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.

相位空间量子力学和量子古典关系量子力学（QM）简短地描述了物理学，“微观”的距离。经典力学（CM）适用于宏观尺度。每个尺度都非常有效。变成更糟糕的是，所谓的经典限制很难理解量子从量子中出现，旨在更好地理解QC的关系。例如，最适合研究QC的关系。 混合QC系统指出问题。自然界中存在许多不同的系统，这些系统似乎由与经典部分相互作用的量子部分组成。示例：分子中的量子电子和经典核。但是，试图为混合质量管理系统制定一致的动力学的尝试失败了。最近，我在PSQM的框架中攻击了这个问题。我和我的学生阿明（Amin）重新修饰并广泛化了以前的关键结果。此外，我们为混合观测值推出了一种构成产品，这使一致的动态成为可能。在第二篇论文中，我们将结果应用于一个简单的模型，为应用程序的应用提供了蓝图。我的研究提案的第一和最大部分利用了这一进步。我们的方法将应用于越来越复杂的系统，接近身体，并最终对实验进行预测。已经提出了其他效果，可以在QM的CM出现中发挥作用。这些包括测量不确定性，热效应，与环境相互作用的破裂以及自发状态崩溃。所有这些都将在PSQM中进行研究，以最终使用我们的结果在实验中区分它们。 如果QM在所有尺度上都是有效的，则必须存在宏观的量子系统“ Schrodinger Cats”，必须存在强烈的狩猎。现在正在进行对它们的搜索。包括搜索宏观量子性的措施。量子性的许多度量已在PSQM中构建的许多量子量。为了改善和概括PSQM的方法和工具，最近的工作将Wigner函数推广到任意运算符集的Quasiprobobility分布。