Equations for the asymmetric Green's functions

Utilizing the Martin–Schwinger method ([6], [9]) and the projection procedure [Z], the equation of motion for asymmetric Green's functions is treated by taking systematically correlations into account. In this way correlations up to the four-point function are included explicitly. The procedure for inclusion of higher correlations is described.     

Green's function theory for the one-dimensional antiferromagnet with antisymmetric exchange

The spin wave spectrum for the one-dimensional antiferromagnet with antisymmetric exchange is obtained from second order Green's function theory. There is a noticeable asymmetry in the spin wave dispersion curve, which has an effect on the static correlation function and the correlation length.     

The retarded solution of the scalar wave equation by means of Green's functions

A formula is obtained for the retarded solution of the scalar wave equation in a curved space-time, with boundary conditions appropriate to the case of asymptotic flatness. By means of a conformal transformation, the retarded solution is evaluated in the slow-motion expansion. It is shown that it is necessary to impose further asymptotic restrictions on the source for the usual iterative method to give the correct retarded solution to the given degree of approximation. The weak field case is briefly considered, with the same result.     

Self-consistent many-body theory for the standard basis operator Green's functions

We propose a self-consistent many-body theory for the standard basis operator Green's functions and obtain an exact Dyson-type matrix equation for the interacting many-level systems. A zeroth order approximation, which neglects all the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadrupolar system and the Hubbard model. In the case of the anisotropic Heisenberg ferromagnet with both exchange and single-ion anisotropy the low-temperature renormalization of the spin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin-1 easy-plane ferromagnet, the critical parameters for the phase transition at zero temperature are determined and compared with other theories. The elementary excitation spectrum of the spin-1 isotropic quadrupolar system is calculated and compared with the random phase approximation and Callen-like decoupling schemes. Finally, the theory is applied to the study of the single-particle excitation spectrum of the Hubbard model.     

Exact solutions for spectra and Green's functions in random one-dimensional systems

For chains of harmonic oscillators with random masses a set of equations is derived, which determine the spatial Fourier components of the average one-particle Green's function. These equations are valid for complex values of the frequency. A relation between the spectral density and functions introduced by Schmidt is discussed. Exact solutions for this Green's function and the less complicated characteristics function-the analytic continuation into the complex frequency plane of the accumulated spectral density and the inverse localization length of the eigenfunctions-are derived for exponential distributions of the masses. For some cases the characteristic function is calculated numerically. For gamma distributions the equations are cast in the form of ordinary, higher order differential equations; these have been solved numerically for determining the characteristic function. For arbitrary mass distributions a cumulant expansion and a peculiar symmetry of the Green's function are discussed.The method is also applied to chains where the spring constants and/or the masses have random values. Also for these systems exact solutions are discussed; for exponential distributions, e.g., of both masses and spring constants the characteristic function is expressed in Bessel functions. The relation with certain random relaxation models is shown. Finally, X-Y Hamiltonians with random exchange constants and/or magnetic fields-or, equivalently, tight-binding electron models with diagonal and/or off-diagonal disorder-are considered. Here the Green's function does not depend on the wave number if the distribution of exchange constants is symmetric around the origin. New solutions for the characteristic function and Green's function are derived for a number of cases, including exponentially distributed magnetic fields and power law distributed exchange constants.     

Generating functional approach to the Green's functions diagrammatic technique for spin and pseudospin lattice systems II. Diagrammatic method for generalized Pauli operators

A diagrammatic technique for spin and pseudospin lattice systems with complicated single- body levels is developed using the generalized Pauli operators. Rules for the construction and evaluation of the diagrams, representing the zeroth-order many-point irreducible Green's functions are given. The diagrams are constructed with only seven types of vertices and they are considerably simpler than those used up to now. The method formulated in this paper is a continuation of the approach to the spin and pseudospin lattice systems, developed in a previous paper.     

Green's function approach to the treatment of spin pair Raman scattering in the paramagnetic region

The paramagnetic region of Heisenberg antiferromagnets has been investigated by means of a Green's function technique, with a second-order decoupling procedure appropriate to the disordered phase. The relevance of this method to the interpretation of spin-pair Raman scattering experiments in this phase is pointed out; in particular, a fair agreement is obtained with measured Raman peak frequencies in the paramagnetic phase of RbMnF₃.     

Lattice Green's function for the simple cubic and tetragonal lattices at arbitrary points

The lattice Green's function for the simple cubic lattice (γ = 1) and tetragonal lattice at an arbitrary point (l, m, n)

$\text{I(a;l,m,n;γ) =}\text{1}\text{π}{}^3\text{∫∫}\text{∫}\text{o}\text{π}\text{cos}\text{lx}\text{cos}\text{my}\text{cos}\text{nx}\text{a?i??γ}\text{cos}\text{x?}\text{cos}\text{y?}\text{cos}\text{x}\text{dxdydz}$

is evaluated, assuming a ? 0, γ ? 0 without loss of generality. The integral I(a; l, m, n; γ) which has singularities at a = ± γ ± 1 ± 1, is expressed in all regions of (a, γ), i.e., for (i) a > 2 + γ, (ii) 2 ? γ > a > γ(γ < 2), (iii) a <γ ? 2 (γ > 2), (iv) a < 2 ? γ (1 < γ < 2) and γ > a (0 < γ < 1), (v) |a ? γ| < 2 and a + γ > 2, in terms of Kampé de Fériet function by the method of the analytic continuation using the Mellin-Barnes type integral. The numerical values are shown in figures. The high temperature susceptibilities of the Heisenberg model of the ferro- and antiferromagnets are calculated using the results of I(a; l, m, n; γ), showing a shift from three to two dimensions and that from three to one dimensions. The correlation function of the isotropic ferromagnet is calculated and the critical index ν is observed to be 1.     

