Correlated calculations of indirect nuclear spin-spin coupling constants using second-order polarization propagator approximations: SOPPA and SOPPA(CCSD)

We present correlated calculations of the indirect nuclear spin-spin coupling constants of HD, HF, H₂O, CH₄, C₂H₂, BH, AlH, CO and N₂ at the level of the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes – SOPPA(CCSD). Attention is given to the effect of the so-called W ₄ term, which has not been included in previous SOPPA spin-spin coupling constant studies of these molecules. Large sets of Gaussian basis functions, optimized for the calculation of indirect nuclear spin-spin coupling constants, were used instead of the in general rather small basis sets used in previous studies. We find that for nearly all couplings the SOPPA(CCSD) method performs better than SOPPA. Received: 6 July 1998 / Accepted: 8 September 1998 / Published online: 23 November 1998     

Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss’ law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss’ law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schrödinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case.     

Hooke＇s Atom in an Arbitrary External Electric Field： Analytical Solutions of Two-Electron Problem by Path Integral Approach

By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analyticalsolutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.     

Unquenched Effects and Quark Mass Dependence of Lattice Gluon Propagator in Infrared Region

In this paper, the gluon propagator in Landau gauge has been studied on a lattice, including the quenched and the unquenched one. The small geometry size of lattice we use is 16³×32, and the big one is 20³×64. For the quenched approximation, we fit the numerical results and give a little different fitting values. We also obtain unquenched effects by comparing the gluon propagator resulting from the quenched and unquenched configurations, for both the two-flavor and three-flavor cases. For the unquenched configurations, an obvious quark mass dependence has not been found in the small quark mass case, but is found in the three-flavor case when the quark mass is big.     

QCD真空凝聚和参数化的夸克传播子

基于整体色对称模型,用完全穿衣服参数化的夸克传播子研究了量子色动力学(QCD)真空的性质,预言了各种表征QCD真空的凝聚值.其结果与其他唯象QCD理论模型的预言是一致的.结果清楚地表明了参数化的夸克传播子是成功和可靠的.讨论了计算QCD真空凝聚值时积分截断参数的问题,提出了一个避免计算的结果对截断参数强烈依赖的物理方法.     

Finite expansion of the inverse matrix in the polarization propagator method

 An alternative theoretical approach to the polarization propagator based on a new finite expansion of a finite-dimensional matrix is presented. The general equations for such an expansion are derived and the validity conditions stated. This method is used to accomplish an approximate scheme for the self-energy of the particle–hole propagator within the superoperator formalism. Within this scheme each contribution includes corrections to infinite order in electronic interaction and so describes collective effects in a natural way. Individual contributions can be interpreted as describing the propagation of the interaction through a particular subset of electronic excitations. Comparison with other known approximation levels, such as the random-phase approximation, is also analyzed. Received: 14 February 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

Size-consistent single-reference methods for electronic correlation: a unified formulation through intermediate hamiltonian theory

 Using the intermediate hamiltonian theory as a unique conceptual frame and the technique of CI matrix dressing, a wide series of single-reference methods for the treatment of the ground state correlation are reviewed, compared, and sometimes improved. These methods range from independent excitation approximation (the very next step beyond MP2) to coupled cluster, going through the so-called electron pair approximations and the (SC)²CI formalism. A hierarchy of these methods can be established according to two criteria: 1. The physical effects incorporated in the model space, the choice of which is flexible. 2. The quality of the evaluation of the coefficients of the external space determinants. This evaluation, which remains based on a single reference expansion of the wave function, may simply ensure the size consistency or incorporate the linked contributions from the outer space. These formulations in terms of diagonalizations of dressed CI matrices avoid convergence problems, but their main advantage is their flexibility, since they apply to multi-reference SDCI spaces as well as to SDCI spaces. The use of a common frame allows one to propose consistent combinations of methods of various costs for the treatment of various parts of the correlation energy. Received May 13, 1996/Final version received December 9, 1996/Accepted December 9, 1996     

Nonlocal condensate model for QCD sum rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the Källén–Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to Q²≈10 GeV²$Q^2\approx 10{\text{GeV}}^2$. It is observed that the nonlocal quark condensate contribution descends like 1/Q²$1/Q^2$, different from the exponential decrease in Q²$Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.     

标准模型中两类中性玻色子混合圈链图传播子的重整化及其e+e-→μ+μ-反应截面

采用电弱统一标准模型, 对光子γ和中间玻色子Z₀ 混合圈链图传播子的构架方式及其重整化问题作了详细分析与讨论, 并完成了有关解析计算, 获得了由参与电弱相互作用的各种混合圈构成的γ和Z₀的重整化链图传播子的解析计算结果. 此外, 我们还将此结果应用于高能物理中备受关注的一类轻子反应e⁺e^-→μ⁺μ^-中, 获得了在γ和Z₀所构架出的重整化混合圈链图传播中e⁺e^-→μ⁺μ^-反应截面的解析计算结果, 并将本文所获得的这一理论计算结果与实验观测值作了对比分析, 发现本文理论计算结果与实验观测值符合非常好, 并由此也获得了有关辐射修正的重要信息. 本文研究结果也可为探讨一般复杂传播子的理论研究与应用提供某些参考. 关键词： 标准模型 链图传播子 重整化 辐射修正     

A randomized method for one‐step extrapolation in reverse time migration

Reverse time migration has drawn great attention in exploration geophysics because it can be used successfully in areas with large structural and velocity complexity. But its computational cost is considerably high. This paper concerns the fast implementation of the optimized separable approximation of the two‐way propagator, which is the most computational expensive step in reverse time migration. On the basis of the low‐rank property of the propagator and the idea of randomized algorithm, a randomized method is introduced for optimized separable approximation‐based one‐step extrapolation. Numerical results of approximating the propagator show that the randomized method is more efficient than the conventional interpolation method. At the same time, numerical experiments of wavefield extrapolation show that the proposed method is much more accurate than the conventional finite‐difference plus pseudo‐spectrum scheme. Copyright © 2014 John Wiley & Sons, Ltd.