Finite Volume Time Domain with the Green Function Method for Electromagnetic Scattering in Schwarzschild Spacetime

The finite volume time domain(FVTD) algorithm and Green function algorithm are extended to Schwarzschild spacetime for numerical simulation of electromagnetic scattering. The FVTD method in Schwarzschild spacetime is developed by filling the flat spacetime with an equivalent medium. The Green function in Schwarzschild spacetime is acquired by solving initial value problems. Both the FVTD code and the Green function code are validated by numerical results. Scattering in Schwarzschild spacetime is simulated with these methods.     

Quasiclassical green function in an external field and small-angle scattering processes

A representation is obtained for the quasiclassical Green functions of the Dirac and Klein-Gordon equations allowing for the first nonvanishing correction in an arbitrary localized potential which generally possesses no spherical symmetry. This is used to obtain a solution of these equations in an approximation similar to the Furry-Sommerfeld-Maue approximation. It is shown that the quasiclassical Green function does not reduce to the Green function obtained in the eikonal approximation and has a wider range of validity. This is illustrated by calculating the amplitude of small-angle scattering of a charged particle and the amplitude of Delbrück forward scattering. A correction proportional to the scattering angle was obtained for the amplitude of charged particle scattering in a potential possessing no spherical symmetry. The real part of the Delbrück forward scattering amplitude was calculated in a screened Coulomb potential.     

Direct Solution of the Inverse Problem for Rough Surface Scattering

We consider the inverse scattering problem for a scalar wave field incident on a perfectly conducting one-dimensional rough surface. The Dirichlet Green function for the upper half-plane is introduced, in place of the free-space Green function, as the fundamental solution to the Helmholtz equation. Based on this half-plane Green function, two reasonable approximate operations are performed, and an integral equation is formulated to approximate the total field in the two-dimensional space, then to determine the profile of the rough surface as a minimum of the total field. Reconstructions of sinusoidal, non-sinusoidal and random rough surface are performed using numerical techniques. Good agreement of these results demonstrates that the inverse scattering method is reliable.     

基于有限元法的光子并矢格林函数重整化及其在自发辐射率和能级移动研究中的应用

任意微纳结构中量子点的自发辐射率和能级移动均可用并矢格林函数表达.当源点和场点在同一位置时,格林函数的实部是发散的.为解决这一发散问题,可采用重整化格林函数方法.本文提出一种计算重整化格林函数和散射格林函数的方法.该方法利用有限元,计算点电偶极子的辐射场,将其在量子点体积内做平均得到重整化的并矢格林函数,减去均匀空间中解析的重整化格林函数,得到重整化的散射格林函数.在均匀空间情况下,本方法所得数值结果与解析解一致.将该方法应用到银纳米球系统,以解析的散射格林函数作为参考,结果表明该方法能准确处理散射格林函数的重整化问题.将该方法应用到表面等离激元纳米腔中,发现有极大的自发辐射增强和能级移动,且该结果不依赖于量子点的体积.这些研究在光与物质相互作用领域具有积极的意义.     

Single-site theory for the random Hubbard alloy

A new theory for the random system with electron correlation is presented, which is an extension of the Hubbard's theory for the random system and also an extension of the CPA for the interacting electron system. The equation of motion for the Green function is solved by the same decoupling method used by Hubbard. The self-consistent relations for the Green function, the self-energy and the effective occupation number are derived. It is predicted in the binary alloy system that tails or satellites of the state density are produced by the combined effect of the randomness and electron correlation. The origin of the tail is the inelastic scattering of the electron byA — B atomic pairs, whose electronic configuration is changed during the scattering. Numerical calculations are reported for a simple model.     

Fractional Green’s Function for the Time-Dependent Scattering Problem in the Space-Time-Fractional Quantum Mechanics

Integral form of the space-time-fractional Schrödinger equation for the scattering problem in the fractional quantum mechanics is studied in this paper. We define the fractional Green’s function for the space-time fractional Schrödinger equation and express it in terms of Fox’s H-function and in a computable series form. The asymptotic formula of the Green’s function for large argument is also obtained, and applied to study the fractional quantum scattering problem. We get the approximate scattering wave function with correction of every order.     

On calculation of electronic states in disordered alloys

A new representation of the Green function for a disordered multicomponent substitution alloy is proposed, using which it is easy to separate one-, two-, etc. contributions to this Green function in corresponding equations. Due to this representation we succeed in obtaining common expressions for the configurationally averaged electron Green function with allowance for the electron scattering on clusters formed by an arbitrary number of atoms. The approach used is equally appropriate to described alloys both in the weak binding model, and in the tight binding one.     

Reducing the calculation workload of the Green function for electromagnetic scattering in a Schwarzschild gravitational field

When the finite difference time domain(FDTD) method is used to solve electromagnetic scattering problems in Schwarzschild space-time, the Green functions linking source/observer to every surface element on connection/output boundary must be calculated.When the scatterer is electrically extended, a huge amount of calculation is required due to a large number of surface elements on the connection/output boundary.In this paper, a method for reducing the calculation workload of Green function is proposed.The Taylor approximation is applied for the calculation of Green function.New transport equations are deduced.The numerical results verify the effectiveness of this method.     

