Formalismus der Greenschen Funktionen in der Elektronentheorie flüssiger Metalle

The Green’s function formalism for liquid metals is developed by use of the functional derivative method. The Hamiltonian of the system, which only contains interactions between electrons and ions, is used to analyse the self-energy structure of the Green’s function. This single particle propagator permits the derivation of a Bethe-Salpeter equation by means of the functional method. Employing the quasi-particle model this in turn allows an approximate determination of the resistivity of liquid metals.     

Application of a green function to a metal containing a vacancy and an impurity atom

A double time Green function is used to obtain the interaction energy between a vacancy and a transition-metal impurity atom in noble metals. The main part of the interaction energy has the RKKY type expression.     

Self-consistent green function approach for calculation of electronic structure in transition metals

We present an approach for self-consistent calculations of the many-body Green function in transition metals. The distinguishing feature of our approach is the use of one-site approximation and the self-consistent quasiparticle wave function basis set obtained from the solution of the Schr?dinger equation with a nonlocal potential. We analyze several sets of skeleton diagrams as generating functionals for the Green function self-energy, including GW and fluctuating exchange sets. Calculations for Fe and Ni revealed stronger energy dependence of the effective interaction and self-energy of the d electrons near the Fermi level compared to s and p electron states.     

Ward identity and effective medium approximation for conductivity of liquid metals

The self-energy to define the ensemble average of a one-electron Green function for a disordered system is related to the vertex correction for the average of the product of two Green functions by the generalized optical theorem or by the so-called Ward identity. Using this relationship, we evaluate the conductivity of liquid metals both by the Ishida-Yomezawa approximation and by the effective medium approximation from the self-energy forms corresponding to respective approximations. The conductivity formulations thus obtained are shown to be identical with those derived from the diagram method.     

Green’s tensor for crystals of the hexagonal system

Expressions for components of the Green’s tensor of the basic equation of the elasticity theory for hexagonal system crystals have been obtained using the Lifshitz-Rozentsveig method. A problem is in principle reduced to finding the roots of a sixth-order algebraic equation. They are either complex or purely imaginary for all known hcp metals. In both cases, the desired components of the Green’s tensor are calculated exactly in contrast to metals of the cubic system. A limiting transition to the isotropic approximation is shown.     

Dynamical susceptibility of intermediate valence systems

The transverse susceptibility if magnetic systems described by the Anderson model is calculated evaluating the self energy for the two particle Green function. The results are applied to semiconductors and metals. In the first case a shift in the resonance frequency is obtained as well as a continuum of excitations corresponding to the promotion of electrons from the localized state to the conduction band states. In the metallic case a Korringa relation for the relaxation time in the magnetic limit is obtained. The real and imaginary parts of the self energy are given as functions of the distance from the localized level to the Fermi level.     

A simple approach to the evaluation of the hall conductivity in impure metals within the green function formalism

A simple method of dealing with the Hall effect in metals with short-ranged impurities in a weak magnetic field is proposed. The method is based on a Schwinger representation for the electron Green function in the magnetic field. The efficacy of the method is demonstrated on a calculation of the antisymmetric components of the conductivity tensor at finite wave vector. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 141–145 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On Recent Analytical Results for Solution of the Scattering Problem for the Sharply Screened Coulomb Potential

Exact representations for the wave function and for the Green function of the Hamiltonian with the sharply screened Coulomb potential are given. The representations are obtained by summing up the partial wave series. The final form of the wave function and the Green function in the region of the coordinate space where the potential is not zero are given in terms of the Coulomb wave function and the Coulomb Green function, respectively. The exact representation has been obtained for the transition operator in the configuration space.     

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.     

有限深水域中三维频域自由面格林函数及其导数的计算方法

三维频域自由面格林函数及其偏导数的数值计算是海洋结构物水动力分析的难点.本文对有限水深格林函数及其偏导数的数值算法作出两点改进:①对原函数的级数表达式进行变形,提出适用于数值计算的形式,解决高频率情况下级数解的计算失真问题;②对Gauss-Laguerre积分法作出改进,解决高频率大水深情况下积分解的数值溢出问题.计算...     

General form of the full electromagnetic Green function in materials physics

In this article, we present the general form of the full electromagnetic Green function which is suitable for the application in bulk materials physics. In particular, we show how the seven adjustable parameter functions of the free Green function translate into seven corresponding parameter functions of the full Green function. Furthermore, for both the fundamental response tensor and the electromagnetic Green function, we discuss the reduction of the Dyson equation on the four-dimensional Minkowski space to an equivalent, three-dimensional Cartesian Dyson equation.     

