采用相位法与极大值法测量超声波声速的准确度的研究

对极值法和相位法测量超声波声速的准确度问题进行了研究,实验与理论分析证明:相位法测量波长比极值法准确度要高.在与简谐运动有关的测量中,测量最大变化率点常常比测量最大值点的准确度要高,这在其他物理实验中也适用.     

声速测量实验原理讨论

本文针对声速测量实验中接收端声压变化的理论推导还不够完善,尤其是对相位比较法的原理解释不清楚的问题,从振幅与声压的关系出发,建立了基于声压方程的多次反射模型.该模型利用平面简谐波函数、声压反射系数公式和波的叠加原理,推导出了接收端的声压振幅和相位随距离的变化公式,并利用该公式解释了驻波法和相位比较法测量的原理.仿真结果表明接收端的声压振幅和相位并不是严格的周期函数,其测量的精度与声吸收系数和声压反射系数等因素有关.最后进行了实验验证,实验测量结果与本文模型的计算结果吻合较好.本文的研究为正确理解该实验的物理本质提供理论指导.     

关于Lewis-Riesenfeld相位和量子几何相位

评注了《大学物理》21 23一文关于量子几何相位与Lewis相位论述与《物理学报》48 2018一文的结论有极大不同.指出前者对Lewis导出的相位与量子几何相位关系的错误陈述，而后者的结论是正确的. 关键词： 量子几何相位 不变量方法 Lewis-Riesenfeld相位     

相干瞬态的量子干涉效应和Berry相位

利用解析方法描述了相干瞬态量子体系中不同类型的量子干涉效应,分别讨论了光学干涉与量子干涉所起的作用,分析了在时域对称光场作用下,几何相位在量子干涉效应中所扮演的角色,从理论上证明了通过适当改变抽运场脉冲面积,可实现对几何相位的测量. 同时研究也发现利用啁啾抽运场可以实现对量子干涉效应的有效控制. 关键词： 相干瞬态 量子干涉 几何相位 啁啾脉冲     

基于参考透镜法的数字全息显微相位畸变校正技术

建立了数值与物理方法结合的参考透镜法,对离轴数字全息显微系统进行畸变相位校正.对离轴全息图进行频谱分析,通过频谱滤波、移位的数值方法对一次相位畸变进行校正.在参考光路中引入参考透镜,根据频谱中心能量判别参考透镜的轴向最佳位置,利用物理方法对多次相位畸变进行校正.在相位校正理论分析的基础上,结合实验用参考透镜法验证其有效性和准确性.微台阶表面形貌测量结果表明,参考透镜法能够准确校正相位畸变,通过校正的相位可以获取44nm标准微台阶形貌数据,测量标准差能够达到0.8nm,且测量结果与轮廓仪测量结果一致.表明参考透镜法能够有效、准确地校正离轴数字全息显微系统的畸变相位.     

实验检验双光子的几何相位

Pancharatnam在研究两束光干涉时提出的几何相位的概念;紧接着Berry发现了量子系统在循环绝热演化下的几何相位.在光子系统中,实验上已经验证了经典光和单光子的几何相位,并观察到几何相位的大小与循环演化过程有关.对于双光子,其几何相位在相同的循环演化下是单光子两倍.我们提出了一种简单的实验方案来观察双光子的几何相位.实验中,通过光路的设计排除了由于光程改变引起的相位改变,直接检测由于几何相位的不同引起的双光子干涉.     

基于几何约束的自适应相位解包裹算法

提出一种通过相机和投影仪的空间几何约束来展开相位包裹的方法,只需要对结构光投影测量系统进行标定,不需要进行传统的时间或空间相位展开.通过投影单周期条纹得到物体的大致高度信息以确定虚拟深度平面,在虚拟平面z0min处,根据结构光系统的标定参数创建最小绝对相位图,物体的包裹相位逐像素与进行比较,即确定条纹级数,实现相位解包裹.该方法具有良好的鲁棒性,对硬件要求低,采集图像少并且不需要额外的物体来获得z0min,能够实现自适应动态测量.实验结果表明,在同等条件下,与传统时间相位展开方法相比,该方法的相对误差降低了14.33%,同时简化了测量方法,能够有效实现物体的三维形貌测量.     

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.     

