Projection evolution in quantum mechanics
A. Gozdz, M. Pietrow, M. Debicki
我们提出了一个统一了么正演化和测量过程的量子物体的时间演化模型。该模型允许将时间与其他动态变量同等对待。
We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Quantum mechanics as an asymptotic projection of statistical mechanics of classical fields: derivation of Schrödinger's, Heisenberg's and von Neumann's equations
我们表明，QM可以表示为一个经典的统计模型在相空间$Ω= H\times H,$，其中$H$是真正的希尔伯特空间的自然投影。统计状态由具有零平均值和非常小的幅度$α$（其被认为是模型的小参数）的分散的$Ω$上的高斯测度给出。这种统计状态可以解释为背景场的涨落，参见。和尼尔森的机械师合作物理变量（例如，能量）由映射$f: Ω\to {\bf R}$（经典场的函数）给出。我们的前量子经典统计模型的常规量子表示是在泰勒展开的基础上构造的（直到变量$f: Ω\to {\bf R}$相对于小参数$\sqrtα.$的真空场点$ψ\_{\rm{vacuum}}\equiv 0)$的二阶项QM的复杂结构由无限维相空间上的辛结构诱导$Ω.$高斯测度（统计状态）在QM中由其协变算子表示。薛定谔方程、海森堡方程和冯·诺依曼方程是$Ω.$上哈密顿动力学的图像。我们的前量子模型的主要实验预测是实验统计平均值可以偏离QM给出的平均值。
Non-Markovian quantum dynamics and the method of correlated projection superoperators
描述开放系统非马尔可夫动力学的有效方法在量子力学的许多应用中起着重要的作用。在这里，我们回顾一些最重要的工具，是基于非平衡统计力学的投影算子技术。将标准的乘积态投影推广到一类新的相关投影超算子，它允许处理强记忆效应，并导致林德布拉德方程的非马尔可夫推广.
What is called "orthodox" quantum mechanics, as presented in standard foundational discussions, relies on two substantive assumptions --- the projection postulate and the eigenvalue-eigenvector link --- that do not in fact play any part in practical applications of quantum mechanics. I argue for this conclusion on a number of grounds, but primarily on the grounds that the projection postulate fails correctly to account for repeated, continuous and unsharp measurements (all of which are standard in contemporary physics) and that the eigenvalue-eigenvector link implies that virtually all interes…
Von Neumann-Lueders projection, and its applicability to EPR experiments
尽管众所周知，冯·诺依曼的投影公设不适用于大多数现实的测量过程，但它一直困扰着量子力学的基础。特别是它的EPR实验的适用性往往是假设。在目前的贡献，这个问题被认为是从量子力学理论的测量的角度来看，允许在EPR实验作为一个特殊的情况下，有条件的准备的投影治疗。该假定可能适用的条件已经阐明。
Time operator within projection evolution model
将投影演化方法应用于粒子探测过程和探测时刻的计算。讨论了系统的基本性质对演化过程的影响。它示出，仅使用投影公设的演化方案允许理解的时间作为一种可观察的。
Quantum Mechanics as a Simple Generalization of Classical Mechanics
给出了用对角投影矩阵和对角密度矩阵表示经典力学的动机。然后量子力学被看作是一个简单的推广，其中一个取代对角实矩阵与适当的厄米矩阵。
The Mori-Zwanzig projection operator formalism is one of the central tools of nonequilibrium statistical mechanics, allowing to derive macroscopic equations of motion from the microscopic dynamics through a systematic coarse-graining procedure. It is important as a method in physical research and gives many insights into the general structure of nonequilibrium transport equations and the general procedure of microscopic derivations. Therefore, it is a valuable ingredient of basic and advanced courses in statistical mechanics. However, accessible introductions to this method - in particular in …
