Measurement of long-range wave-function correlations in an open microwave billiard

We investigate the statistical properties of wave functions in an open chaotic cavity. When the number of channels in the openings of the billiard is increased by varying the frequency, wave functions cross over from real to complex. The distribution of the phase rigidity, which characterizes the degree to which a wave function is complex, and long-range correlations of intensity and current density are studied as a function of the number of channels in the openings. All measured quantities are in perfect agreement with theoretical predictions.     

相移相位测量的全息再现算法及测量误差分析

用全息原理和方法研究相移相位测量,得到了N步整周期相移再现物光波复振幅同步叠加函数(N步相移函数),同时提出一种新的相移相位测量误差分析和最大误差估计方法。N步相移干涉图是以理想平行光为参考光的无衍射同轴全息图,将其与对应的相移参考光相乘后求和得到N步相移函数;在理想情况下,这是一种复振幅分离、测量和物光波复振幅函数同步叠加方法,存在误差时计算出的相位是最小二乘方法的最佳期望结果。利用N步相移函数得到的N 1步相移函数,说明非理想N步相移函数是理想N步相移函数与误差函数之和,可以把相位型误差转化为与振幅和强度相对误差同等的误差来对待,降低了相位测量中误差估计的难度,给出了N步相移算法最大误差的估计方法和公式。     

Topological Distillation by Principal Component Analysis in Disordered Fractional Quantum Hall States

We study the behavior of two-dimensional electron gas in the fractional quantum Hall(FQH) regime in the presence of disorder potential. The principal component analysis is applied to a set of disordered Laughlin ground state model wave function to enable us to distill the model wave function of the pure Laughlin state.With increasing the disorder strength, the ground state wave function is expected to deviate from the Laughlin state and eventually leave the FQH phase. We investigate the phase tr...     

Periodic Wave,Solitary Wave and Compacton Solutions of a Nonlinear Wave Equation with Degenerate Dispersion

In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.     

Noniterative phase retrieval from a single diffraction intensity pattern by use of an aperture array

A noniterative method for retrieving the phase of a wave field from a diffraction intensity measurement in a coherent wave field is proposed. In this method, the phase can be calculated from analytic equations based on the properties of entire functions by use of Fourier transforms. This method requires only a single measurement of the intensity of a diffracted wave through an array filter of rectangular apertures and then does not need to use any lens systems and coherent reference waves. Therefore, it provides a potentially useful means for coherent imaging in a wide class of wave fields such as optical, x ray, electron, and atomic waves.     

Interference, Reduced Action, and Trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the trajectories of the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function’s trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.     

Magnetic field dependent dielectric function for zero-gap semiconductors

Using the random phase approximation and the Yafet wave functions the inter and intraband static dielectric functions of degenerate zero-gap semiconductors placed in a magnetic field are calculated in the long wavelength limit. It is shown that the values of the dielectric function for gapless semiconductors differ considerably from the result obtained previously for the one-band model with parabolic energy dispersion ands-type wave functions. Finally the dielectric function is used to find the static screening of a point impurity charge.     

Separability of amplitude,phase and polarization information in the Jones calculus

The two-component Jones vector is cast in a form that achieves the separation of the information on the polarization ellipse from that on the amplitude and phase of the light wave. The shape, sense of rotation and orientation of the elliptic vibration of the electric field are described by the complex polarization variable χ while the amplitude a (size) and temporal phase ? of that vibration are described by the complex amplitude A = aexp(i?). The transformation of the complex amplitude of the wave A after passing through an optical system leads to a complex-amplitude transfer function (CATF) which is a nonanalytic function of the complex polarization variable χ. The CATF is, in turn, separable into polarization-dependent (real) amplitude and phase transfer functions (ATF and PHTF). Together with the polarization transfer function PTF (the transformation of χ), the ATF and PHTF provide a useful set of tools that complement the well-known Jones calculus.     

Interaction-free measurements of the second type: Concepts and proposal for a feasible experiment

Wave aspects inherent in quantum physics lead to observable consequences, which are far removed from classical intuition. The possibility of interaction-free measurement is one consequence of quantum wave nature at the single particle level. To date, all experiments, which have studied interaction-free measurements, have dealt with modification of the amplitude of the wave function. In this paper, we discuss interaction-free measurements of a second type, where only the phase of the wave function is modified. We show that an example discussed by Penrose is in this class and clarify the physical reasons for loss of interference in such measurements. We discuss the experimental feasibility of interaction-free measurements of the second type, employing micromaser cavities and atom interferometers. One scheme leads to the possibility of interactionfree measurement of the finesse of the cavity by observing atoms that never interacted with the cavity. The loss of interference, in this case, is due to a random spinor phase and there is no Heisenberg momentum back-action. This is the first experimental proposal for interaction-free measurements of pure phase changes.     

Schrödinger propagation of initial discontinuities leads to divergence of moments

We show that the large phase expansion of the Schrödinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.     

非对易相空间Dirac oscillator的研究

在极坐标系中研究了非对易相空间中的Dirac oscillator问题.研究显示:系统的波函数可以表示为合流超几何函数,而非对易相空间Dirac oscillator的量子行为类似于朗道问题.最后,对η=0和对易极限两种特殊情况进行了简单讨论.     

