基于关联基的壳模型截断计算

提出了一种新的用于壳模型截断计算的基矢空间的构建方法,即关联基的方法。关联基是利用壳模型中每个粒子数分布下哈密顿量的本征态作为基矢。在此基矢之上,可以很自然地通过考虑能量相对较低的关联基矢进行相应的截断计算。当所有的关联基矢都被考虑时,计算结果回到一般jj耦合给出的结果。最后,对关联基下壳模型的计算与标准的壳模型计算进行了比较,计算结果表明,关联基下壳模型能量和波函数有着良好的收敛性,同时表明关联基计算的有效性。     

金属电子关联函数的实空间变分计算

本文求解了在相关基函数理论框架下得到的实空间关联函数的积分方程,得到了金属铝(r_s=2.07)和铯(r_s=5.65)的关联函数,关联能和多体波函数。改进了其它多体理论,本文得到的关联函数是恒正的,并且满足归一化条件。 关键词：     

Correlated ground state of the Hubbard model

The variational many-body approach or, more generally, the method of correlated basis functions initiated for a quantitative analysis of strongly interacting quantum fluids may be adapted with minor modifications for exploring the properties of lattice models. This is demonstrated by performing an explicit analysis of the paramagnetic ground state of the Hubbard model. In a first step of the approximation scheme we represent the correlated state by a spin-dependent wave function of Jastrow-type. We analyze in detail the associated density-matrix elements and set up the corresponding Fermi hypernetted-chain equations which determine the irreducible constituents of these quantities. The solutions are discussed and constructed by iteration in terms of cluster approximants. Specializing the input data and the formal results provides a Fermi hypernetted-chain analysis of the correlations induced by a ground state wave function of the Gutzwiller form.     

A correlated-basis-functions approach to realistic nuclear matter

The method of correlated basis functions is adapted to the nuclear-matter problem with two-nucleon potentials containing tensor as well as central components. Procedures are described for evaluating through three-body cluster order the energy expectation value with respect to a constrained trial ground-state wave function incorporating tensor and central correlations, and for calculating in two-body cluster approximation the second-order perturbation correction in a basis of likewise-correlated functions. Results for the 5100, 5200, Gammel-Christian-Thaler and Hamada-Johnston potentials are presented and dissected.     

APW dispersion relation for plasmon in metals

Following Ichikawa's technique we derived a dispersion relation for plasmons in metals using APW (Augmented Plane Wave) wave functions. The formula contained herein may be used to acquire information concerning the filling of the energy bands and so data needed in explaining electrical and magnetic properties of metals.     

Generalized Lanczos method for systematic optimization of tensor network states

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states(TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.     

采用振速测量的改进统计最优近场声全息方法

针对常规统计最优近场声全息在空间多源声场重建过程中所需波函数项数多、重建精度不理想的问题,本文提出了一种基于振速测量的改进统计最优近场声全息算法。与常规算法不同,改进算法主要根据声源特点选取合适的波函数组合来计算声场传递矩阵。通过数值仿真初步验证了该方法的准确性和有效性,并与常规算法进行了详细的对比分析。仿真结果表明,改进算法重建精度高,随频率的变化相对误差波动较小,且随着频率的增大相对误差有逐渐减小的趋势;此外,不同的波函数组合,重建效果差异很大,当选取的波函数与声源共形且数量一致时重建效果最好。     

Bose-Einstein condensation, phase coherence, and two-fluid behavior in 4He

It is shown that the assumption that the many particle wave functions describing superfluid 4He have some phase coherence properties of correlated basis functions provides a new explanation of the link between Bose-Einstein condensation and two fluid behavior. This assumption also implies that the condensate fraction is proportional to the superfluid fraction, in agreement with experiment, and provides a simple quantitative explanation of the anomalous reduction in spatial order and liquid density, observed as the temperature is lowered in superfluid 4He.     

多重散射方法研究轴对称空腔覆盖层的声学特性

发展了一种多重散射方法研究声学覆盖层的半数值半解析模型,分析了影响轴对称空腔结构声学性能的主要能量耗散机制。在球坐标条件下推导出轴对称空腔结构的位移和应力场基函数,通过对空腔表面基函数的数值积分,得到散射波和入射波之间的传输矩阵方程,结合分层介质声传播理论计算了周期性空腔结构覆盖层的反射、透射和吸声性能。研究结果表明;空腔共振是低频能量耗散的主要形式,边界条件对材料空腔结构的谐振特性影响很大,利用双空腔耦合共振可以拓宽材料的低频吸声频带;背衬对材料的高频吸声影响较小,材料的高频能量损耗取决于空腔的散射和波型转换特性。      

Simplified SCF calculations on the diatomic alkali metal molecules

An account is given of a new formalism for calculating energy levels in molecules using techniques that derive from the band theory of metals. After showing how the molecular potential may be transformed into a cellular potential we define the basis set of muffin-tin orbitals and discuss some of their properties. The relationship between the scattered wave formulation of Johnson, which is restricted to muffin-tin potentials, and our more general approach based on the use of a linear combination of muffin-tin orbitals (L.C.M.T.O.) is explicitly indicated. We then show how the properties of the muffin-tin orbitals, together with the technique of cellular integration, give rise to a hamiltonian matrix. This matrix is as general as, but simpler than that obtained by the use of atomic orbitals, and it is linear in energy and therefore computationally faster than the secular matrix of the scattered wave method.     