量子相变与几何相位

量子相变是凝聚态物理中的重要研究课题，而几何相位的发现是近几十年来量子力学中的重要进展，它们毫无关联地各自发展。但最近的研究表明，它们之间有密切联系：多体体系基态的几何相位在量子相变点附近具有标度性；不可收缩的几何相位可用来作为量子相变的标志等，文章将介绍最近在量子相变和几何相位的关系方面的研究进展，并用XY自旋链模型来详细说明．这些结果应会吸引凝聚态和几何相位领域工作的研究人员的关注和兴趣。     

几何法测量棱镜的折射率

用几何法测量棱镜的折射率,它不需要分光计,只需要一块等边或等腰棱镜和一块包括量角器的三角尺.而所得实验结果精确度很高,一次测量可得到小数点后两位数值,多次测量,平均之后可得到小数点后第三位数值.这个实验步骤简便,不需要像分光计那样要测最最小偏向角.因此,它可以做为中学生物理实验中一个分组实验.让中学生做这个实验,不仅有利于同学们学习     

The Schrödinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

We investigate the non-relativistic Schrödinger and Pauli-Dirac oscillators in noncommutative phase space using the five-dimensional Galilean covariant framework. The Schrödinger oscillator presented the correct energy spectrum whose non isotropy is caused by the noncommutativity with an expected similarity between this system and the particle in a magnetic field. A general Hamiltonian for the 3-dimensional Galilean covariant Pauli-Dirac oscillator was obtained and it presents the usual terms that appears in commutative space, like Zeeman effect and spin-orbit terms. We find that the Hamiltonian also possesses terms involving the noncommutative parameters that are related to a type of magnetic moment and an electric dipole moment.     

Anandan quantum phase for a neutral particle with Fermi–Walker reference frame in the cosmic string background

We study geometric quantum phases in the relativistic and non-relativistic quantum dynamics of a neutral particle with a permanent magnetic dipole moment interacting with two distinct field configurations in a cosmic string spacetime. We consider the local reference frames of the observers are transported via Fermi–Walker transport and study the influence of the non-inertial effects on the phase shift of the wave function of the neutral particle due to the choice of this local frame. We show that the wave function of the neutral particle acquires non-dispersive relativistic and non-relativistic quantum geometric phases due to the topology of the spacetime, the interaction between the magnetic dipole moment with external fields and the spin–rotation coupling. However, due to the Fermi–Walker reference frame, no phase shift associated to the Sagnac effect appears in the quantum dynamics of a neutral particle. We show that in the absence of topological defect, the contribution to the quantum phase due to the spin–rotation coupling is equivalent to the Mashhoon effect in non-relativistic dynamics.     

Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations

This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle as well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics.     

Perturbations of unitary representations of the Galilei group: Mass operators with continuous spectra

We present a systematic procedure for constructing mass operators with continuous spectra for a system of particles in a manner consistent with Galilean relativity. These mass operators can be used to construct what may be called point-form Galilean dynamics. As in the relativistic case introduced by Dirac, the point-form dynamics for the Galilean case is characterized by both the Hamiltonian and momenta being altered by interactions. An interesting property of such perturbative terms to the Hamiltonian and momentum operators is that, while having well-defined transformation properties under the Galilei group, they also satisfy Maxwell’s equations. This result is an alternative to the well-known Feynman-Dyson derivation of Maxwell’s equations from non-relativistic quantum physics.     

Gravitational geometric phase in the presence of torsion

We investigate the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle subject to an external electromagnetic field in the presence of a cosmic dislocation. We analyze the explicit contribution of the torsion in the geometric phase acquired in the dynamics of this neutral spinorial particle. We discuss the influence of the torsion in the relativistic geometric phase. Using the Foldy–Wouthuysen approximation, the non-relativistic quantum dynamics is studied and the influence of the torsion on the Aharonov–Casher and He–McKellar–Wilkens effects are discussed. An erratum to this article can be found at     

Physical theories in Galilean space-time and the origin of Schrödinger-like equations

A method to develop physical theories of free particles in space-time with the Galilean metric is presented. The method is based on a Principle of Analyticity and a Principle of Relativity, and uses the Galilei group of the metric. The first principle requires that state functions describing the particles are analytic and the second principle demands that dynamical equations for these functions are Galilean invariant. It is shown that the method can be used to formally derive Schrödinger-like equations and to determine modifications of the Galilei group of the metric that are necessary to fullfil the requirements of analyticity and Galilean invariance. The obtained results shed a new light on the origin of Schrödinger’s equation of non-relativistic quantum mechanics.     

Dynamical symmetries in mechanics

The object of this review is to discuss methods that enable one to trace the origin of symmetries and conservation laws in mechanics to geometrical symmetries of space-time. Starting with the basic Newtonian assumptions on absolute space and time classical mechanics is developed in configuration space and phase space independently together with the related structures such as force-less mechanics. Heuristic considerations on geometric symmetries in configuration space reveal their intimate relation to conservation laws. Using the methods of differential geometry this relationship is put on a formal footing and symmetry groups of all spherically symmetric single term potentials are classified. The method of infinitesimal canonical transformations is presented as an alternative method of deducing dynamical symmetries of an arbitrary system in phase space. These methods also apply to non-relativistic quantum theory. Possible extension to special and general relatively is also discussed.     

Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration can equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle.