On self-consistent approximations for random anharmonic systems

A model with random 1-, 2-, and 3-point potentials is used to study the elementary excitations in substitutionally disordered crystals. The equations of motion for the 1- and 2-point Green's functionsG(1),G(12) are derived and averaged over the ensemble of random configurations. An extension of the coherent potential method is proposed, which leads to a self-consistent set of equations for the averaged 1- and 2-point Green's functions, including corresponding conditional averages. The theory takes into account that randomness effects the anharmonic interactions both via the explicit configuration dependence of the cubic vertices and via the implicit dependence through the Green's functions. The final equations take a similar form as in the usual CPA if the harmonic potential of the pure system and the harmonic single-site impurity potential are replaced by corresponding functionals of averaged and conditionally averaged 1- and 2-point functions, and the definition of the single-site mass-operator is appropriately generalized.Work supported by the Deutsche ForschungsgemeinschaftExtract from thesis, D 26     

Superconformal invariants and extended supersymmetry

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N = 2 and N = 4 supersymmetric Yang-Mills theory can be evaluated up to constants.     

Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity

This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.     

Green's functions in an exterior gauge field

We consider the problem of evaluating the fermion Green's functions in an exterior Abelian-like gauge field. It is shown that in the field considered, the fermion Green's functions are expressed in terms of spinor particle Green's functions in some exterior electromagnetic field. The Green's functions are found in a combination of a constant homogeneous field and a plane wave field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 67–70, September, 1987.In conclusion the authors wish to express thanks to V. G. Bagrov and D. M. Gitman for helpful discussions of the problems touched upon in the article.     

Linked-Cluster Expansion of the Ising Model

The linked-cluster expansion technique for the high-temperature expansion of spin modes is reviewed. A new algorithm for the computation of three-point and higher Green's functions is presented. Series are computed for all components of two-point Green's functions for a generalized 3D Ising model, to 25th order on the bcc lattice and to 23rd order on the sc lattice. Series for zero-momentum four-, six-, and eight-point functions are computed to 21st, 19th, and 17th order respectively on the bcc lattice.     

On dynamic plane elasticity problems of 2D quasicrystals

In this Letter, the dynamic plane elasticity problems of 2D quasicrystals is considered. By use of the Fourier transform and matrix transformations the system is reduced to uncoupled ordinary differential equations. Fourier images of Green's functions for dynamic plane elasticity problems of 2D dodecagonal, pentagonal and decagonal quasicrystals are obtained explicitly by the suggested method.     

Path integral for relativistic oscillators: model of the Klein-Gordon particle in AdS space

Explicit path integration is carried out for the Green's functions of special relativistic harmonic oscillators in (1+1)- and (3+1)-dimensional Minkowski space-time modeled by a Klein-Gordon particle in the universal covering space-time of the anti-de Sitter static space-time. The energy spectrum together with the normalized wave functions are obtained. In the non-relativistic limit, the bound states of the one- and three-dimensional ordinary oscillators are regained. Received: 29 June 2002 / Revised version: 3 February 2003 / Published online: 24 March 2003     

Focusing of electromagnetic waves into a uniaxial crystal

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal. To that end we start from existing exact solutions for the transmitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we specialize to the case in which the medium of the incident wave is isotropic and derive explicit expressions for the dyadic Green's functions associated with the transmitted fields as well as integral representations suitable for asymptotic analysis and efficient numerical evaluation. Relevant integral representations for focused 3D electromagnetic waves are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem, and derive dyadic Green's functions, integral representations suitable for asymptotic and numerical treatment, and integral representations for focused TM fields. Numerical results for focused 2D TM fields based on these integral representations as well as corresponding experimental results will be presented in forthcoming papers.     

Relaxation and dephasing in a many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a fluctuating force generated by a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate Green's functions and discuss relaxation and dephasing of a single extra particle added above the Fermi sea. We also extend our analysis to a more generic coupling between system and bath that results in complete thermalization of the system.     

Double-time Green's functions for crystals with defects

A general method for the calculation of the double-time Green's function of displacements for a crystal with arbitrary symmetry and arbitrary point defect is given in a harmonic approximation. Green's function is derived in two forms. In the first form Green's function of the ideal crystal is modified by the defect, in the second form Green's function of the defect molecule is modified by the ideal part of the crystal.     

Finite temperature contributions to the renormalized energy-momentum tensor for an arbitrary curved space-time

The finite temperature contributions to the effective Lagrangian and energy-momentum tensor in the cases of scalar and spinor fields are evaluated by means of the Green's function method. The results are obtained in an arbitrary curved space-time by adiabatic expansions of the Green's functions.We would like to thank professor D. Ivanenko for support of our work and many stimulating discussions.     

Magnetic field effects on the quantum wire energy spectrum and Green's function

We analyze the energy spectrum and propagation of electrons in a quantum wire on a 2D host medium in a normal magnetic field, representing the wire by a 1D Dirac delta function potential which would support just a single subband state in the absence of the magnetic field. The associated Schrödinger Green's function for the quantum wire is derived in closed form in terms of known functions and the Landau quantized subband energy spectrum is examined.     

