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.     

Advanced linked cluster expansion scalar fields at finite temperature

Linked cluster expansions provide a useful tool for both analytical and numerical investigations of lattice field theories. The expansion parameter(s) being the interaction strength(s) fields at neighboured lattice sites are coupled, they result into convergent hopping parameter-like series for free energies, correlation functions and in particular susceptibilities. We consider scalar fields with O(N)-symmetric nearest-neighbour interactions on hypercubic lattices with possibly finite extension in some directions, thus including field theories at finite temperature T. We improve known and develop new techniques and algorithms to increase the order n. The expansions can be computed too in such a way that detailed information on critical behaviour can be extracted from the susceptibility series. This concerns both simple moments as well as higher correlations such as 4- and 6-point functions used to define renormalized coupling constants. Particular emphasis is done on finite-temperature field theory. In order to be able to measure finite-temperature critical behaviour, the order of explicit computation n has to be sufficiently large compared to T⁻¹ in lattice units. 2- and 4-point susceptibility series are computed up to and including the 18th order and beyond.     

Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for S _z = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates. Received 1st August 2000 and Received in final form 22 December 2000     

Discrete phase space II. Relativistic lattice wave equations and divergence-free green's functions

Therelativistic lattice Klein-Gordon equation, Dirac equation, electromagnetic equations, and gauge field equations are presented as partialdifference equations. Various lattice Green's functions are constructed (except for non-abelian gauge fields). It is proved that many of the lattice Green's functions are non-singular or divergence-free. Moreover, it is conjectured that all lattice Green's functions are non-singular.     

Magnetism and electrical transport in Kondo lattices

The Anderson lattice model is studied via time ordered perturbation theory in order to derive approximate results for dynamical susceptibility and electrical conductivity in the Kondo regime. A classification of processes on the lattice contributing to the susceptibility leads to expressions containing renormalized band Green's functions and local vertex parts. These quantities are determined by integral equations. Explicit results are obtained via a decoupling procedure for the local parts, which can be motivated in physical terms. It is shown that the formation of the Abrikosov-Suhl resonance near the Fermi level works against, and may actually suppress the tendency towards formation of a magnetic phase. Using a simple, but well founded form for the temperature dependent self energy of band electrons near the Fermi level the influence of coherence on the electrical conductivity at low temperatures can be demonstrated.Dedicated to B. Mühlschlegel on the occasion of the 60th birthday     

半无限-和无限平方晶格的格林函数的关系及其应用

利用半无限平方晶格的晶格格林函数的积分表达式(见:物理学报,44(1995),987)以及由此导出的它与无限平方晶格的晶格格林函数之间的内在关系式,计算了半无限平方晶格的局部态密度和表面具有单点对角杂质时定域态的存在条件.     

A Non-Equilibrium Approach to Coupled-Mode-Induced Hot-Electron Energy Loss Rate

Hot-electron energy loss to the lattice through electron-phonon interactions is studied using Keldysh closed-time-path Green's functions. To the lowest order in electron-phonon coupling, Kogan's formula for the energy-loss rate is obtained. When higher order interactions are included, however, we find that the coupled-mode contribution is exactly zero.     

QUANTUM FLUCTUATION OF THE ORDER PARAMETER AND THE OPTICAL ABSORPTION IN POLYACETYLENEO

We study in this paper the effects of lattice quantum fluctuations upon the order parametert in the Peierls systems by using the Green's function technique.We start from the discrete Su-Schrief fer-Heeger model with quantized phonon field and derive a coupled system of equations for the order parameter and Green's functions.It turns out that the order parameter is reduced compared with the adiabatic value but the Peierls instability survives the quantum fluctuations in agreement with,Monte Carlo results.The band-to-band optical absorption coefficient of polyacetylene with lattice fluctuation being accounted for is also calculated and compared with the experimental data.     

各向异性立方晶体的弹性格林函数及其应用

本文计算了各向异性立方晶体的弹性格林函数的级数展开式,给出了直到二级近似的展开式的系数。将所得结果应用于弹性偶极子模型,给出了对称中心所产生的位移场及两对称中心间的弹性相互作用的表示式。应用于Cu,K等强各向异性立方晶体,虽然级数的收敛较慢,但所得关于对称中心的位移场,及二对称中心间的互作用能的数值结果,竟与基于点阵的不连续性作出的点阵静力学计算所得的结果基本一致。从而表明,本文给出的直到二级近似的弹性格林函数的解析表示提供了一个可以普遍应用的简便的方法。它可以较准确地描述立方晶体的某些力学行为。 关键词：     

Extension Theory for Magnon of a Ferromagnetic Superlattice

We prove that the extension theory for lattice Green's functions can be used to study Heisenberg ferromagnetic systems. As an example, the magnon spectrum of a ferromagnetic superlat tice is calculated by the extension theory for lattice Green's functions cooperated with the transfer matrix technique. The spectrum of magnetic excitation near the surface of a ferromagnetic superlattice is also presented.     

Lattice dynamics of quantum crystals

A theory of lattice dynamics for quantum crystals is developed. This is done by summing an infinite class of diagrams of the usual anharmonic expansion and by avoiding the harmonic approximation as starting point. The zero order of the expansion given in this paper corresponds to the harmonic approximation with an effective potential. Higher orders correspond to higher anharmonic corrections with the same potential. Since the new potential varies more slowly the expansion seems to converge more rapidly than the usual anharmonic expansion. Numerical calculations on bcc He³ show that the ground state energy is lowered by about 3–4 cal/mol by taking into account long range correlations due to phonons. The elastic constants and the Debye temperature are calculated in zero and second order. The lowering of the bulk modulus due to the second order is about 10%. Experiments agree quite well with the second order results.     

