Variational calculations of vibrational energy levels for XY4 molecules 1. Stretching states

A variational method for calculating excited stretching states of symmetric tetrahedral pentaatomic molecules is presented based on the use of Radau coordinates and Morse oscillator-like basis functions. Symmetry is used both to reduce the size of the secular matrix to be diag-onalized and to calculate the potential energy matrix elements over a reduced grid of quadrature points. Test results are presented for methane, silane and germane. For CH₄, stretch-bend coupling is found to be significant, whereas it is less important for the more strongly local mode SiH₄ and GeH₄ molecules. Converged results are obtained for stretching states significantly higher than considered in previous calculations. These states will be used to represent stretching motions in a fully coupled stretch-bend calculation.     

Refined local mode analysis of the stretching vibrational levels of C2D2

Dideuteroacetylene, C₂D₂, is a remarkable species for which the stretch-bend separability of the vibrational states is such that all the experimentally known stretching levels can be reproduced with an rms of 1.1 cm^?1 by using a simple stretching coordinate Hamiltonian model. The only two levels which deviate significantly from the calculations point out the effect of the 1/244 stretch-bend resonance previously identified. The local mode parameters retrieved from the fit of the experimental levels allow for a very satisfactory prediction of the available energy levels of the ¹²C¹³CD₂ species. A comparison between the local mode and normal mode approaches is presented.     

Evaluation of entanglement of CV-pair

Practical realizations of qubits and systems of qubits are implement by particles with states from infinite-dimensional space, such as space of wave functions for coordinate representation of quantum mechanics. Properties of the entangled states of continuous variables differ from such for discrete variables. That occurs due to existence of unlimited operators of observables and their uncertainties. In this work we used and extended idea of entanglement estimation for the case of continuous variables with the help of covariance matrix norm. Well-known concurrence was calculated with the help of covariance of observables. The goal of this paper is to check if it is possible to apply this idea to continuous variables. We consider coherent electron pair as the object of our investigation. We also consider coordinate and momentum of coherent electron pair as basis of observables. In this work, a new characteristic of entanglement is proposed. We evaluated that using correlation function instead of covariance. For the small distances between particles, it coincides with covariance matrix norm but for the big distances, it remains restricted.     

The application of the nonrigid bender Hamiltonian to a quasilinear molecule

The form of the nonrigid bender has changes that here we do render. We add, nicely paired, a term to J² and regroup factors that are singular. As a result, the nonrigid bender Hamiltonian can now be set up using only Van Vleck perturbation theory, for any triatomic molecule (linear, quasi-linear, or bent). It can be used to calculate the rotation-vibration energies of the molecule to high $\text{J(?10)}$ from the bending potential energy function and the stretch and stretch-bend force constants.     

Studying adequacy, completeness, and accuracy of quantum measurement protocols

A new methodology of statistical estimation of the quality of quantum measurement protocols is considered. The method is based on studying the completeness, adequacy, and accuracy of quantum measurement protocols. The completeness is estimated on the basis of considering a singular decomposition of a special matrix, which is constructed based on the measurement operators. The estimate of adequacy supposes the presence of redundancy in the measurement protocol as compared to the minimally possible number of measurements that are necessary for full reconstruction of a quantum state. The adequacy of quantum measurements is estimated as the degree of how much the redundant statistical data agree with the laws of quantum theory. The accuracy characteristics of the statistical reconstruction of arbitrary quantum states are studied based on the universal statistical distribution for accuracy losses. Examples of applying the developed methods are presented for seven quantum protocols based on the geometry of polyhedra with a high degree of symmetry.     

A generalized internal axis method for high barrier tunneling problems,as applied to the water dimer

When more than one large-amplitude vibrational motion is present in a molecule, it is often not possible to define a global internal-axis-method (IAM) coordinate system and set of basis functions. In the present work, a method is presented for extending the IAM treatment to tunneling problems in such cases, using as an illustration a model for the water dimer with three large-amplitude vibrational coordinates. The method involves the construction of two different sets of local IAM-like coordinate systems. The first of these contains n coordinate systems, one for the small neighborhood surrounding each of the n equilibrium frameworks. The second contains on the order of $\text{n}{}^2\text{2}$ coordinate systems, one for each feasible tunneling path between each pair of frameworks. Basis functions written in the second set of local IAM-like coordinates are used to determine the complex phase factors associated in this method with tunneling matrix elements of the phenomenological rotational Hamiltonian in the high barrier limit. These phase factors govern the way in which the various real tunneling frequencies in the molecule constructively and/or destructively interfere in the Hamiltonian matrix elements and final energy expressions. Various mathematical approximations are involved in using the local IAM-like basis sets to obtain matrix elements; the full extent of the adverse effects of these approximations will not be known until an attempt to fit experimental data is carried out.     