面向天基引力波探测的时间延迟干涉技术

时间延迟干涉技术(Time-delay?Interferometry,TDI)对中国引力波探测项目及其它天基激光精密测量任务具有重要的参考价值.在天基引力波探测任务中,需利用激光干涉仪对无拖曳检验质量块间实现十皮米量级的位移测量精度.其中,激光源频率噪声和时钟频率噪声是两项主要噪声.在欧洲主导的LISA(Laser?I...     

Lagrange method and boundary conditions for the intensity correlation functions in turbulent media

An exact functional integral representation for the two-point intensity correlation function was previously obtained by the author for a collimated beam wave by solving the moment equation. The variable functions of integration involved therein can be effectively limited to a set of functions determined so that the entire phase term of the integrand becomes stationary against arbitrary variation of the variable functions, exactly according to the Lagrange variational principle in dynamics. The result is free from any expansion and is presented with a set of unperturbed equations of closed form. When making a formal expansion, it leads to the zeroth- and first-order expressions similar to those obtained by an improved two-scale method. With exactly the same procedure, the three-point intensity correlation and the two-frequency intensity correlation were also obtained.The Lagrange method leads to the 'equation of motion' subjected to boundary conditions to continue the phase term from the incident beam wave. The boundary conditions were previously found based on a physical reasoning, while the same conditions are found here purely based an the variational principle. A focused beam wave is assumed for the incident wave, including both spherical and plane waves as special cases.     

Hadronic quark distribution amplitudes from QCD sum-rule moments

We discuss the reliability of hadronic wave functions (quark distribution amplitudes) determined by a finite number of QCD sum-rule moments. Although the expansion coefficients for polynomial models of the wave function are uniquely determined by the moments, the inherent uncertainty in such moments leads to a considerable indeterminacy in the wave functions because minimal changes of the moments can lead to large oscillations of the model function. In particular, the freedom in the moments left by QCD sum rules leads to a nonconverging polynomial expansion. This remains true even if additional constraints on the wave functions are used. As a consequence of this, the widely used procedure of constructing polynomial models of hadronic wave function from QCD sum rule moments does not guarantee even a reasonable approximation to the true wave function. The differences among the model wave functions persist also in the calculations of physical observables like hadronic form factors. This implies that physical observables calculated by means of such model wave functions are in general very unreliable. As specific examples, we examine the pion and nucleon wave functions and show that Gegenbauer as well as Appell polynomial expansions constructed from QCD sum rule moments are ruled out. The implications for the wave functions which are generally used in the literature are discussed.     

Acoustic anisotropy and birefringence in fibre-reinforced composite materials

All nine elastic moduli of an orthotropic composite material, namely, polypropylene reinforced with glass fiber, are determined from the measured values of the bulk acoustic wave velocities along specific directions in the planes of symmetry of the material. These data are used to calculate the angular dependences of phase velocities, polarization vectors, and directions of ray velocities of bulk waves in the composite. It is demonstrated that the difference in the velocities of shear waves polarized along and across the glass fiber gives rise to an acoustic birefringence and can lead to an elliptical polarization of waves. The measurement of the phase velocities of shear waves as functions of the wave polarization is suggested as a method for the determination of the fiber orientation in a composite material.     

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single‐valuedness of wave functions.     

The chirality of exceptional points

Exceptional points are singularities of the spectrum and wave functions of a Hamiltonian which occur as functions of a complex interaction parameter. They are accessible in experiments with dissipative systems. We show that the wave function at an exceptional point is a specific superposition of two configurations. The phase relation between the configurations is equivalent to a chirality which should be detectable in an experiment. Received 9 April 2001 and Received in final form 19 July 2001     

基于相位分析的时间平均数字全息测振研究

传统的时间平均全息术通过对再现像光强分布的测量来实现振幅分布的检测,由于噪音影响往往得不到满意的结果.第一类零阶贝塞尔函数相位只有0和π两个取值,所以利用再现光场的相位可以确定振幅分布.理论分析发现,以往的讨论忽略了照明光之间位移引起的相位变化,研究通过叠加一个相位因子对此进行了修正,并利用贝塞尔函数平方的相位特点提出了消除该相位因子的办法.实验结果表明,该相位因子确实存在并影响测量,用本文所提出的方法可以很好地消除该相位因子的影响,使利用时间平均数字全息再现光场的相位检测振动物体的振幅分布变得方便和准确.     

Scattering of a plane wave from a periodic random surface: a probabilistic approach

This paper deals with a probabilistic formulation of the wave scattering from a periodic random surface. When a plane wave is incident on a random surface described by a periodic stationary stochastic process, it is shown by a group-theoretic consideration that the scattered wave may have a stochastic Floquet form, i.e. a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then written by a harmonic series representation similar to a Fourier series, where Fourier coefficients are mutually correlated stationary processes instead of constants. The mutually correlated stationary processes are represented by Wiener - Hermite functional series with unknown coefficient functions called Wiener kernels. In case of a slightly rough surface and TE wave incidence, low-order Wiener kernels are determined from the boundary condition. Several statistical properties of the scattering are calculated and illustrated in figures.