二元合金振动哈密顿量的对角化

本文中提出合金振动格林函数的晶体理论,采用置换群约化理论使合金构型对称化,采用晶格平移群使合金哈密顿量变成方块对角阵。文末说明声子哈密顿量。 关键词：     

Electromagnetic volume scattering in the half-space: a moment-method analysis without Sommerfeld integrals or their approximations

Traditionally, in moment-method analyses of electromagnetic scattering, the elements of the impedance matrix are calculated as convolutions of the basis elements with the appropriate dyadic Green's function. However, for scattering in the half-space, the vertical and azimuthal copolar terms of the Green's function require evaluation of Sommerfeld integrals which are computationally burdensome. In this paper, it is shown that, in populating the impedance matrix for the half-space problem, evaluation of Sommerfeld integrals is, in fact, not necessary. For monochromatic excitation, the plane-wave expansion of the scattered field constitutes a Fourier transform, in the horizontal plane, of a vector spectral function. This vector function results from the convolution, in the vertical dimension, of the respective angular spectra of the Green's function and the equivalent current. On application of the moment method, through the Weyl identity, the impedance-matrix elements corresponding to the singular terms of the Green's function are convolutions in the horizontal plane of spherical potentials, and Fourier transforms of scalar spectral functions. These scalar functions are derived from the basis elements and, with a judicious choice of basis, they are well behaved and of compact support, and consequently their Fourier transforms can be computed as FFTs.     

A variational approach to distribution function theory

We present a novel formalism for the generation of integral equations for the distribution functions of fluids. It is based on a cumulant expansion for the free energy. Truncation of the expansion at theKth term and minimization of the resulting approximation leads to equations for the distribution functions up toKth order.The formalism is not limited to systems with two-body interactions and does not require the addition of closure relations to yield a complete set of equations. In fact, it automatically generates superposition approximations, such as the Kirkwood three-body superposition approximation or the Fisher-Kopeliovich four-body one.The conceptual approach is adapted from the cluster variation method of lattice theory.     

Internal equilibrium and crystal dynamics of tantalum

A lattice dynamical model for bcc metals, which satisfies the internal force equilibrium condition of the lattice is proposed. The present model combines a linearized Thomas-Fermi Theory for the electron-ion interaction and the central pair potential for ion-ion interaction. as an application, the computed phonon dispersion, vibrational spectrum, and lattice specific heat of tantalum show fairly good agreement with experiments.     

Localized partial traps in diffusion processes and random walks

Reaction-diffusion equations, in which the reaction is described by a sink term consisting of a sum of delta functions, are studied. It is shown that the Laplace transform of the reactive Green's function can be analytically expressed in terms of the Green's function for diffusion in the absence of reaction. Moreover, a simple relation between the Green's functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained. Several applications are presented and the formalism is used to establish the relationship between the time-dependent geminate recombination yield and the bimolecular reaction rate for diffusion-influenced reactions. Finally, an analogous development for lattice random walks is presented.     

Green's functions for body-centred cubic lattices

The presented paper contains the tables of Green's functions for bcc lattices for outband frequencies 1·0/ _m 1·6. The central-force model is used, the interaction with 8 nearest and 6 next-nearest neighbours is considered and the number of different Green's functions is fairly decreased by symmetry. Numerical difficulties arising by computing Green's functions are discussed. The derivation of symmetry relations for a dynamical matrix is generalized for the matrix of Green's functions.     

Kernel polynomial representation for imaginary-time Green's functions in continuous-time quantum Monte Carlo impurity solver

Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green s functions G(τ),we develop an alternate and superior representation for G(τ) and implement it in the hybridization expansion continuous-time quantum Monte Carlo impurity solver.This representation is based on the kernel polynomial method,which introduces some integral kernel functions to filter the numerical fluctuations caused by the explicit truncations of polynomial expansion series and can improve the computational precision significantly.As an illustration of the new representation,we re-examine the imaginary-time Green's functions of the single-band Hubbard model in the framework of dynamical mean-field theory.The calculated results suggest that with carefully chosen integral kernel functions,whether the system is metallic or insulating,the Gibbs oscillations found in the previous Legendre orthogonal polynomial representation have been vastly suppressed and remarkable corrections to the measured Green's functions have been obtained.     

A hybrid modal analysis for enclosed sound fields

A hybrid modal expansion that combines the free field Green's function and a modal expansion will be presented in this paper based on a review and an extension of the existing modal analysis theories for the sound field in enclosures. The enclosed sound field will be separated into the direct field and reverberant field, which have been treated together in the traditional modal analysis. Studies on a point source in rectangular enclosures show that the hybrid modal expansion converges notably faster than the traditional modal expansions, especially in the region near the source, and introduces much smaller errors with a limited number of modes. The hybrid modal expansion can be easily applied to complex sound sources if the free field responses of the sources are known. Damped boundaries are also considered in this paper, and a set of modified modal functions is introduced, which is shown to be suitable for many damped boundary conditions.     

New Form for the Coulomb Potential in Complex Crystals. Part I

The Coulomb potential is constructed for a crystal with a basis by the method of the Green's functions approximated by the lattice sum of spherically symmetric electron densities of free atoms. The application of the new method with improved convergence of the lattice series in the Green's function has allowed us to obtain an additional term in the electron part of the potential, which describes attraction and can be considered as a potential of the Coulomb hole. The method was applied to calculate the potentials for carbon in the diamond lattice and for TiC solid solution in the direction of four nearest neighbors. Some typical results are presented to illustrate the capabilities of the method.