Second-order Green's function theory of a Heisenberg paramagnet

The Heisenberg paramagnet in one, two, and three dimensions is analyzed by a second-order Green's function theory similar to that used by Knapp and ter Haar. This theory, which incorporates the exact values for the zero, first, and second moments of the relaxation function as boundary conditions, yields results satisfying the rotational symmetry of the paramagnetic region as well as the principle of detailed balance. We find that our predictions for equal time properties in the classical limit are identical with the RPA Green's function theory of Liu as well as the spherical model results of Lax. The quantum limit is analyzed, and our predictions for the 1/T series coefficients for both internal energy and susceptibility are compared with exact results.Supported by National Science Foundation.     

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.     

时间反演对称和非平衡统计定常态(Ⅰ)

本文是作者从微观量子统计理论出发应用微观可逆性原理讨论非平衡统计定常态普遍性质的第一部份。文中给出了非平衡量子统计格林函数(闭路格林函数)在定常态上关于时间反演对称的表达方式。把生成泛函技术和时间反演对称结合起来,得到了具有时间反演对称性的非平衡统计定常态上统计格林函数和顶点函数所满足的时间反演对称关系。 关键词：     

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.     

Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

Negative-refractive bicrystal with broken symmetry produces asymmetric electromagnetic fields in guided-wave heterostructures

Heterostructure arrangements of uniaxial bicrystals have been discovered to produce electromagnetic fields with asymmetric distributions in guide wave structures. The property behind this remarkable phenomenon is the broken crystalline symmetry which allows the new physics to be seen in unsymmetric distributions. Here the theory behind this phenomenon is presented, numerical calculations are performed using an ab initio anisotropic Green's function approach, and the results provided at 10 GHz for a realistic crystal system with nominal permittivity of 5. Asymmetric distributions seen here are one facet of the broken symmetry property which generates negative refraction for impinging waves on a bicrystal.     

Temperature effects on the two-magnon Raman-scattering of antiferromagnets

In this first of two papers we investigate the temperature effect on the spin wave energy and the two-magnon Raman scattering cross section for an antiferromagnet with rutile structure in the spin wave scheme. In the Heisenberg hamiltonian we consider the exchange interaction between magnetic neighbors up to the third order, an effective anisotropy field, and an external magnetic field. In the effective Raman hamiltonian an anisotropy factor, allowed by the crystal symmetry, is taken into account.The theory employs a Green's function method, where the Green's functions are obtained from equations of motion. The results are similar to published ones obtained with diagrammatic techniques.Extract from thesis, Munich, 1974     

The mobility edge problem: Continuous symmetry and a conjecture

An apparently overlooked symmetry of the disordered electron problem is derived. It yields the well-known Ward-identity connecting the one- and two-particle Green's function. This symmetry and the apparent shortrange behaviour of the averaged one-particle Green's function are used to conjecture that the critical behaviour near the mobility edge coincides with that of interacting matrices which have two different eigenvalues of multiplicity zero (due to replicas). As a consequence the exponents of the d.c. conductivity is expected to approach 1 for real matrices and 1/2 for complex matrices as the dimensionality of the system approaches two from above. In two dimensions no metallic conductivity is expected.     

Method of projectors and the construction of Green's function of the wave equation

In the present article problems related to the propagation of waves in elastic anisotropic media with arbitrary types of symmetry are considered. Such problems are important for solid-body physics and for geophysics. An expansion of Green's function of the wave equation of the theory of elasticity is presented in the form of additive terms corresponding to the contributions of each of the three waves propagating in a solid body with designated anisotropic characteristics. An appropriate representation for the roots of the characteristic equation specifying the rate of wave propagation is presented. To illustrate the computation technique examples of certain types of media are considered. A representation is obtained for the static Green's function that does not require knowledge of the exact roots of the characteristic equation (assuming there is no degeneracy present).Moscow University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 101–111, April, 1995.     

电磁场标量格林函数在奇异点邻域内的普适特性

讨论电磁理论中标量格林函数在源点附近的等值线或等值面分布情况。包括各种有界及无界空间两维及三维格林函数。分析表明,无论边界形状如何,在奇异点附近的邻域内,两维格林函数的等值线趋于圆,三维格林函数的等值面趋于球面。有边界约束的格林函数无论形式上如何复杂,都与相应的自由空间格林函数一样,具有普适性。这为积分方程的正则化分析带来很大方便。     

用重整化群流方程方法求解t-J模型元激发能谱

t-J模型是研究电子强关联作用和高T_c超导理论的重要模型之一.将重整化群方法应用于t-J模型，得出相应的流方程，再由流方程求解t-J模型的元激发能谱，并利用函数的对称性，解出t-J模型在零温条件下能谱的具体表达式，最后与常规的格林函数方法所得的结果作了比较. 关键词： 重整化群 t-J模型 流方程     

Unified Green's function retrieval by cross correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green's function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green's function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in "remote sensing without a source."     