有限尺寸宏粒子空间电荷场研究

 用格林函数理论导出了圆柱对称系统中有限尺寸宏粒子一维和二维空间电荷场权函数的表达式，比较了有限尺寸宏粒子空间电荷场权函数与圆盘或圆环模型空间电荷场权函数的差别，得到了与圆盘或圆环模型空间电荷场权函数[1]不同的、更合理的计算结果。并用这两种空间电荷场权函数模拟了螺旋线行波管中的注波互作用过程，得到了其输出功率曲线，表明了用有限尺寸宏粒子计算的互作用输出功率比圆盘或圆环模型计算的输出功率饱和位置提前，饱和值增加。     

Collective Excitations in Spin-2 Bose-Einstein Condensates

The Green＇s functions and the correlation functions in spin-2 Bose-Einstein condensates at finite temperature are defined and the generalized Dyson-Beliaev equations are introduced. We discuss the spin conservation in z direction and decouple the Green＇s functions and the generalized Dyson-Beliaev equations according to different spin conservations in z direction. The anomalous vertex functions are introduced and the self-energies are separated into the proper self-energies and the improper self-energies. The generalized Dyson-Beliaev equations are decoupled according to separation of the self-energies. We calculate the Green＇s functions step by step in the Bogoliubov approximation and discuss the collective excitations in spin-2 Bose-Einstein condensates in the polar, ferromagnetic, and cyclic cases, respectively.     

Method for breaking chains of equations for green's functions

This article presents a new method for closing infinite systems of equations for Green's functions. Its basis is a procedure for simultaneously splitting two higher-order Green's functions. There is a particular relationship between the three Green's functions that result. These Green's functions are self-consistent. Known Green's functions are used to reconstruct the corresponding correlation functions. An example is provided by the problem of magnetization for a spin system in the Heisenberg model with first-and secondorder approximations in the spin-spin interaction. The first-order approximation corresponds to the molecular-field approximation. The second-order computation corresponds to obtaining general relations determining the magnetization of a system. V. I. Lenin Moscow State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 42–47, August, 1996.     

夸克-反夸克束缚态的B-S相互作用核的封闭表示式(英文)

根据从 QCD生成泛函所建立的夸克和反夸克的传播子、四点格林函数及其它类型的格林函数所满足的运动方程 ,推导出了夸克 -反夸克束缚态的 Bethe- Salpeter方程中相互作用核的明显且封闭的表示式 ,给出了这个表示式的未重整化和重整化了的形式 .这个表示式不仅易于进行微扰计算 ,而且适于进行非微扰的计算 ,特别是它提供了求解夸克禁闭问题一个恰当的理论出发点.The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived from the Bethe-Salpeter equations satisfied by the quark-antiquark four-point Green s function. The latter equations are established based on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green s function and some other kinds of Green s functions which follow directly from the QCD generating function. The Bethe-Salpeter kernel derived is an exact...     

Localized vibrations of point defects in body-centred cubic lattices

The paper gives an exact calculation of the localized frequencies of substitutional defects in a body-centred cubic lattice by the method of Green's functions and compares it with the approximate calculation carried out after [14]. The exact calculation is based on newly computed Green's functions of a b.c.c. lattice [18]. It is shown how by means of group theory the symmetry of the system can be used both in an approximate and in the exact calculation. Some symmetry relations between Green's functions, which limit the number of functions necessary for numerical calculations, are derived.     

Spectral dyadic Green's function formulation for uniaxial bianisotropic superstrate-substrate structure

In this paper, spectral-domain dyadic Green's functions for the time harmonic electric current source embedded in a two-layer grounded uniaxial bianisotropic media are obtained using Fourier tranform. It is shown that in the uniaxial bianisotropic medium, total spectral electromagnetic field can also be separated into the superposition of transverse electric (TE) and transverse magnetic (TM) wave. Because of the generality of constitutive relations our results include the special cases of achiral, uniaxial, reciprocal and nonreciprocal biisotropic media.     

Extreme limit in linear polarisation ratio in step-index single- mode fibres with a central dip

From Maxwell's equations, using a Fourier expansion, spatial harmonic balance and Green's functions, closed-form expressions are found for the longitudinal electric and magnetic fields, for two orthogonally polarised modes of a birefringent fibre with or without a central index dip. Propagation constants can then be calculated to the desired degree of accuracy. Corrections up to third order are found to be significant. The linear polarisation ratio in the core and in the cladding is almost insensitive to birefringence but exhibits large variations in the central dip, where it deteriorates as the birefringence increases.     

Green's functions of linear and three dimensional oscillators in a constant and homogeneous electromagnetic field

The retarded Green's functions are found for linear and three dimensional harmonic oscillators in constant and uniform electric and magnetic fields. These results are applied to the problem of the motion of wave packets of Gaussian shape.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 29–33, August, 1973.In conclusion the authors thank A. A. Sokolov for a discussion of the obtained results.