Chemical reaction kinetics and Heisenberg spin exchange of the ethyl radical with oxygen

A sample of liver from the marine mammalDugong dugong was found to have an iron concentration of 137 000 g g^–1 Fe dry weight. Histological examination of the tissue revealed dense extracellular deposits of iron-containing particles about 40 to 80 m in diameter. Mössbauer spectra of the sample at temperatures between 17 and 200 K show superparamagnetic behaviour with a mean superparamagnetic blocking temperature of about 67 K, with the sextet being extinguished between 160 and 200 K. The blocking temperature and spectral parameters are indicative of the goethite-like form of hemosiderin that has previously been reported in some iron-loaded thalassemic human tissues.     

Green's function for an electron in one-dimensional conductor with finite correlation length of impurity potential

The scattering of electrons by impurities in one-dimensional conductor is treated as a result of their interaction with quantized fields, the excitons of which carry the quanta of electronic relaxation time or mean free path. The relaxation process is represented as a consequences of exchange of those quanta between the electrons and is shown to be affected by fluctuations of dissipative fields. The Green's function of electrons is calculated and the dependence of the full mean free path on the electronic energy and on the scattering parameters is discussed.     

Green's function approach in the theory of interaction of exciton-polaritons in semiconductors with direct band gaps

The renormalization procedure of perturbation theory is applied to study polariton effects in the optical processes involving photons with energies near that of an exciton: resonant Raman scattering, resonant electronic Raman scattering, and resonant high — order optical harmonic generation. To demonstrate the general method and the computation technique we consider in this work a simple model with the following properties: (a) The semiconductor has a direct band gap with allowed electrical dipole transition and with nondegenerate valence and conduction bands. (b) We consider only the photons in a definite polarization state; they are in resonance with one bound state of an electron-hole pair, and we take into account only the transition between this exciton state and the photon in the given polarization state. We work in the framework of the Green's function approach and we shall see that this approach provides for the inclusion of damping effects in a relatively rigorous manner.     

A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange

A new approximation method is proposed for the calculation of the magnetic susceptibility of one-dimensional assembly of spins and the critical temperature of two-dimensional one both with the anisotropic Heisenberg exchange. In a linear chain system, every spins are grouped into pairs of adjacent spins (pair-approximation) or clusters of adjacent three spins ((q+1)-approximation), and the partition function of the total spin system is approximated as a sum of products of the partitions functions for the pairs or the clusters. Then the partition function of the anisotropic Heisenberg spin system is shown to reduce into a form of the Ising spin system with modified coupling constants. The exact result for the Ising chain system enables us to obtain an analytical expression for the magnetic susceptibility of anisotropic Heisenberg chain system. The same approximations are also applied to two-dimensional lattices, and the critical temperatures of the square, triangular, and honeycomb lattices with anisotropic Heisenberg exchange are calculated as a function of anisotropy parameter. The results are compared with those of the existing theories and shown to be quite excellent.     

Non-analyticity of the entropy and Nernst's law in random spin systems

It is shown explicitly for a soluble model that a random spin system can have an entropy which is non-analytic at (H = 0, T = 0), with $\text{(}\text{?S}\text{?H}\text{)}{}_{\mathrm{H=0}}$ and/or $\text{(}\text{?}{}^2\text{S}\text{?H}{}^2\text{)}{}_{\mathrm{H=0}}$non-vanishing in the T → 0 limit, while nevertheless Nernst's law is satisfied.     

Functional approach to the parametric derivatives of renormalized green's functions with multiple insertions

Functional derivation of formulae for parametric derivatives of renormalized Green's functions with multiple insertions of composite operators is presented. An application to the derivative with respect to the ultraviolet cutoff in the Pauli–Villars regularized ?⁴₄ theory is given.     

The equations of motion for green's functions and superconductivity solutions in particle physics

Three quantum field models are treated in a unified manner by using the method familiar from statistical many-body theory of solving the equations of motion for the Green functions in a particle number representation, with the following results: While the Nambu model does undergo dynamical symmetry breaking in its (1 + 1) dimensional version, it fails to do so in the original (3 + 1) dimensional case. For spinor QED, we get a critical value of the coupling parameter $\text{α}{}_{\mathrm{<mtext>c</mtext>}}\text{≡}\text{e}{}_{\mathrm{<mtext>c</mtext>}}{}^2\text{4π}\text{= 2π}$, above which the model becomes unstable.     

The dependence of exchange and coulomb energies on wave functions of the interacting systems

First-order energies have been calculated for the He₂ system using a number of He wave functions. The convergence to the Hartree-Fock limit has been studied and a two-term expansion in Slater orbitals gives about 98 per cent of this limit. The effect of correlation has been examined by adding s′² and p ² configurations to the wave function and a change of approximately 10 per cent in the effective first-order energy has been noted.     

Effects of oxygen vacancy location on the electronic structure and spin density of Co-doped rutile TiO₂ dilute magnetic semiconductors

According to density functional theory (DFT) using the plane wave base and pseudo-potential, we investigate the effects of the specific location of oxygen vacancy (VO) in a (Ti,Co)O 6 distorted octahedron on the spin density and magnetic properties of Co-doped rutile TiO2 dilute magnetic semiconductors. Our calculations suggest that the V O location has a significant influence on the magnetic moment of individual Co cations. In the case where two Co atoms are separated far away from each other, when the V O is located at the equatorial site of a Co-contained octahedron, the ground state of the two Co cations is d6 (t3 2g ↑, t 3 2g ↓) without any magnetic moment. However, if the V O is located at the apical site, these two Co sites have different ground states and magnetic moments. The spin densities are also observed to be modified by the exchange coupling between the Co cations and the location of V O . Some positive spin polarization is induced around the adjacent O ions.