Comparison of the molecular cluster model with the phonon model for Jahn—Teller active impurities in crystals

For comparing the molecular cluster model with the phonon model in describing the Jahn-Teller interaction for magnetic impurities in crystals, the Jahn-Teller energy and the Ham reduction factors are expressed in terms of the phonon Green's function of the host crystal for an orbital triplet coupled to E_g modes of vibrations. Numerical results for the case of MgO lattice have been obtained using the phonon Green's function derived from the breathing shell model.     

Field-theoretic approach to the properties of the solid state

The techniques of quantum field theory are used to investigate the thermodynamic ion displacement correlation function—or Green's function of the phonon field—in a crystal and especially in a metal. The structure of thermodynamic Green's functions is outlined and the method for solving for them at finite temperature is fully discussed.The analytic structure of the phonon Green's function is then considered. This function is shown to be bounded and invertible everywhere off the real axis; a spectral form is derived for its inverse. The symmetries imposed by the point group of the crystal are then discussed.Assuming small ionic oscillations, we find the inverse of the phonon Green's function as a linear function of the electronic contribution to the dielectric response function of the metal. This dielectric function is shown to be simply related to the longitudinal part of the conductivity tensor that gives the response of the electrons to the effective electric field in the metal. The assumption of translational invariance then leads to an explicit expression for the phonon Green's function in terms of this conductivity.The deformations in the lattice induced by an arbitrarily time varying external force are calculated in terms of the retarded phonon Green's function. In the static long wavelength limit the phonon Green's function yields the macroscopic elastic constants of the crystal. Their relation to the conductivity is exhibited, and several elastic constants are estimated. We also see that the complete phonon spectrum and the lifetimes of the phonon states may be calculated from this Green's function. A relation between the long wavelength acoustic attenuation in metals and the de conductivity is derived, which is in good agreement with recent experiments. Furthermore, the ions in a metal are shown to have a high-frequency oscillation along with the electrons, at essentially the electron plasma frequency.     

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.     

Small coupling (low temperature) expansions of nonabelian Yang-Mills fields on a lattice in temporal gauge

A systematic approach to large β expansions of nonabelian lattice gauge theories in temporal gauge is developed. The gauge fields are parameterized by a particular set of coordinates. The main problem is to define a regularization scheme for the infrared singularity that in this gauge appears in the Green's function in the infinite lattice limit. Comparison with exactly solvable two-dimensional models proves that regularization by subtraction of a naive translation invariant Green's function does not work. It suggests to use a Green's function of a half-space lattice first, to place the local observable in this lattice, and to let its distance from the lattice boundary tend to infinity at the end. This program is applied to the Wilson loop correlation function for the gauge group SU(2) which is calculated to second order in $\text{1}\text{β}$.     

Generating functional approach to the Green's functions diagrammatic technique for spin and pseudospin lattice systems: I. General theory

The theory of the irreducible many-point Green's functions, describing spin and pseudospin lattice systems, is formulated with the help of the generating functional approach. The diagrammatic technique for the generating functional is also developed. Special attention is paid to the construction and summation of the diagrammatic series for the one- and two-point Green's functions. Closed formulae for the one-point Green's function and the generalized Vaks-Larkin- Pikin equation are obtained. The $\text{1}\text{z}$ expansion scheme near the critical temperature of the order-disorder phase transition, is discussed, where z denotes the effective number of nearest- neighbours for a given site in a crystal lattice.     

Evaluation of the spin wave Green's functions for rutile structure Heisenberg antiferromagnets with exchange between ions both on the same and opposite sublattices

A straightforward method is presented for the evaluation of the spin wave Green's function appropriate to the Raman scattering in the xy and xz geometry in rutile structure Heisenberg antiferromagnets with exchange between ions both on the same and on opposite sublattices and arbitrary local anisotropy. The analytical asymptotic behaviour of the Green's functions near the singularities is explicitly given and the problem of the numerical evaluation of their real and imaginary parts is discussed. Tables of the imaginary parts, calculated at the points corresponding to a Gaussian quadrature procedure in the appropriate interval, are supplied on request.     

Hydrogenic atom multiphonon ionization by intense fields with green's method

An expression for n-photon cross-section ionization of hydrogenic atoms by intense linearly polarized light is obtained using the second quantification formalism for the radiation and the Green's function method. It is shown that it reduces into Stobbe's formula in the one photon case.     