An anhomomorphic logic for quantum mechanics
虽然在过去已经考虑了量子力学的非同态逻辑的各种方案，但我们将主要集中于二次或二阶方案。在这个方案中，2级真值函数被称为共事件。我们讨论的性质的共同事件，投影空间的共同事件和主观察。我们证明了投影的集合构成一个正交模偏序集。我们引入了排除共同事件的概念，并表明这比之前研究的排除共同事件的概念更强。排除共事件是根据主可观察量自然定义的。一个结果，表现出的二元性之间的排除和排除共事件。给出了一些简单的例子。
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator method. Imposing the additional constraints to eliminate the reduntant degrees of freedom, it is shown that the resultant noncommutative quantum system on the curved space is represented with two kinds of the constrained quantum systems, which are equivalent with each other. Then, it is shown that the resultant Hamiltonians contain the …
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposi…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schrödinger equation allows the derivation of an alternative expression for the evolution operator, which differs from the traditional chronological exponent. An appropriate choice of projection operators results in the possibility of studying the diagonal and non-diagonal elements of the evolution operator separately. The suggested expression implies a particular form of perturbation expansion, which leads to a new fo…
From Fischer projections to quantum mechanics of tetrahedral molecules: new perspectives in chirality
中心分子手性的代数结构可以从四面体分子键的几何表示开始，作为极性形式的复数，以及有机化学中使用的经验费舍尔投影。本文导出了一个广义正交O（4）代数，并由此得到了一个手性指数，它与分子的非手性、非对映异构体和对映异构体的分类有关。因此，四面体链的手性特征可以通过分子构造来预测。此外，推导了一个相容的薛定谔方程，其解是复数表示的四面体分子的键。从这个结果出发，O（4）代数可以被认为是一个量子手征代数。证明了这样一个代数的算子保持整个系统的奇偶性。
Delayed Choice Phenomena in the Projection Evolution Model
本文探讨了光子通过马赫-曾德干涉仪的时间波函数轮廓，展示了延迟选择实验可通过干涉仪中光子与设备的时间重叠解释。
Remarks on Our Understanding of Quantum Mechanics
对出现在量子力学几本优秀教科书中的关键概念，如不确定关系、动能、可观测值、概率分布、波函数假设的投影或坍缩、离散值与连续值的解释进行了回顾，发现与我们目前对量子理论的理解不一致。提出了可能的替代办法。
Quantum mechanics allows for multiple predictions for the outcome of an EPR experiment. The correct calculation must be used, guided by the physical conditions of the experiment. The quantum joint prediction for EPR correlation is derived and shown to involve a single sampling. The solution for separated measurement, where there are two private samplings, is then developed using orthodox quantum mechanics with Luders' rule for state projection on measurement. The separated solution is shown to duplicate the predictions of the quantum joint solution. However, it is shown that this solution requ…
Asymptotic expansion of Gaussian integrals of analytic functionals on infinite-dimensional spaces and quantum averages
