Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids

Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for detecting flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Quantitative ultrasonic scattering models include components of transducer beam patterns as well as microstructural scattering information. Here, the Wigner distribution is used in conjunction with the stochastic wave equation to model this scattering problem. The Wigner distribution represents a distribution in space and time of spectral energy density as a function of wave vector and frequency. The scattered response is derived within the context of the Wigner distribution of the beam pattern of a Gaussian transducer. The source and receiver distributions are included in the analysis in a rigorous fashion. The resulting scattered response is then simplified in the single-scattering limit typical of many diffuse backscatter experiments. Such experiments, usually done using a modified pulse-echo technique, utilize the variance of the signals in space as the primary measure of microstructure. The derivation presented forms a rigorous foundation for the multiple scattering process associated with ultrasonic experiments in heterogeneous media. These results are anticipated to be relevant to ultrasonic nondestructive evaluation of polycrystalline and other heterogeneous solids.     

Wigner function for a free particle in two dimensions: A tale of interference

The familiar wave function for a free particle in two dimensions and in a state with definite values of energy and angular momentum shows some unusual effects. We identify the origin of these subtleties as interference in two-dimensional space where Huygens’ principle breaks down. Our arguments are based upon the corresponding Wigner function.     

Quantum Dynamical Behavior of the Morse Oscillator: the Wigner Function Approach

We explore the quantum dynamical behavior of the Morse oscillator in the phase space using the Wigner function. For an initial wave packet excited with Gaussian probability distribution, we calculate the associated Wigner function and compute its time evolution. By calculating the marginal probabilities, we study the formation of quantum carpets both in the position space and in the momentum space. In addition, in view of these probabilities, we present the time evolution of the position and momentum expectation values. The structure of quantum carpets and the time-evolved expectation values mimic the emergence of quantum revivals and fractional revivals.     

The Wigner Functions for a Spin-1/2 Relativistic Particle in the Presence of Magnetic Field

This paper provides a study of Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field. Since the Dirac equation is described as a matrix equation, it is necessary to describe the Wigner function as a matrix function in phase space. What’s more, this function is then proved to satisfy the Dirac equation with ⋆-product. Finally, by solving the ⋆-product Dirac equation, the energy levels as well as the Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field are obtained.     

Bragg scattering of cooper pairs in an ultracold Fermi gas

We present a theoretical treatment of Bragg scattering of a degenerate Fermi gas in the weakly interacting BCS regime. Our numerical calculations predict correlated scattering of Cooper pairs into a spherical shell in momentum space. The scattered shell of correlated atoms is centered at half the usual Bragg momentum transfer, and can be clearly distinguished from atoms scattered by the usual single-particle Bragg mechanism. We develop an analytic model that explains key features of the correlated-pair Bragg scattering, and determine the dependence of that scattering on the initial pair correlations in the gas.     

Schwinger Bose实现下自旋相干态Wigner函数的特性分析

在Schwinger Bose实现下,引入纠缠态表象及Wigner算符在该表象下的表示,得到自旋相干态的Wigner函数,数值计算画出相空间中Wigner函数的分布图,并加以分析,发现在SchwingerBose实现下自旋相干态确实体现出纠缠特性。     

A New Derivation of the Quantum Navier–Stokes Equations in the Wigner–Fokker–Planck Approach

A quantum Navier–Stokes system for the particle, momentum, and energy densities is formally derived from the Wigner–Fokker–Planck equation using a moment method. The viscosity term depends on the particle density with a shear viscosity coefficient which equals the quantum diffusion coefficient of the Fokker–Planck collision operator. The main idea of the derivation is the use of a so-called osmotic momentum operator, which is the sum of the phase-space momentum and the gradient operator. In this way, a Chapman–Enskog expansion of the Wigner function, which typically leads to viscous approximations, is avoided. Moreover, we show that the osmotic momentum emerges from local gauge theory.     

Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function.     

Correlation effects on the charge radii of exotic nuclei

The structures and distributions of light nuclei are investigated within a microscopic correlation model. Two particle correlations are responsible for the scattering of model particles either to low momentum- or to high momentum-states. The low momentum states form the model space while the high momentum states are used to calculate the G-matrix. The three and higher order particle correlations do not play a role in the latter calculation especially if the correlations induced by the scattering operator are of sufficient short range. They modify however, via the long tail of the nuclear potential, the Slater determinant of the (A) particles by generating excited Slater’s determinants.      

Minimum uncertainty states in angular momentum and angle variables for charged particles in structured electromagnetic fields

We study the phase-space properties of a charged particle in a static electromagnetic field exhibiting vortex pairs with complementary topological charges and in a pure gauge field. A stationary solution of the Schrödinger equation that minimizes the uncertainty relations for angular momentum and trigonometric functions of the phase is obtained. It does not exhibit vortices and the angular momentum is due to the gauge field only. Increasing the topological charge of the vortices increases the regions where the Wigner function in the angle–angular momentum plane takes negative values, and thus enhances the quantum character of the dynamics.     