Generalized density expansion in the kinetic theory and the resistivity of liquid metals

For the system of electrons and immovable interacting centers an exact equation for averaged electron Green's function is formulated. The expansion of self-energy part over the one-particle t-matrices and explicit Green's functions is derived. It represents a kind of a generalized density series containing the correlation functions of the centres. In the low approximation over t-matrix, the transition probability (t)²S in the kinetic equation is obtained (S = the structure factor of centers).     

A comment on functional integrals and many-body systems

Green's functions for systems of non-interacting particles at T=0 are obtained through ab initio calculations using functional integral algorithms. It is shown in detail how the correct Green's functions are computed and how one recovers the structure of the ground state (which in the usual derivations is the starting point).     

A class of interface state models. I

The Green's function matching procedure of Garcia-Moliner and Rubio is applied to a class of one and three dimensional band models, based on separable Pseudopotentials, for which the Green's functions can be obtained in analytic form. Surface and interface states are obtained corresponding to the [100] and [110] surfaces for a simple cubic, single gap case.     

A green's function analysis of atomic and molecular (e, 2e) reactions

Investigation of Atomic and molecular (e, 2e) spectra will be discussed in terms of a Green's function approach. The energy, intensity and momentum distribution of energy levels observed by electron coincidence ionization spectroscopy, are directly related to the poles, pole strengths and generalized overlap amplitude of the one particle propagator or Green's function. The theoretical calculation of these observable quantities via the Green's function technique will be discussed. In particular, the position and intensity of satellite (or “shakeup”) lines, relative to the main lines, will be analysed in some detail.     

Solution of the path integral for the H-atom

The Green's function of the H-atom is calculated by a simple reduction of Feynman's path integral to gaussian form.     

The classical limit of temperature Green's function expansions

Rules are obtained for calculating the classical limit of Green's function diagrammatic expansions. The classical cluster expansion is derived by calculating the classical limit of the exact Green's function. Other operators of interest in linear response theory may be calculated in the classical limit. The retarded real-time spin density correlation function, proportional to the magnetic susceptibility, is shown to be exactly proportional to the density in this limit. The relation of this work to other approaches is discussed.     

Ferromagnetic 3d-metals: On the definition of “local bands”

The basic concept of a picture for itinerant ferromagnetism is discussed. The central point is that a local exchange splitting and local moments, exist even above the transition temperature T_c. Transverse fluctuations (and not magnitude fluctuations, as in Stoner theory) are the dominant source for the phase transition to the paramagnetic state. The author's Green's function method is extended to the use of a full bandstructure including hybridization and general electron-electron interactions. Spin waves are also discussed.     

The t2 ← e transition at the Cu impurity in ZnS crystal

The excitation energy for the localized t₂ ← e transition is calculated by the Green's function method in CNDO approximation using a parent system model.     

Exact and quasiclassical Green's functions of two-dimensional electron gas with Rashba–Dresselhaus spin–orbit interaction in parallel magnetic field

New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba–Dresselhaus spin–orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that allows an exact analytical solution is also highlighted. To demonstrate the advantages of our approach we apply the obtained Green's function to calculation of electron density and magnetization.     

A cluster plus effective medium tight-binding study of SiOx systems

The valence band density of states of SiO_x amorphous systems is calculated using a tight-binding treatment. The Green's function method is applied to a small cluster embeddied in a suitable effective medium. An average of this Green's function is then performed assuming a statistical distribution of composition for the small clusters. The effective medium is treated as a Bethe lattice of the correct composition. The results are completely consistent with experiment if the Si O Si angle is assumed to decrease with x.     

Far-IR lattice absorption spectra in ZnS:Be system

Calculated far-IR lattice absorption due to a small concentration of beryllium impurities in cubic zinc sulphide has been reported for the first time. The method of calculation follows the Green's function technique. The evaluation of the involved Green's function for zinc sulphide is made by incorporating the real phonons obtained from a second-neighbor-ionic (SNI) model. A defect model that considers the change of mass at the impurity site as well as the changes in the nearest-neighbor (central and angular interactions) is employed in calculating the absorption and the impurity modes. The experimentally observed IR absorption below 100 cm^?1 can be understood only if one takes into account the changes in the angular force constants around the impurity. The calculated absorption is compared and discussed with the existing experimental data.     

The intrinsical character of the electronic correlation in an electron gas

By introducing the phase transformation of electron operators, we map the equation of motion of an one-particle Green's function into that of a non-interacting one-particle Green's function where the electrons are moving in a time-depending scalar potential and pure gauge fields for a D-dimensional electron gas, and we demonstrate that the electronic correlation strength strongly depends upon the excitation energy spectrum and collective excitation modes of electrons. It naturally explains that the electronic correlation strength is strong in the one dimension, while it is weak in the three dimensions.