我们研究无穷维空间（希尔伯特和核Frechet）上解析泛函的高斯积分的渐近展开。我们得到一个渐近等式耦合高斯积分和轨迹的合成标度的高斯测度和第二（Frechet）导数的功能的协变算子。通过这种方式，我们耦合经典平均（由无限维高斯积分给出）和量子平均（由冯诺依曼迹公式给出）。我们可以把这种数学构造解释为量子力学的“去量子化”过程。我们把量子力学表示为经典统计力学在无限维相空间中的渐近投影。这个空间可以被表示为经典场的空间，所以量子力学被表示为“前量子经典统计场论”的投影。
Unitarity of black hole evaporation in final-state projection models
Almheiri等人强调，关于黑洞蒸发的其他合理信念与量子力学的一般性质量子纠缠的一夫一妻制是不相容的。研究了Horowitz和Maldacena提出的黑洞蒸发的末态投影模型，指出该模型允许量子态的克隆和多偶纠缠，使得蒸发过程的么正性与黑洞事件视界的光滑性相协调.虽然该模型似乎需要仔细调整动力学以确保黑洞S矩阵的精确么正性，但对于一般的终态边界条件，在黑洞熵中，与么正性的偏差是指数级的小;此外，黑洞内部的观察者不需要检测到与标准量子力学的任何偏差。虽然在旧黑洞内部进行的测量可能会产生违反因果关系的现象，但解码霍金辐射的计算复杂性可能会使因果关系违反不可观察。末态投影模型说明了标准量子力学的不可侵犯的原则如何在量子引力理论中被规避。
Valuations on Functionally Closed Sets of Quantum Mechanical Observables and Von Neumann's 'No-Hidden-Variables' Theorem
我们应用投影格和冯·诺依曼代数的机器来分析模态解释如何能够（并且确实）规避冯·诺依曼臭名昭著的“无隐变量”定理的问题。
Incompatible and contradictory retrodictions in the history approach to quantum mechanics
我们举例说明两个简单的自旋的例子表明，在一致的历史方法量子力学可以追溯与确定性不兼容或矛盾的命题对应于非正交或，分别正交投影。V.2 vs. V1：以前被引用为“d'Espagnat的例子”的例子现在被正确地引用为“Griffiths的例子”。阿哈罗诺夫和Vaidman以前的工作参考添加。
Quantum measurement driven by spontaneous symmetry breaking
量子力学中的测量过程通常由冯·诺依曼投影公设描述，它构成了量子力学定律的基本组成部分。由于这一假设需要系统的外部观察者，因此很难将量子力学应用于整个宇宙。因此，我们提出量子测量过程实际上是一个与普遍存在的自发对称性破缺机制有关的物理过程。在此基础上，我们构造了一个量子测量模型，其中冯·诺依曼投影被描述为动力学的前相干过程。此外，经典可区分的指针参数作为c-数序参量出现在封闭时间路径量子场论的形式体系中。我们还讨论了测量的精度和玻恩概率假设的可能推导。
Evolution of Schrodinger Uncertainty Relation in Quantum Mechanics
本文讨论了量子力学的基本关系之一--测不准关系。1930年，也就是海森堡之后的几年，薛定谔将量子力学中著名的测不准关系进行了推广，使其比原来的测不准关系更加精确。本研究讨论了最近的概括薛定谔的工作，并解释了为什么他的论文仍然几乎被遗忘在上个世纪。
Algebras of Measurements: the logical structure of Quantum Mechanics
在量子物理学中，测量是由希尔伯特空间的某个闭子空间上的投影表示的。我们研究从希尔伯特空间的闭子空间上的投影代数中抽象出来的算子代数。这些运营商的属性是合理的认识论的理由。测量的交换是感兴趣的中心话题。经典的逻辑系统可以被看作是所有测量可交换的测量代数。关键词：量子测量，测量代数，量子逻辑。PACS：02.10.-诉
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the …
Complementarity of representations in quantum mechanics
我们表明，玻尔的互补原理之间的位置和动量的描述，可以制定严格的要求存在的表示的CCR。特别是，在任何位置算符有本征态的表象中，都没有动量算符，反之亦然。等价地，如果存在对应于尖锐位置值的非零投影，则动量算子的所有谱投影映射到零元素上。
Three-dimensional harmonic oscillator and time evolution in quantum mechanics
分析了三维谐振子时间（或相位）算符的定义问题。导出了该算子的一个新公式。结果已被用来证明在扩展的希尔伯特空间结构的框架中表示量子力学的时间演化的可能性。对扩展结构的物理解释也进行了简短的讨论。
Quantum clock in the projection evolution formalism
本文基于投影演化方法将时间作为可观测量引入量子力学，探讨了构建在演化中按概率在时间轴定位的量子时钟，并提出了一个二态模型作为最简示例。
Unitary time evolution in quantum mechanics is a stronger physical postulate than linear time evolution
该研究从第一性原理探讨量子力学中时间演化的幺正性能否由线性假设及其他公理推导，发现两种等价公理表述推广为线性假设后结果不同，提出幺正性是独立的可证伪公理。
Which operator generates time evolution in Quantum Mechanics?