RELATIVISTIC EQUAL-TIME EQUATION OF BOSE-FERMI SYSTEM

The relativistic equal-time equation of Bose-Fermi system and its conjugate equation are found.The hermiticity of equal-time potential and equal-time scattering amplitude is discussed. The result shows that if the Feynman Green function is replaced by the retarded Green function, the hermiticity of equal-time potential and equal-time-scattering am-plitude will be confirmed.     

浅海波导中目标散射的边界元方法

提出了一种计算三维散射体在声速剖面随深度变化、距离无关浅海波导中散射声场的数值方法波导边界元方法。当散射体不十分靠近波导界面因而边界多次散射可以忽略时,在边界元计算中可以用自由场格林函数近似波导格林函数。应用镜像法和球波函数加法定理推导了理想波导中球体散射声场的解析解,用来验证波导边界元方法的计算精度,证明该数值方法是准确的。对浅海波导中水下潜器散射声场数值模拟的结果表明,浅海波导海面、海底界面反射、声速剖面等对目标散射声场的幅值和方向性都有很大的影响。      

A General Solution of the Problem of Elastic-Wave Scattering by a Plane Crack

Doklady Physics - The 3D problem of elastic-wave scattering by cracks in a homogeneous isotropic medium is considered. Using the method of Green’s function and specially introduced auxiliary...     

Resonance interaction of optical phonons with localized states

The optical-phonon Green’s function averaged over the positions of defects—both point and line— is calculated with allowance for possible localized states near the boundary of the continuous spectrum and for their intrinsic damping. The frequency-transfer dependence of the cross section for Raman scattering is calculated with the aid of this Green’s function.     

Scattering of an Acoustic Field by Refraction–Density Inhomogeneities with a Small Wave Size and Solution of the Problem of Direct Scattering in an Inhomogeneous Medium

The paper considers acoustic wave scattering by inhomogeneities with a small wave size using the Green’s function apparatus, which makes it possible universally to take into account both the refraction and density components of an inhomogeneity. Estimates for the multipole components of a field scattered by a nonresonance inhomogeneity are presented. For an inhomogeneity with small dimensions, it suffices to consider only monopole and dipole scattering. These conclusions are confirmed by an analysis of the field scattered by a circular cylinder with a small wave radius. The results are used to numerically simulate a Lippmann–Schwinger equation. The form of the discretized matrix Green’s function for identical values of the spatial arguments is presented. This makes it possible to take into account multiple scattering processes within a discretization element with a small wave size. Its use automatically fulfills the relations between the phase and amplitude of secondary acoustic field sources.     

Green function and scattering amplitudes in many-dimensional space

Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation.     

Lifetimes of long wavelength longitudinal phonons in impure metals

The standard Green function theory of electron-phonon interaction in metals is extended to include the effect of impurities moving with the lattice. The importance of various diagrams in the perturbation expansion of the phonon Green function is discussed in the light of the accepted theories of ultrasonic absorption in impure metals. The screened impurity potential is treated as arbitrary function of the scattering angle.     

Kinetic equations for the density matrix of two-level particles in a strong field

On the basis of the Green’s function method for nonequilibrium systems, the kinetic equation for two-level particles in a strong field is derived. In the binary approximation, all diagrams are expressed in terms of the reducible vertex part, whose calculation is reduced to the problem of two-channel scattering and finding the corresponding scattering amplitudes.     

The thermalization length by the green function method

We study the concept of the thermalization lenght by the Green function method, using Sobolev's escape and destruction probabilities. A unique analytical procedure yields the usual numerical estimates for the noncoherent scattering case (with complete redistribution in frequency) as well as for the case of coherent scattering. The on-the-spot approximation is used to remove the assumption of an infinite geometry. Rybicki and Hummer's longest flight approximation is shown to yield the on-the-spot approximation. A generalization to the multilevel case is sketched.     

Surface green function matching approach to the surface dynamics of ionic crystals: I. Equivalence with the invariant green function method

The surface Green function matching (SGFM) method is shown to be equivalent to the Green function method in its translationally and rotationally invariant formulation (IGF). Such equivalence between matching and invariance conditions makes the SGFM method easily applicable to the surface dynamics of ionic crystals, due to the existing possibility of deriving an effective short-range perturbation from the invariance conditions. An application to the inelastic scattering of He from LiF(001) in the eikonal approximation is presented.     

Optical potential in the gas approximation

Using the gas approximation the optical potential is expressed as a function of the scattering matrix of nucleon-nucleon scattering. The formalism of Green functions is used. The imaginary part of the optical potential in nuclear matter is calculated for high energies using the experimental phase shifts. In addition, a calculation of the imaginary part is made using theS-wave part of the Tabakin potential.     

磁多层金属系统的界面反射效应

考虑到磁多层金属系统中的粗糙界面散射效应,运用量子统计的格林函数方法和久保理论,计算磁多层金属系统的单粒子传播格林函数和电导率.所得结果依赖于电子在界面处的反射波幅和空间尺寸,并能展示巨磁电阻的主要实验特征. 关键词：