Phase Space Quantum Mechanics and the Quantum-Classical Relation

相空间量子力学和量子-经典关系量子力学（QM）描述在短的“微观”距离上的物理。经典力学（CM）适用于宏观尺度。每一种都在其体制下运作得非常好。然而，量子-经典（QC）关系还没有被很好地理解。例如，如果想象从微观到宏观，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。我提出了一个旨在更好地理解QC关系的研究计划。更好的理解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在QC制度中正在开发的技术也很重要。我的工作使用相空间量子力学（PSQM）。这是最适合研究质量管理关系的质量管理公式。例如，PSQM和CM都存在于相空间中，它们都不使用算子。混合质量控制系统指出了问题。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。例子：分子中的量子电子和经典原子核。然而，为混合质量控制系统制定一致动力学的尝试失败了。最近，我在PSQM的框架下解决了这个问题。我的学生阿明和我重新推导和推广了以前的主要结果。此外，我们引入了混合可观测的组合产品，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，为其他物理系统的应用提供了蓝图。我的研究计划的第一部分也是最大的一部分是利用这一进步。我们的方法将应用于越来越复杂的系统，接近物理，并最终对实验进行预测。据推测，在从QM中出现CM的过程中，其他效应也发挥了作用。这些包括测量不确定度、热效应、与环境相互作用的退相干和自发态坍缩。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中区分它们。如果量子力学在所有尺度上都有效，那么宏观量子系统——“薛定谔猫”——必然存在。一场激烈的搜捕正在进行中。其中包括对宏观量子测量的研究。在PSQM中已经建立了许多量子测量。我建议研究它们对各种尺寸概念的依赖，以便确定宏观量子的候选测量。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Wigner函数推广到任意算子集的准概率分布。我打算研究是否可以引入PSQM的其他元素，比如明星产品。

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.