我们吸引注意力的一个有趣的家庭的量子系统中的生成元$H_{(gen)}$的时间演化的波函数不等于哈密顿量$H$。我们描述的差异$H_{(gen)}-H$的起源和解释它作为一个压缩的其他相关观测信息的载体。
Projection hypothesis in the setting for the quantum Jarzynski equality
本文结合投影量子测量中投影假设的哈密顿过程实现与事件读取所需功的已有结果，提出一个量子热力学方案，以同时实验检验这两个相互独立的理论结果。
Temporal evolution of a forced optomechanical system with linear and quadratic field -- mechanical oscillator couplings
本研究利用李代数方法求解了具有线性和二次耦合的光机系统的时间演化算符，包括无驱动和受迫两种情况，并通过数值模拟验证了结果的准确性。
Feshbach projection formalism for open quantum systems
本文提出了一种新的研究开放量子系统的方法，该方法是在适当的Hilbert空间中基于Feshbach投影方法。而不是寻找一个主方程的动力学映射在空间中的密度算子，我们提供了相应的方程的希尔伯特空间中的系统的演化。它的解使人们能够构造一个合理的量子演化（完全正的和保迹的）。这种方法的最大优点是能够执行一致的近似，这在标准的Nakajima-Zwanzig方法中产生了臭名昭著的问题。新方案是由著名的自旋玻色子模型超越旋转波近似说明。
The Nature of Information in Quantum Mechanics
在 *-代数环境中，量子力学和经典力学的一个合适的统一统计公式使我们得出结论，在量子力学中，信息本身是非交换的。具体地说，我们在这里指的是观察者关于物理系统的信息。这被视为与经典力学的主要区别，在经典力学中，观察者关于物理系统的信息服从经典概率论。然后，量子力学被看作是一个纯粹的数学框架的概率描述的非交换信息，与投影公设是一个非交换推广的条件概率。这个观点澄清了许多围绕着量子力学解释的问题，特别是与测量过程有关的问题。
A Reconstruction of Quantum Mechanics
我们制定了一个一般原则，取代一个经典系统的内在属性的布尔σ-代数的一个σ-复合体（一个联盟的σ-代数）的量子系统的外在属性，引起与其他系统的相互作用。我们应用经典物理学中的可观测量、状态、组合系统、对称性和动力学的规范定义来推导标准的量子特征，包括薛定谔方程和冯·诺依曼-吕德投影法则。这种对量子力学的明显一致的重建然后被用来讨论和解决正统解释的困境。
This paper is a comparison of two theories of the probability of a history in quantum mechanics. One is derived from Copenhagen quantum mechanics using the projection postulate and is the basis of the "consistent histories" interpretation; the other is based on a proposal by Bell, originally for the "pilot state" theory but here applied to pure unitary quantum mechanics. The first can be used for a wider class of histories but depends on the projection postulate, or "collapse", which is widely held to be an unsatisfactory feature of the theory; the second can be used in a theory of the univers…
On unitary evolution and collapse in Quantum Mechanics
在干涉设置的框架中，只有两种结果是可能的（如在马赫-曾德尔干涉仪的情况下），我们讨论了一个简单的和教学的方式之间的差异，一个标准的，酉量子力学演化和存在的真正的波函数的崩溃。此外，我们还介绍了Elitzur-Vaidman炸弹，延迟选择实验，和退相干的影响。最后，我们提出了两个简单的实验来可视化退相干和测试纠缠粒子的作用。
Quantum Lissajous Figures via Projection
本研究针对角频率可公度的二维简谐振子，通过将普通相干态投影到简并子空间得到沿经典利萨如图形局域的新型量子定态，并揭示概率流密度与量子干涉的关联，为涡旋态提供了自洽解释。
Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to find all optimal Bell inequalities under some constraints, which may be given by some symmetry or other linear conditions. In this paper we extend this work in several directions. We use the method to generalize the I4422 inequality to three particles and a so-called GYNI inequality to four particles. Additionally, we find Bell inequalities for three partic…
Explanation, Evolution and Subjective Probability in Everett Quantum Mechanics with Positive Preclusion
通常的量子力学解释规则指出，当结果的权重为零时，结果不会发生，这一规则被改变，以排除权重小于一个小但正值的结果。有了这个“积极排除”规则，在没有任何客观概率概念的情况下，埃弗雷特量子力学就有能力解释有机体的进化，这些有机体对概率的主观期望符合玻恩规则。正排除还允许在涉及有限数量的测量的情况下导出权重和相对频率之间的联系。
On the relation between quantum mechanical probabilities and event frequencies
在两个连续时刻进行测量的概率“测度”是非加性的。另一方面，这些概率可以由测量事件的相对频率的极限来确定，其本质上是加性的。我们证明，只有两种方法来解决这个问题。第一个解决方案强调连续测量的条件概率概念的精确使用。物理上正确的条件概率定义了两次测量的加性概率。这些概率显式地取决于物理设备的分辨率，并且因此不对应于相关联的投影算子的函数。因此，量子理论区分了物理事件和关于事件的命题，后者不能用投影算子来表示，两次实验的结果不能用量子逻辑来描述。另一种解释是相当激进的：可以想象，两次测量的相对频率不会收敛，除非满足特定的一致性条件。如果这是真的，那么对量子力学形式主义的一个强有力的修正可能被证明是必要的。我们强调，有可能进行实验来区分这两种选择。
A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. III : Measurements and von Neumann Projection/Collapse Rule
在前两篇论文中发展起来的普适力学Supmech，把量子力学和经典力学都作为子学科（为了完整起见，本文还包括了一个简要的大纲）;这个特点有利于在基于Supmech的量子测量处理中，把仪器作为一个量子系统，用经典系统很好地近似处理。考虑到明确的事实，即在设备上的观察时，它已经“定居下来后的测量相互作用”，并限制在宏观上可区分的指针读数，（系统+设备）状态的不必要的叠加显示被抑制;这提供了一个真正的物理为基础的理由（传统的\emph{postulated}）冯诺依曼投影/塌陷规则。这种由观测约束所引起的退相干机制不受传统退相干方案的影响。
