相干态的性质与若干应用

相干态是近代物理学中的一个重要概念,它最初是由薛定格于1926年提出的[1].他指出,需要在一个给定位势下找一个遵循经典粒子运动规律的量子力学态.对于谐振子位势,他找到了这样的量子态.薛定格的这一物理思想直到六十年代才由Glauber[2]加以理论上的发展和给予实际上的应用,Glauber系统地建立起量子力学的相干态表象,证明了谐振子相干态是消灭算符的本征态,是使测不准关系取极小的态(即最接近于经典情况).在实际应用方面,Glauber首先用相干态来研究激光辐射场,当激发度足够高,激光分布趋近于相干态的统计律(泊松分布).Glauber还证明一个经…     

量子扩散方程的导出和相干态在扩散通道中的演化

我们利用相干态表象将经典扩散方程自然地推广到量子力学形式,并讨论了相干态在扩散通道中的演化问题,发现相干纯态在扩散通道中会演化为混态,并给出任意时刻的终态表达式。同时,我们得到光子数在扩散通道中会增加。     

矩形弹子球中的量子谱和经典周期轨道

利用SU(2)相干态的表示,我们构造了二维矩形弹子球中与经典周期轨道对应的波函数.经典周期轨道和量子波函数之间的关系可以通过物理图像清晰的表示出来.另外,利用周期轨道理论,我们计算了二维矩形弹子球体系的量子谱的傅立叶变换ρ(L).变换谱|ρN(L)|2对L图像中的峰可以和粒子在二维矩形腔中运动的经典轨迹的长度相比较.量子谱中的每一条峰正好对应一条经典周期轨道的长度,表明量子力学和经典力学的对应关系.     

从流体、电场到几率波、连续性方程的对比

 量子力学是反映微观粒子运动规律的理论,它的诞生是对经典物理的突破。正因如此,建立在统计和测不准关系上的量子力学概念和原理具有很高的抽象性,对于习惯于经典理论的初学者,理解和接受这些概念和原理有相当的困难。如果我们能在经典理论中找到量子力学中对应的概念和原理,将二者进行比较,实现认识上的由实到虚,无疑将大大降低对其理解的难度。作为一个实例,本文简略地对比了从流体、电场到几率波的连续性方程,以显示这种对比法在帮助理解量子力学的概念和原理中所起的作用。     

浅谈利用薛定谔方程计算量子态的时间演化

量子力学教学中,薛定谔方程是描述一个量子系统变化的核心部分.学生对薛定谔方程的学习,可以理解量子物理和经典物理的不同之处,在量子物理教学中,薛定谔方程的讲解是一个非常重要的内容.然而在教学中学生对于薛定谔方程的理解,通常局限在定态薛定谔方程,而对于量子态随着时间的变化部分并不清楚,因此我们引入耦合腔模型:一个单光子在一个耦合的腔系统中,求光子在不同腔中出现概率随着时间变化关系.在教学中利用最简单的哈密顿量描述光子在耦合腔中的跳跃过程,给出几率随着时间变化的解析表达式,从而更加直观的理解微观粒子在一个量子系统中的规律.     

多晶铁氧体的微波物理参量

一、引 言 在微波多晶铁氧体物理中,有三个很基本的问题.第一个问题是在稳恒磁场和交变磁场的同时作用下,铁磁体的磁矩或磁化强度矢量的运动规律问题,也就是通常所说的运动方程问题.对这个问题,有量子力学与经典两类描述方法.由于量子力学描述需具备一定的量子力学知识,而经典描述有形象具体之优点,并且在许多问题上与实验结果符合,所以在这里我们只介绍经典描述.在铁磁体的磁矩或磁化强度矢量运动规律的经典唯象描述中,对于磁矩或磁化强度矢量运动受阻现象,在历史上引进过多种阻尼项来描述,在说明实验现象方面都取得了很大的成功,但是在目…     

量子Berry相因子与相位教学

回顾了经典物理和量子力学中的相位问题,着重讨论了量子几何Berry相位及在量子力学中如何进行量子相位教学的问题.     

量子力学定态不是驻波

作为一种经典或半经典的观点，可以认为定态是由波的干涉形成的驻波，但在量子力学中，定态本身是基本的，不是驻波。     

量子芝诺效应的物理诠释探讨

本文试图从基本的量子力学规律出发，对测量问题中的量子芝诺现象进行分析和讨论，并分别结合一些经典实验和某些学派的解释，着重于动力学退相干模型，对其本身作出物理层面的诠释.     

包含在连续谱量子体系中的决定论性

当一连续谱量子体系具有某一确定能量时,通常的量子力学用单个连续定态来描写它的性质,所得到的任何力学量的期待值都将为零或无穷大。本文以数学定理的形式指出该体系具有一类新的决定论的、物理内容明显的结果。经典力学结果是这些结果的经典极限,通常的量子力学期待值作为一种统计结果而包含在本文结果之内。 关键词：     

Quantum Physics and Classical Physics—In the Light of Quantum Logic

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can be established which is given by an orthomodular lattice. By means of the Solèr condition and Piron's result one obtains the classical Hilbert spaces. However, this approach is not fully convincing. There is no plausible justification of Solèr's law and the quantum ontology is partly too weak and partly too strong. We propose to replace this ontology by an ontology of unsharp properties and conclude that quantum mechanics is more intuitive than classical mechanics and that classical mechanics is not the macroscopic limit of quantum mechanics.     

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments.     

TIME-REVERSAL SYMMETRY AND TIME-DEPENDENT PHYSICS

In this letter I study the concept of time-reversal invariance in both classical and quantum physics in the absence of time-translation invariance (explicit time dependence/external time-dependent fields). Accordingly I generalize the concept of time-reversed process when the time-origin of the process has physical significance. The cases of classical physics, standard quantum mechanics and time-neutral quantum mechanics with and without explicit time dependence are discussed.     

Much Polyphony but Little Harmony: Otto Sackur’s Groping for a Quantum Theory of Gases

The endeavor of Otto Sackur (1880–1914) was driven, on the one hand, by his interest in Nernst’s heat theorem, statistical mechanics, and the problem of chemical equilibrium and, on the other hand, by his goal to shed light on classical mechanics from the quantum vantage point. Inspired by the interplay between classical physics and quantum theory, Sackur chanced to expound his personal take on the role of the quantum in the changing landscape of physics in the turbulent 1910s. We tell the story of this enthusiastic practitioner of the old quantum theory and early contributor to quantum statistical mechanics, whose scientific ontogenesis provides a telling clue about the phylogeny of his contemporaries.     

A general information theoretical proof for the second law of thermodynamics

It is shown that the conservation and the non-additivity of the information, together with the additivity of the entropy, make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the non-additivity of information is also true in other fields in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive. Supported by the National Natural Science Foundation of China (Grant No. 10305001)     

Logical foundation of quantum mechanics

The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to adialogic semantics that is adequate in the case of a formal language for quantum physics. The system ofsequential logic which is comprised by the language is more general than classical logic; it includes the classical system as a special case. Although the system of sequential logic can be founded without reference to the empirical content of quantum physical propositions, it establishes an essential part of the structure of the mathematical formalism used in quantum mechanics. It is the purpose of this paper to demonstrate the connection between the formal language of quantum physics and its representation by mathematical structures in a self-contained way.     

Bell inequalities with no quantum violation and unextendable product bases

The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality-displayed, in particular, by quantum mechanics, meaning that quantum mechanics can outperform classical physics at tasks associated with such Bell inequalities. Interestingly, however, there exist situations in which this is not the case. We associate an intriguing class of bound entangled states, constructed from unextendable product bases with a wide family of tasks, for which (i) quantum correlations do not outperform the classical ones but (ii) there exist supraquantum nonsignaling correlations that do provide an advantage.     

Contextuality in Classical Physics and Its Impact on the Foundations of Quantum Mechanics

It is shown that the hallmark quantum phenomenon of contextuality is present in classical statistical mechanics (CSM). It is first shown that the occurrence of contextuality is equivalent to there being observables that can differentiate between pure and mixed states. CSM is formulated in the formalism of quantum mechanics (FQM), a formulation commonly known as the Koopman–von Neumann formulation (KvN). In KvN, one can then show that such a differentiation between mixed and pure states is possible. As contextuality is a probabilistic phenomenon and as it is exhibited in both classical physics and ordinary quantum mechanics (OQM), it is concluded that the foundational issues regarding quantum mechanics are really issues regarding the foundations of probability.     

2T Physics, Scale Invariance and Topological Vector Fields

We construct, in classical two-time physics, the necessary structure for the most general configuration space formulation of quantum mechanics containing gravity in d+2 dimensions. This structure is composed of a symmetric Riemannian metric tensor and of a vector field that defines a section of a flat U(1) bundle over space-time. This construction is possible because of the existence of a finite local scale invariance of the Hamiltonian and because two-time physics contains, at the classical level, a local generalization of the discrete duality symmetry between position and momentum that underlies the structure of quantum mechanics.