Exact hole-bound states for semiconductor quantum wells with arbitrary potential profiles

An efficient numerical-analytical method for finding confined and continuum states in quantum-well systems with arbitrary potential profiles, described by coupled Schrödinger equations, is presented. The method is based on the analytical properties of the wave functions, in particular, the power series representation of solutions of the corresponding coupled differential equations. Using only the general properties of the coefficients of a system of an arbitrary number of coupled Schrödinger equations, and imposing for definiteness the simplest boundary conditions, we derive exact expressions for the wave functions and present methods for accurate calculations of the energies and wave functions of confined states and of the wave functions of continuum states in quantum wells. The method is applied to the calculation of the dispersion of hole bound states in a single GaAs quantum well with truncated parabolic confining potentials of different strengths. The results are compared with data available from previous calculations.     

Anisotropy of positron wave function in 4d transition metals

The positron wave functions have been calculated employing the method of expansion of symmetrized plane waves in some 4d transition metals. Systematics of the positron wave functions along the three symmetry directions [100], [110], [111] in these metals, have been discussed. The anisotropies of the ψ₊ have been found to be strongly dependent upon the crystal symmetries. The results of the band structure calculation of 2γ-angular correlation in Rh and Ag are presented.     

准一维体系的电子关联的变分计算

对于具有库仑相互作用的准一维电子体系,本文提出了一种新的模型,得到了准一维体系的电子有效库仑势形式。在相关基函数理论框架下,根据电子气的集体振荡行为,给出该体系的多体波函数,并得到不同密度的电子体系的关联函数和关联能,本文得到的关联函数是恒正的,且满足归一化条件。     

Ground-state correlations and finite temperature properties of the transverse Ising model

We present a semi-analytic study of Ising spins on a simple square or cubic lattice coupled to a transverse magnetic field of variable strength. The formal analysis employs correlated basis functions (CBF) theory to investigate the properties of the corresponding N-body ground and excited states. For these states we discuss two different ansaetze of correlated trial wave functions and associated longitudinal and transverse excitation modes. The formalism is then generalized to describe the spin system at nonzero temperatures with the help of a suitable functional approximating the Helmholtz free energy. To test the quality of the functional in a first step we perform numerical calculations within the extended formalism but ignore spatial correlations. Numerical results are reported on the energies of the longitudinal and the transverse excitation modes at zero temperature, on critical data at finite temperatures, and on the optimized spontaneous magnetization as a function of temperature and external field strength.     

The method of generating functions for the calculation of matrix elements in the deformed-harmonic oscillator basis

The method of generating functions which was previously only employed for the spherical basis of harmonic-oscillator single-particle wave functions is here generalized to the deformed (=cylindrical = asymptotic) basis. One-center and two-center matrix elements which are important in fission or heavy-ion scattering theories are obtained for various operators and potentials, i.e., spin-orbit, l-squared, Gaussian, or Gaussian multiplied by a polynomial, etc. If they cannot be calculated explicitely, recurrence formulae are evaluated. The method circumvents integrating the matrix elements by the introduction of generating parameters and looking for the coefficient of some power of the generating parameter in the expansion of the generating function. The method is further simplified by transforming the operators acting on the wave functions into operators which act onto the generating function or into functions to be multiplied by the generating integral.     

应用改进的特征基函数法和自适应交叉近似算法快速分析导体目标电磁散射特性

特征基函数的构造是特征基函数法的关键步骤之一, 传统方法在构造特征基函数时, 需要在每个子域设置足够多的入射波激励, 生成的特征基函数个数较多, 奇异值分解时间较长. 为了加快特征基函数的构造, 本文提出了一种改进的特征基函数法. 该方法充分考虑每个子域之间的耦合作用, 求出每个子域的次要特征基函数, 从而降低入射波激励的个数, 大大减少了特征基函数的个数; 并且结合自适应交叉近似算法加速阻抗矩阵元素的计算, 提高了次要特征基函数求解和缩减矩阵构建过程中的矩阵矢量相乘的速度. 数值结果证明了本文方法的精确性和高效性. 关键词： 电磁散射 矩量法 特征基函数法 自适应交叉近似     

Weighted-Residual Methods for the Solution of Two-Particle Lippmann–Schwinger Equation Without Partial-Wave Decomposition

Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves. The aim of the present work is to show that the weighted-residual approach in combination with local basis functions give rise to convenient computational schemes for the solution of the multi-variable integral equations without the partial wave expansion. The weighted-residual approach provides a unifying framework for various variational and degenerate-kernel methods for integral equations of scattering theory. Using a direct-product basis of localized quadratic interpolation polynomials, Galerkin, collocation and Schwinger variational realizations of the weighted-residual approach have been implemented for a model potential. It is demonstrated that, for a given expansion basis, Schwinger variational method exhibits better convergence with basis size than Galerkin and collocation methods. A novel hybrid-collocation method is implemented with promising results as well.     

Nuclear shape measurement and the validity of the collective model for light nuclei

We have carried out calculations of collective transition properties using wave functions projected from a range of HF wave functions of a wide range of basis dimensionalities and corresponding to different effective interactions. Particular calculations show that the best HF wave functions have multipole moments which are closer to experimental values than elementary analysis has suggested. More general results, intended to be useful in the interpretation of inelastic scattering, are given.