We derive the projection hypothesis in projective quantum measurement by restricting the set of observables. This projection hypothesis accompanies a bipartite system with the von Neumann-type interaction, which consists of a quantum mechanical system, with a meter variable to be measured, and a quantum field theoretically macroscopic extended object, that is, a spatiotemporally inhomogeneous Bose-Einstein condensate in quantum field theory with the quantum coordinate, that is, the zero-energy Goldstone mode(s) of the spontaneously broken global spatial translational symmetry. The key steps in…
On uniqueness of quantum measurement theory
本文讨论了量子力学的结构及其公设的唯一性。量子概率的玻恩定则被量子心灵感应不存在的要求所固定。冯·诺依曼投影公设描述了无相互作用测量条件下量子态的变换。在量子测量结果一定的条件下，投影公设可以看作是向条件概率的过渡。
An idea for an application of the quantum annealing mechanism to construct a projection measurement in a collective space is proposed. We use the annealing mechanism to drive the pointer degree of freedom associated with the measurement process. The parameters in its problem Hamiltonian is given not as classical variables but as quantum variables (states). By additionally introducing successive short interactions so that the back reaction to the quantum state (to be measured) can be controlled, we invent a quantum mechanically parametrized quantum annealing process. Applying to a particular pr…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation for a probability density. We extend this theory in two respects: (1) The same structure is defined for arbitrary observables. Thus we have all of the above entities generated not only by Hamilton's function but by every observable. (2) We introduce for each observable a phase space function representing the classical action. This is a redundant quantity in…
On the problem of Eigenschaften in the Quantum and Classical Mechanics
与经典物理不同，量子力学中的测量应该同时提供所有相关的相对振幅（纯态和它们之间的跃迁）和所有相关的相对相位的信息。同时性是必要的，因为一般来说，测量会改变系统的状态（在量子物理学和经典物理学中也是如此）。我们称这种测量过程为全息检测。在数学上，它是由一组相互交换的自伴算子描述的，这些算子与投影相似且密切相关。我们提出明确的例子，并讨论相应的实验装置，我们确定为量子参考系的一般特征。
Whose Projection Postulate?
本文梳理了Dirac、冯·诺依曼、Lüders三人提出的投影公设版本，厘清其发展脉络，批评了二人对连续谱可观测量的处理，并探讨了该公设的独立地位。
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations is given. Taking the Gaussian functions as the distributions of the tomographic parameters the correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators in the form of singular…
We discuss the problem of time in quantum mechanics. In the traditional formulation time enters the model as a~parameter, not an observable. In our model time is a quantum observable as any other quantum quantity and it is also a component of the spacetime position operator. In this case, instead of the unitary time evolution, other operators, usually projection or POVM operators which map the space of initial states into the space of final states at each step of the evolution can be used. The quantum evolution itself is a stochastic process. This allows to treat time as a quantum observable i…
Generalized Kochen-Specker Theorem
证明了一个推广的Kochen-Specker定理。它表明，存在的$n$投影算子，表示$n$是-否的问题，量子系统，使没有$2^n$可能的答案是兼容的总和规则强加的量子力学。也就是说，如果一个可交换投影算子的子集和成一个只有偶数或奇数特征值的矩阵，那么“是”的答案的数量应该分别是偶数或奇数。这一要求可能导致矛盾。提供了一个例子，涉及9个投影算子在一个4维空间。
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory. This article proposes an alternative formulation of the Standard Quantum Mechanics, in which the Projection Postulate is replaced with a version in which measurements and observations are not assumed as fundamental. More precisely, the Wigner functions representing the quantum states on the phase space are required to be tightly constrained to regions of the…