GREEN'S FUNCTION THEORY OF THE KONDO LATTICE(I) —MAGNETIC ORDERING AND KONDO EFFECT

The periodic s-d model is investigated by Green's function methods. A closed set of equations for Green's function of Kondo-lattice system and a formula of single electron self-energy are obtained in the presence of a broken rotational symmetry. The formula can-be used to discuss low temperature anomalous properties of Kondo-lattice system with spontaneous magnetization or in an external magnetic field. We have evaluated the influence of magnetic ordering on logarithmic sin-gularity of electron self-energy by perturbative method to Leading logarithmic order (LLO).The result obtained indiGates there exists a competition between Kondo effect and Zong range magnetic ordering. The static susceptibility in the paramagnetic case has been evaluated, too.     

Magnetoelastic excitations and structural phase transitions in tetragonal paramagnets

The systematic discussion of the elastic and structural properties of the tetragonal paramagnetic model with the maximum value of the total angular momentumJ=1 in an external magnetic field along thez orx direction is given. The sound velocities of all the symmetry modes are calculated by using the standard perturbation theory and Green's function method. It is shown that only in the presence of the external field directed along thez-axis, for some values of this field and temperature one of the symmetry elastic constantsc ₄₄ orc _B becomes zero and the phase transition to monoclinic (triclinic) or volume change transition can occur.     

立方半导体中双空位态的电子结构(Ⅰ)——基本方程组

利用Koster-Slater的格林函数方法,给出了决定立方半导体中理想双空位在禁带中引入的不同对称态的能级和波函数的完整的方程组。主体半导体的能带结构用一经验的紧束缚哈密顿量来描述,缺陷引入的微扰势则采用在位势近似。在此基本假定下,这些方程组仅涉及到主体半导体的在位(on-site)和离位(off-site)格林函数以及这些格林函数对能量E的微商。 关键词：     

Extracting the Green's function from measurements of the energy flux

Existing methods for Green's function extraction give the Green's function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green's function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green's function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green's function can be retrieved from measurement of the flux of scattered particles through a closed surface.     

Inclusions and inhomogeneities in electroelastic media with hexagonal symmetry

For a long time, the absence of explicit Green's functions (fundamental solutions) for electroelastic media has hindered progress in the modelling of the properties of piezoelectric materials. Michelitsch's recently derived explicit electroelastic Green's function for the infinite medium with hexagonal symmetry (transversely isotropic medium) [4] is used here to obtain compact closed-form expressions for the electroelastic analogue of the Eshelby tensor for spheroidal inclusions. This represents a key quantity for the material properties of piezoelectric solids and analysis of the related electroelastic fields in inclusions. For the limiting case of continuous fibers our results coincide with Levin's expressions [8]. The derived method is useful for an extension to non-spheroidal inclusions or inhomogeneities having an axis of rotational symmetry parallel to the hexagonal c-axis. Received 14 September 1999     

Derivation of Effective Chiral Lagrangian Involving PSGB and Vector Bosons from QCD

The effective chiral Lagrangian for a matter field content consisting of pseudo-scalar Goldstone bosons and vector bosons (with hidden symmetry) is derived from the underlying QCD theory. No approximations are made. All the free parameters of the effective chiral Lagrangian are expressed in terms of QCD-based Green's functions. These may be regarded as the QCD definitions of these Lagrangian coefficients.     

非平衡耗散系统定常态的Goldstone模

在有时空结构的非平衡定常态上,由于对称性的自发破缺,形成非零能、带耗散的Goldstone模。本文以么模激光的饱和状态为例,从普遍的相位对称性出发,应用闭路格林函数中的Ward-Takahashi恒等式,具体地导出了这种带耗散的推广的Goldstone定理的一个形式,讨论了相应的Goldstone模式的物理意义。求得了饱和状态光量子态的分裂。具体给出了状态从相位有序→相位无序的转化规律,从而给自发破缺的对称性的恢复一个具体的描述。 关键词：     

Vector Green's function algorithm for radiative transfer in plane-parallel atmosphere

Green's function is a widely used approach for boundary value problems. In problems related to radiative transfer, Green's function has been found to be useful in land, ocean and atmosphere remote sensing. It is also a key element in higher order perturbation theory. This paper presents an explicit expression of the Green's function, in terms of the source and radiation field variables, for a plane-parallel atmosphere with either vacuum boundaries or a reflecting (BRDF) surface. Full polarization state is considered but the algorithm has been developed in such way that it can be easily reduced to solve scalar radiative transfer problems, which makes it possible to implement a single set of code for computing both the scalar and the vector Green's function.