Indeterminancy of the potential matrix in redundant coordinates

The use of redundant internal coordinates in vibrational problems leads to an indeterminate potential matrix. Two formulations are given which express the indeterminancy by sets of arbitrary parameters. All potential matrices related by these formulations within a given set of internal coordinates lead to the same vibrational eigenvalues and eigenvectors. The indeterminancy is illustrated by examples and by possible application in practical normal coordinate analysis.     

像散椭圆高斯光束的M2因子矩阵的理论与实验研究

对像散椭圆高斯光束, 传统的M²因子测量采用M_x²和M_y²来描述光束质量. 当光束绕z轴旋转, M_x²和M_y²会随之变化, 单纯采用M_x²和M_y²来评价激光光束质量并不唯一. 为此采用了像散椭圆高斯光束的M²因子矩阵, 理论推导出了在同一坐标系下光场绕z轴旋转不同角度后的M²因子矩阵, 找出了光场旋转前后的M²因子矩阵元的不变量关系. 数值模拟、 实验测量得到M²因子矩阵主对角元随光斑旋转角度的变化轨迹曲线, 及反对角元随旋转角度的变化规律. 理论推导与实验结果相符. 结果表明, 像散椭圆高斯光束在主方向上时M_x²与M_y²之和最小; 在其他方向上的M_x², M_y²之和大于在主方向上的M_x², M_y²之和; 反对角元随旋转角度呈周期变化, 在主方向上为零. 关键词： M²因子矩阵')" href="#">M²因子矩阵 像散椭圆高斯光束 实验测量 矩阵光学     

Laser probing of ions in a storage ring: A method for selective determination of lifetimes of metastable states

A collinear laser probing technique is introduced for use in ion storage rings. This method can be used for high resolution studies of the decay properties of metastable states in ions. An experiment on singly charged xenon utilizing this technique is presented. By selective excitation of individual hyperfine states a drastic hyperfine induced quenching was observed. Systematic effects from ion beam neutralization in the rest gas and mixing effects occurring in the bending magnets are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Some aspects of redundant states in nucleon-nucleus scattering solutions with antisymmetrization

Redundant states are known to appear as solutions to the scattering equation when an incident particle is antisymmetrized with respect to a target nucleus represented by a Slater determinant. Using criteria which have been found to characterize a potential which produces a continuum bound state (CBS), we demonstrate that a redundant solution can be identified as a CBS which appears at every positive energy. This identification provides a procedure for isolating and removing that portion of the potential responsible for redundant states. The remaining portion of the potential generates solutions to the original scattering equation which we demonstrate to be orthogonal to the redundant states which have been eliminated.     

Self-consistent models of collective and single-particle structures and their test by inelastic scattering: The case of 54Fe

Generator coordinate wave functions built from angular momentum and particle number projected Hartree-Fock-Bogoliubov states that were constrained to different quadrupole deformations and allowing two-quasiparticle excitations are tested by their use in analyses of inelastic proton scattering. Transitions to low-lying states in ⁵⁴Fe are used as the specific examples and comparisons are made with appropriate, albeit smaller basis, shell-model predictions.     

Construction of microscopic boson states and their relevance for IBM-2

We investigate four methods for the construction of collective shell model states which may be mapped onto boson states of the IBM-2. These methods use, as building blocks for the wave functions, particle-particle pair operators, particle-hole operators, pair operators with seniority projection and energy-weighted quadrupole operators. It is demonstrated that one obtains stronger collectivity with the energy-weighted quadrupole operator than with the other methods.On the basis of a comparison of calculated and empirical IBM-2 interaction parameters we can rule out the seniority projection method. This implies that particle-particle and particle-hole approaches difler.The ratios between quadrupole matrix elements of the microscopic boson states appear to be similar to the IBM predictions. For states corresponding to those with two d-bosons coupled to J = 0 there is a smaller quadrupole matrix element when subshells with small angular momenta dominate near the Fermi level. Especially for this type of states the collective quadrupole space will be larger than represented in the IBM, however, which may compensate the smaller proton-neutron quadrupole coupling.The calculated bare quadrupole interaction between like bosons is found to be weak.     

A generalized Talmi-Moshinsky transformation for few-body and direct interaction matrix elements

A set of basis states for use in evaluating matrix elements of few-body system operators is suggested. These basis states are products of harmonic oscillator wave functions having as arguments a set of Jacobi coordinates for the system. We show that these harmonic oscillator functions can be chosen in a manner that allows such a product to be expanded as a finite sum of the corresponding products for any other set of Jacobi coordinates. This result is a generalization of the Talmi-Moshinsky transformation for two equal-mass particles to a system of any number of particles of arbitrary masses. With the help of our method the multidimensional integral which must be performed to evaluate a few-body matrix element can be transformed into a sum of products of three dimensional integrals. The coefficients in such an expansion are generalized Talmi-Moshinsky coefficients. The method is tested by calculation of a matrix element for knockout scattering for a simple three-body system. The results indicate that the method is a viable calculational tool.     