Nonlinear evolution as a possible explanation for quantum mechanical statevector reduction
本文提出了一种非定域玩具模型，用于模拟二态量子系统的"波函数谱“。塌缩是由一个对绝对相位极其敏感的非线性演化方程驱动的。假设该相或其一部分显示出混沌行为。这种混沌行为可以解释我们在单个量子系统中所经历的不确定性。通过这种随机性，我们不再需要统计的“整体”行为来描述单个量子系统。并对“度量问题”作了简要介绍。
Completely positive projections and biproducts
最近引入的CP*-结构将量子信道和经典系统结合在一起，将早期的CPM-结构归入范畴量子力学。我们比较这个建设，以解决这个问题的两个较早的尝试：自由地添加biproducts到CPM，并自由地分裂在CPM幂等元。CP*-结构嵌入前者，并嵌入后者，但两者都不是等价的。
Starting with unitary quantum dynamics, we investigate how to add quantum measurements. Quantum measurements have four essential components: the furcation, the witness production, an alignment projection, and the actual choice decision. The first two components still lie in the domain of unitary quantum dynamics. The decoherence concept explains the third contribution. It can be based on the requirement that witnesses reaching the end of time on the wave function side and the conjugate one have to be identical. In this way, it also stays within the quantum dynamics domain. The surjection hypot…
We present a constructive proof of Floquet's theorem for the special case of unitary time evolution in quantum mechanics. The proof is straightforward and suitable for study in courses on quantum mechanics.
Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an experimenter to determine which measurement bases have been used by another experimenter. As a consequence, quantum mechanics allows a situation in which two experimenters witness incoherent stories without being able to detect such incoherence, even if they are allowed to communicate freely by exchanging iterative and bilateral messages.
Rotations in 3 dimensional space are equally described by the SU(2) and SO(3) groups. These isomorphic groups generate the same 3D kinematics using different algebraic structures of the unit quaternion. The Hopf Fibration is a projection between the hypersphere $\mathbb{S}^3$ of the quaternion in 4D space, and the unit sphere $\mathbb{S}^2$ in 3D space. Great circles in $\mathbb{S}^3$ are mapped to points in $\mathbb{S}^2$ via the 6 Hopf maps, and are illustrated via the stereographic projection. The higher and lower dimensional spaces are connected via the $\mathbb{S}^1$ fibre bundle which co…
Optimal Semiclassical Regularity of Projection Operators and Strong Weyl Law
本文证明投影算子在半经典极限下收敛于相空间特征函数，并具有与特征函数相同的最大量子Sobolev正则性，回答了投影算子作为初始数据的可能性问题，并给出Weyl定律的强收敛结果。
Time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics
本文讨论$PT$对称量子力学中的时间演化和绝热近似.给出了一类$PT$ -对称哈密顿量的时间演化方程和一类$PT$ -对称哈密顿量绝热近似的条件.
Observing controlled quantum state collapse in a single quantum trajectory of a mechanical oscillator
量子理论的一个基本预测是，在连续测量下，一个系统的状态在时间上描绘出一个“量子轨迹”，这取决于它的测量记录，并且在某些情况下，系统的量子态随机地以有限的速率向随机本征态坍缩。另一方面，量子理论也预言，环境耦合会产生相反的效果，将波函数扩散到混合态。研究这两个相互竞争的过程，当它们的强度比变化时，对量子态分布的影响，在任何环境下都是基本的兴趣，但在机械领域尤其如此。然而，一个关键的问题是，这样的物理学的基础研究不能涉及一个先验假设的投影公设本身，和贝叶斯推断可能因此不被用来观察量子态。在这项理论工作中，我们提出了一个可行的方法来执行这样一个基本的测试与机械波函数的能量本征基。该方案是基于一个光学机械设置，其中光场提供了一个直接探测的能量变化的机械波函数。这样的能量变化探测器在任何类型的系统中都是前所未有的。结合投影假设的数值模拟预测，随着连续测量强度与耗散之比的增加，时间平均能量方差单调下降。在所提出的计划的测量强度是可调的原位，和行为预测的模拟，因此意味着该计划相当于一种方法来验证控制原位的时间平均方差的机械波函数在一个单一的量子轨迹的过程。
Recently I proposed the linguistic interpretation of quantum mechanics, which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized in the linguistic interpretation. And furthermore, I propose the justification of the von Neumann-Lüders projection p…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。