Marginal Distributions of Wigner Function in a Mesoscopic L-C Circuit at Finite Temperature and Thermal Wigner Operator

Wigner function in phase space has its physical meaning as marginal probability distribution in coordinate space and momentum space respectively, here we endow the Wigner function with a new physical meaning, i.e., its marginal distributions’ statistical average for q ²/(2C) and p ²/(2L) are the energy stored in capacity and in inductance of a mesoscopic L-C circuit at finite temperature, respectively. PACS numbers: 03.65.-w, 73.21.-b     

Feshbach resonances in positron scattering from sodium

S-, P- and D-wave Feshbach resonances in positron-sodium scattering have been investigated by using the momentum space coupled-channels optical method. The target continuum and positronium (Ps) formation channels are included via an optical potential. Feshbach resonances below the target excitation and Ps (n = 2) formation thresholds are predicted and the effects of channel-coupling scheme, target continuum and Ps formation channels on the resonance energy and resonance width are discussed. We have also found the Wigner cusp structures at the inelastic channel-opening thresholds in positron-sodium scattering cross sections.     

TheN/D method off the mass shell for the Klein-Gordon equation and the inversion problem

The relativistic analogon of a procedure demonstrating the link between theS-wave off-the-mass- shellN/D equations (variables: the momentum, energy and radial coordinate of a scattered particle) and the Marchenko equations of the inversion problem is presented in the static scattering. For the Klein-Gordon formalism the transition from the former type of the equations to the latter requires: a decomposition of theN/D equation quantities into the components without theE-branch points, a suitable deformation of the integration path in theN/D equations and an assumption on the regular behaviour of the off-the-mass-shellN function discontinuities.     

Solutions of the integral equations for four identical particles

Using the separable representation of the scattering amplitudes for the subsystems 3 + 1 and 2 + 2, the integral equations for four identical particles with a separable two-particle interaction are reduced to a set of single variable integral equations. By solving the equations obtained, the binding energies and wave functions of the low-lying 0⁺ states of the system of four identical bosons, as well as the scattering length of a particle scattered by three bound particles, are calculated. The solution of the set of integral equations, describing the bound state of four nucleons, is performed, approximating the space wave function by a symmetric one, and the binding energy and wave function of the nucleus ⁴He are calculated.     

Photon momentum in a surface plasmon

It is shown that the photon momentum in a surface plasmon is ? k, where k is the plasmon wave vector. In a significantly delayed plasmon on a thin metal film or filament, the photon momentum is several hundred times larger than the momentum of a photon of the same frequency in a plane wave in free space. The plasmon-plasmon and free-space plane wave-plasmon scattering by a free electron is considered. It is shown that, in contrast to the plane wave-plane wave scattering, the electron acquires a significant momentum, while the scattered plasmon frequency significantly changes. The former process is similar to the Compton effect: scattering of X-ray and γ quanta (having a significant momentum) by an electron. In the latter process, the system composed on an incident photon and an electron at rest, which has a small total momentum, generates a photon and an electron, each having a large momentum. A device for detecting electrons from plasmons excited in nearby metal nanofilms and nanowires can be developed on the basis of this principle.     

Quantum Discord in Scattering Processes by Fixed Spin Impurities

The dynamic behavior of the quantum discord in one-dimensional scattering of a qubit (a spin-1/2 particle) by single and double well-localized fixed spin impurities is investigated theoretically. It is assumed that the incident particle is scattered by the spin impurities through the Ising and/or Heisenberg interactions. These potentials create quantum mechanical correlation between the reflected and transmitted parts of the scattered system and the impurities. It is shown that the incident momentum, strength of the interaction potentials, and the separation between the impurities can be regarded as the control parameters for the quantum discord and concurrence manipulations. In particular, it has been found that the correlations are periodic functions of the wavelength of the incident particle when it is scattered by the double spin impurities.     

Wigner Distributions in Light-Front Quark Models

We discuss the quark Wigner distributions which represent the quantum-mechanical analogues of the classical phase-space distributions. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse momentum dependent parton distributions, which encode the most general one-body information of partons in momentum space. In particular, we present a study within light-front quark models. The quark orbital angular momentum is also obtained from the phase-space average of the orbital angular momentum operator weighted with the Wigner distribution of unpolarized quark in a longitudinally polarized nucleon. The corresponding results calculated within different light-front quark models are compared with alternative definitions of the quark orbital angular momentum as given in terms of generalized parton distributions and transverse momentum dependent parton distributions.