Overlaps of deformed and non-deformed harmonic oscillator basis states

A systematic approach for expanding non-deformed harmonic oscillator basis states in terms of deformed ones, and vice versa, is presented. The objective is to provide analytical results for calculating these overlaps (transformation brackets) between deformed and non-deformed basis states in spherical, cylindrical, and Cartesian coordinates. These overlaps can be used for reducing the complexity of different research problems that employ three-dimensional harmonic oscillator basis states, for example as used in coherent state theory and the nuclear shell-model, especially within the context of ab initio symmetry-adapted no-core shell model.     

Elimination of Compressive Stress in Helical-Toroidal-Coil Advanced Structure for Reactor Plasmas

Calculations of inductance for helical toroidal coils are of great interest to researchers since they are the basis of optimal design with target functions such as the maximization of the ratio of the stored magnetic energy with respect to the volume of the toroid or the used conductor, the elimination or the balance of stress in certain coordinate directions, and the attenuation of leakage flux. In this paper, using Neumann's equation, formulas are presented to calculate the self-inductance and mutual inductance of the helical toroidal coil in superconductivity conditions. It is shown that calculation of self-inductance is similar to that of mutual inductance if the diameter of the conductor's cross section is smaller than 0.4 of the minor radius. Comparison between experimental and empirical results with numerical results indicates that the presented formulas are highly reliable. Plotting contours for the magnetic flux density shows that a special design approach must be taken so that the coil eliminates the leakage flux. It is also shown that the optimal design of the coil to eliminate or balance the stress in certain coordinate directions requires selection of geometrical parameters from accurate inductance equations, and therefore, the use of approximate equations for this purpose is not recommended.      

改进的三维分离变量表象方法计算振动光谱

用改进的三维分离变量表象(DVR3D)方法研究了基态电子态H2S和H2O的振动光谱。哈密顿形式在Jacobi坐标下给出,每个坐标都用一组DVR基函数表示.角度部分的DVR基组选择勒让德多项式形式,而径向坐标采用正弦函数形式.为了降低需要对角化的最终哈密顿矩阵的维数,采用连续对角化截断方法.用H2S和H2O振动能级的计算验证算法的正确性.     

A new particle-hole approach to collective states

The relevance of the particle-hole space is demonstrated by showing that in some commonly used formalisms the first excited state lies entirely within the particle-hole space generated from the correlated ground state. This property is proved for several cases of angularmomentum projection — projected Hartree-Fock method (PHF) — and for the generator coordinate method in the Gaussian overlap approximation, while in other cases it has been verified only numerically. A new method is presented for the approximate calculation of energies and transition amplitudes of particle-hole excited states. Only hermitian one-body operators are used to generate the excited states. The two-body density matrix of a correlated state approximating the ground state is required as input data. The formula is tested on the 2⁺ and 3^? states of ⁸Be and ¹²C by using the PHF ground state. Where comparison is possible the method gives better agreement with PHF and experiment than the extended random-phase approximation.     

Quantum teleportation of an entangled pair for continuous variables

The teleportation of a two-particle entangled state, using a Greenberger-Horne-Zeilinger triplet, for continuous variables is studied. The basis for joint three-particle measurements is found, where the vectors describe the states in which only two of three particles are entangled. It represents the measurement of the momentum of one particle and the difference of coordinates and the sum of momenta of the two other particles. An optical realization of this scheme is presented, which uses squeezed states of light and reduces the measurement of momentum and coordinate to the detection of quadrature operators of the electromagnetic field.     

波导弯曲半径与弯曲损耗的关系

介绍了分析波导弯曲损耗的保形变换法和归一化方法以及由此得到的波导弯曲半径与弯曲损耗的关系式.建立了弯曲损耗经验公式,由该公式得出了四种常用材料的波导弯曲半径与弯曲损耗的曲线,并将已报道的相应材料制作的AWG中的最小弯曲半径及其对应的损耗实验数据与这些曲线上的相应数值进行了比较,结果表明,弯曲损耗经验公式在确定AWG中的最小弯曲半径时,有一定的参考价值.     

Vibrational modes of the stibine molecule

In this paper, we use the algebraic approach to describe the vibrational modes of stibine molecule (of C_3v molecular symmetry group) up to 21 quanta. As the stibine molecule exhibits stretch-bend resonances, we build an algebraic pyramidal coupling operator between stretching modes and bending modes adapted to this molecule. The standard deviation associated to the fit of the vibrational levels is 1.75 cm⁻¹.