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.     

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

The electroelastic 4 × 4 Green’s function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form ((73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm’s method [2]. In the case of vanishing piezoelectric coupling the derived Green’s function coincides with two well known results: Kröner’s expressions for the elastic Green’s function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge. The obtained electroelastic Green’s function is useful for the calculation of the electroelastic Eshelby tensor [16].     

Orbital and spin magnetism and dielectric response of electrons in metals

A survey is given of the theory of orbital and spin magnetism of electrons in metals, and of the relation of this to dielectric response theory. In particular, the orbital magnetic behaviour of Bloch electrons in a static but spatially varying magnetic field is discussed. It is shown that the treatment of Hebborn and Sondheimer can be generalized to include this spatial dependence of the applied magnetic field and that the result may be written compactly in terms of the zero field canonical density matrix, or Green function.

It is further shown that the frequency dependence of both the orbital and spin susceptibility can be obtained, again from the density matrix, by calculating the current. The connection with neutron scattering is exhibited and for the case of nickel the way in which such experiments can lead to estimates of the role of the electron interactions is discussed.

The effect of a magnetic field on phonon spectra in metals is considered briefly. Finally it is suggested that it may be of interest to study the effect of the magnetic field on the periodic potential usually employed to calculate energy levels of electrons in magnetic fields. Some modifications of pair forces between ions is to be expected in very high fields.     

Integrals of the motion,green functions,and coherent states of dynamical systems

The connection between the integrals of the motion of a quantum system and its Green function is established. The Green function is shown to be the eigenfunction of the integrals of the motion which describe initial points of the system trajectory in the phase space of average coordinates and moments. The explicit expressions for the Green functions of theN-dimensional system with the Hamiltonian which is the most general quadratic form of coordinates and momenta with time-dependent coefficients is obtained in coordinate, momentum, and coherent states representations. The Green functions of the nonstationary singular oscillator and of the stationary Schrödinger equation are also obtained.     

Calculation of the Green function for the Laplace equation

A modification of the traditional method of calculating the Green function in a layered medium is suggested that allows one to substantially increase its accuracy. In addition, a technique for calculating the Green function that makes it possible to control the accuracy of the calculated potential is offered. This technique is based on the properties of the Bessel and Struve functions. An example of calculation using the suggested technique is illustrated. The results may be extended for a wide class of problems the solution to which requires calculation of the Green function for the Laplace equation in a layered medium.     

The use of low-frequency noise in passive tomography of the ocean

A possible design of the mode tomography of the ocean with the use of a scheme requiring no expensive low-frequency radiators is considered. The design is based on the widely discussed method of estimating the Green’s function from the cross-coherence function of noise field received in a great number of observation points. The relationship between the Green’s function and the noise coherence function is derived from the Helmholtz-Kirchhoff integral. The use of the vertical multielement arrays composed of vector receivers is suggested to decrease the duration of noise signal accumulation required for a reliable determination of the Green’s function. The solution of the tomographic problem is based on the determination of the mode structure of acoustic field from the eigenvectors and eigenvalues of the cross-coherence matrix of the received noise field.     

Analytical study of non-linear transport across a semiconductor-metal junction

In this paper we study analytically a one-dimensional model for a semiconductor-metal junction. We study the formation of Tamm states and how they evolve when the semi-infinite semiconductor and metal are coupled together. The non-linear current, as a function of the bias voltage, is studied using the non-equilibrium Green’s function method and the density matrix of the interface is given. The electronic occupation of the sites defining the interface has strong non-linearities as a function of the bias voltage due to strong resonances present in the Green’s functions of the junction sites. The surface Green’s function is computed analytically by solving a quadratic matrix equation, which does not require adding a small imaginary constant to the energy. The wave function for the surface states is given.     

Gauge invariant quark Green’s functions with polygonal Wilson lines

Properties of gauge invariant two-point quark Green’s functions, defined with polygonal Wilson lines, are studied. The Green’s functions can be classified according to the number of straight line segments their polygonal lines contain. Functional relations are established between the Green’s functions with different numbers of segments on the polygonal lines. An integrodifferential equation is obtained for the Green’s function with one straight line segment, in which the kernels are represented by a series of Wilson loop vacuum averages along polygonal contours with an increasing number of segments and functional derivatives on them. The equation is exactly solved in the case of two-dimensional QCD in the large-N _c limit. The spectral properties of the Green’s function are displayed.