类锂离子里德堡态中的自旋-其它轨道相互作用

以多电子原子精细结构哈密顿的球张量形式和三价原子的非相对论性能级结构理论为基础,借助不可约张量理论,建立了计算类锂离子里德堡态中的自旋-其它轨道相互作用能的一种解析理论形式.完成了所有的角向积分和自旋求和计算,自旋-其它轨道相互作用能最终用径向积分来表示.应用所建立的理论对类锂离子(1s2np)2Pj态的自旋-其它轨道相互作用能进行了具体分析.     

类碳体系基态能量的精细结构(英文)

以多电子原子精细结构哈密顿的球张量形式和不可约张量理论为基础,建立了计算多电子原子精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用)能量的一般性解析理论形式,应用所建立的理论对类碳体系(Z=6～8)基态的精细结构能量进行了具体计算,计算结果与实验数据符合得较好.     

氦原子自旋-其它轨道相互作用精细结构参数的理论计算

以多电子原子精细结构哈密顿的球张量形式和氦原子非相对论性能级结构理论为基础,借助不可约张量理论,建立了计算氦原子自旋-其它轨道相互作用精细结构参数的一种解析理论形式.完成了所有的角向积分和自旋求和计算,自旋-其它轨道相互作用精细结构参数最终用若干个径向积分来表示.以氦原子(1s2p)3P态为例,借用类氢形式的径向函数对这些径向积分进行了近似计算.计算结果表明:在氦原子的精细结构中,自旋-其它轨道相互作用与纯自旋-轨道相互作用的作用效果相反;在总自旋-轨道相互作用精细结构参数中,自旋-其它轨道相互作用起决定性作用,它决定着精细结构分裂的顺序.     

类铍离子1s~22snp~3P(n=2～6,Z=5～8)态能级和精细结构参数的理论计算

在准相对论框架下,以多电子原子精细结构哈密顿的球张量形式为基础,借助不可约张量和角动量耦合理论,导出类铍离子1s22snp(n=2-6)3P态精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用)和精细结构参数的解析表达式,并利用我们所开发的程序,对各项进行了具体地计算,计算结果与文献符合地较好.     

铍原子1s22snp 3P态精细结构的理论计算

以多电子原子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,对铍原子1s22snp(n=2-6) 3P态精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用)进行了具体地计算,并将计算结果与文献结果进行了比较,符合地较好。同时,计算了1s22snp(n=2-6) 3P态精细结构参数A和B的值。     

碳原子1s22s22pns 3P态精细结构的理论计算

提出了构造碳原子1s22s22pns 3P态波函数的新方法,以多电子原子精细结构哈密顿的球张量形式和不可约张量理论为基础,开发了一套计算碳原子1s22s22pns 3P态精细结构的Mathemtica程序,具体计算了碳原子1s22s22pns 3P(n=3-6)态的精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用),计算结果与实验值非常接近。     

铍原子1s22snp3P态精细结构的理论计算

以多电子原子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,对铍原子1s22snp(n=2～6) 3p态精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用)进行了具体地计算,并将计算结果与文献结果进行了比较,符合地较好.同时,计算了1s22snp(n=2～6)3p态精细结构参数A和B的值.     

用QED理论建立多电子原子的精细结构哈密顿

利用QED理论,采用一种类似于代数的方法,建立了多电子原子的精细结构哈密顿,并将自旋-其他轨道、自旋-自旋以及轨道-轨道等相互作用项转化成便于计算的球张量形式.     

碳原子1s~22s~2pns~3P态精细结构的理论计算

提出了构造碳原子1s~22s~2pns~3P态波函数的新方法,以多电子原子精细结构哈密顿的球张量形式和不可约张量理论为基础,开发了一套计算碳原子1s~22s~2pns~3P态精细结构的Mathemtica程序,具体计算了碳原子1s~22s~22pns~3P(n=3～6)态的精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用),计算结果与实验值非常接近.     

碳原子1s~22s~22pns~3P态精细结构的理论计算

提出了构造碳原子1s~22s~22pns ~3P态波函数的新方法,以多电子原子精细结构哈密顿的球张量形式和不可约张量理论为基础,开发了一套计算碳原子1s~22s~22pns ~3P态精细结构的Mathemtica程序,具体计算了碳原子1s~22s~22pns ~3P(n=3～6)态的精细结构(包括自旋-轨道相互作用、自旋-其它轨道相互作用和自旋-自旋相互作用),计算结果与实验值非常接近.     

Elliptic dark states: Explicit invariant form

An analysis is made of coherent population trapping as a result of resonant interaction of elliptically polarized light with atoms whose energy levels are degenerate with respect to the projection of the angular momentum and are coupled by a dipole transition. Explicit invariant expressions for dark states are obtained in tensor form for all transitions where population trapping occurs. A correspondence is established between the vector of the elliptic polarization and the pair of associated spinors. It is shown that all dark states can be constructed from these spinors by means of a multiple tensor product. For integer values of the angular momenta of the transitions these constructions reduce to spherical functions of a complex variable. As applications analytic expressions are obtained for the dark magneto-optic and geometric potentials, and the change in their profile with increasing angular momenta is analyzed.     

