of a quantum part interacting with a classical part. Example: quantum electrons and classical nuclei in a molecule. However, attempts to formulate consistent dynamics for hybrid QC systems have failed. Recently, I attacked this problem in the framework of PSQM. My student Amin and I rederived and generalized key previous results. Furthermore, we introduced a composition product for hybrid observables that made a consistent dynamics possible. In a 2nd paper, we applied the results to a simple model, providing a blueprint for applications to other physical systems. The first and largest part of my research proposal capitalizes on this advance. Our methods will be applied to more and more complex systems, approaching physicality, and eventually, making predictions about experiments. Additional effects have been conjectured to play a role in the emergence of CM from QM. These include measurement uncertainties, thermal effects, decoherence by interaction with the environment, and spontaneous state collapse. All will be studied in PSQM, for eventual use of our results in distinguishing them experimentally. If QM is valid at all scales, then macroscopic quantum systems, "Schrodinger cats'', must exist. An intense hunt is now underway for them. Included is a search for measures of macroscopic quantumness. Many measures of quantumness have been constructed in PSQM. I propose to investigate their dependence on various notions of size, in order to identify candidate measures of macroscopic quantumness. A second aim of my proposed research is to improve and generalize the methods and tools of PSQM. For example, recent work generalizes the Wigner function to quasiprobability distributions for arbitrary sets of operators. I plan to investigate if other elements of PSQM, like a star product, can also be introduced.

相空间量子力学和量子-经典关系量子力学（QM）描述了短距离的物理学，“微观”距离。经典力学（CM）适用于宏观尺度。每一个都在其制度中运作得非常好。然而，量子-经典（QC）关系还没有得到很好的理解。例如，如果一个人想象从微观移动到宏观，QM不会变成CM。更糟糕的是，所谓的经典极限变得奇异，很难理解经典是如何从量子中产生的。 我提出了一个研究计划，旨在更好地了解QC关系。理解的提高将代表物理学基础的进步。这对目前正在进行的许多实验和正在质量控制制度下开发的技术也很重要。 我的工作使用相空间量子力学（PSQM）。这是最适合研究QC关系的QM公式。例如，PSQM和CM都存在于相空间中，并且都不使用算子。 混合QC系统指出了问题。自然界中存在许多不同的系统，它们似乎是由量子部分与经典部分相互作用组成的。例如：分子中的量子电子和经典原子核。然而，试图制定一致的动态混合QC系统失败了。最近，我在PSQM的框架中攻击了这个问题。我和我的学生Amin重新推导并推广了以前的关键结果。此外，我们还引入了一种混合观测量的合成乘积，使一致的动力学成为可能。在第二篇论文中，我们将结果应用于一个简单的模型，为其他物理系统的应用提供了蓝图。我的研究计划的第一个也是最大的一个部分就是利用了这一进步。我们的方法将应用于越来越复杂的系统，接近物理性，并最终对实验进行预测。额外的影响已被证实在CM从QM出现中发挥作用。这些因素包括测量不确定性、热效应、与环境相互作用引起的退相干以及自发态崩塌。所有这些都将在PSQM中进行研究，以便最终使用我们的结果在实验上区分它们。 如果量子力学在所有尺度下都成立，那么宏观量子系统，即“薛定谔猫”，必然存在。一场激烈的追捕正在进行中。其中包括对宏观量子性的测量。在PSQM中已经构造了许多量子性的度量。我建议调查他们的依赖于各种概念的大小，以确定候选措施的宏观量子。 我提出的研究的第二个目的是改进和推广PSQM的方法和工具。例如，最近的工作将维格纳函数推广到任意算子集的准概率分布。我计划调查是否也可以引入PSQM的其他元素，比如星星产品。