Tensor Expressions for Solving Einstein's Equations by the Method of Sequential Approximation

The main aim of this paper is to develop a mathematical tool for General Relativity (GR). For this purpose useful tensor expressions have been worked out, which considerably ease various calculations using the sequential approximation in Einstein's GR. Based upon these expressions, compact and explicit formulae have been worked out for the covariant and contravariant components of the metric tensor and its determinant.     

Torsion and related concepts: An introductory overview

The aim of this paper is to provide an overview of all the basic aspects of the torsion of a manifold, with particular stress on the expressions in an anholonomic basis. After a brief review of anholonomic bases and Koszul covariant derivative, we show how the expressions for the torsion and the Riemann tensors in a general (anholonomic) basis arise from their expressions in a coordinate basis. We further derive the expression for the contortion tensor, which arises from the requirement that an affine connection with torsion be metric (preserving). The latter requirement is related to the equivalence principle, whose mathematical aspects in a manifold with torsion are discussed next. Finally, we derive the expression for the distortion tensor, which is an analog of the curvature tensor but arising from the torsion rather than the metric tensor.     

Constraining conformal field theory with higher spin symmetry in four dimensions

We analyze the constraints on the general form and the singularity structure of the correlation functions of the symmetric, traceless and conserved stress-energy tensor implied by conformal invariance and higher spin symmetry in four dimensions. In particular, we show that all these correlation functions will have at most double pole singularities. We then compute the 4-, 5- and 6-point functions of the stress-energy tensor and find that they are linear combinations of the three free field expressions (scalar, fermion and Maxwell field). This is a strong indication that all such theories are essentially free.     

A method of analysis of distributions of local electric fields in composites

A method of prediction of distributions of local electric fields in composite media based on analysis of the tensor operators of the concentration of intensity and induction is proposed. Both general expressions and the relations for calculating these operators are obtained in various approximations. The analytical expressions are presented for the operators of the concentration of electric fields in various types of inhomogeneous structures obtained in the generalized singular approximation.     

On the determination of the volume dependence of Grüneisen parameters in cubic and non-cubic solids

For a material of orthorhombic symmetry under hydrostatic stress, three generalized Grüneisen parameters relative respectively to the three principal directions of the deformation can be defined. Finite strain expressions for these parameters are derived in terms of the Lagrangian strain tensor and the frame-indifferent analogue of the Eulerian strain tensor. The expressions require for their evaluation the thermal expansion coefficients, the elastic moduli and their pressure and temperature derivatives, and the specific heat of the material, so that there are no arbitrary constants or “curve fitting.” In the case of cubic materials, it is possible to determine the unique Grüneisen parameter as a function of volume directly. For non-cubic materials, the volume dependence of the Grüneisen parameters is calculated using a quasi-harmonic finite strain model of equation of state. Numerical applications are given for some cubic and hexagonal metals and the results are discussed.     

Simulation of Characteristic Radiation of Highly Ionized Laser Plasma

In the tensor form, using the generalized Rayleigh–Gans–Debye approximation, the problem of the sum-frequency generation from a thin nonlinear layer deposited on a dielectric spherical particle placed in a dielectric medium is solved. The second-order nonlinear dielectric susceptibility tensor is chosen in a general form containing chiral components. In the vector and tensor forms, expressions are obtained that describe the spatial distribution of the sum-frequency radiation field generated by two plane electromagnetic elliptically polarized waves. Limiting expressions that describe the spatial distribution of the sum-frequency harmonic at small and large radii of the spherical layer are obtained. It is revealed that, at small radii of the spherical layer, the radiation due to the chiral anisotropy coefficients makes a dominant contribution to the generation.     

A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.     

任意多面体隐身罩材料参数的推导及验证

基于坐标变换理论推导了任意多面体隐身罩的隐身条件,并得到了相应隐身罩材料参数的张量表达式.根据导出的材料参数的张量表达式,通过全波仿真分别对正四面体和十四面体隐身罩进行仿真验证,仿真结果证实了所得材料参数张量表达式的正确性,研究结果为三维复杂形状隐身罩的设计奠定了理论研究基础. 关键词： 坐标变换 多面体隐身罩 张量表达式 全波仿真     

Numerical and analytic results for the macroscopic magneto-transport of three-dimensional periodic composites

The strong-field magneto-transport in a generic three-dimensional composite with a periodic microstructure where all the constituents are normal metals is considered. The macroscopic response in such systems turns out to be considerably simpler than it is in the absence of a magnetic field. Closed form asymptotic expressions are found for the microscopic current distributions and macroscopic effective magneto-resistivity tensor components. Numerical calculations of the current distributions and effective magneto-resistivity tensor components are also performed and compared with the closed form asymptotic expressions. A new critical point is identified.