Equations For Green Functions Research Articles

Green's-function theory of the spin-1 exchange-interaction model of ferromagnetism.

Double-time Green's functions are used to study dipolar and biaxial ordering in the presence of a uniaxial field for the spin-1 exchange interaction model of ferromagnetism. The decoupling of the Green's function equations of motion hierarchy is based upon the identification of the members of the spin-1 basis operator set whose diagonal susceptibilities diverge in the ordered phase as the statistically independent members of the basis set. In contrast to standard double-time Green's function techniques, the results are unambiguous and the result for the critical temperature in the vanishing field limit compares very favorably with the high-temperature series expansion result.

Model description of molecular adsorption in zeolites

For the quasi-microscopic description of molecular adsorption in zeolites a modified gas lattice model is proposed. By solving the Green function equation of motion in mean field approximation, the energy levels of the molecule inside the zeolite and the expressions for coverage, net heat of adsorption and heat capacity are obtained. A new adsorption isotherm which contains the standard ones as limiting cases is obtained. The expressions are used to fit the experimental data on N 2 adsorption in Na FAU (NaX).

An asymptotically exact mean-field approach for Hubbard X-operators

The authors consider a systematic projection method for terminating the Green function equations of motion for Hubbard X-operators. This gives a set of mean fields that depend on the operators chosen. When applied to lowest order in the N-fold-degenerate U to infinity Anderson model an expression for the one-electron Green function is obtained that is exact for N=1 and in the limit N to infinity . This approach avoids the necessity of introducing auxiliary fields, such as constraint fields or slave bosons, to obtain asymptotically exact mean fields in the large-N limit and has general applicability in similar strongly correlated problems.

Spin‐Phonon Interaction beyond the Limit of Spin‐wave Approximation

AbstractBy solving the system of equations for the doubletime Green functions, an expression for the energy spectrum of the spinsystem with the correction due to spin‐phonon interaction is derived. The utilized commutation relations for spin‐operators are more complicated than in the case of the spin‐wave approximation. In the lower temperature region, our expression becomes the one obtained by the spin‐wave approximation. The temperature dependence and the wave‐vector dependence of the broadening of the energy level are evaluated.

Two‐Particle Monte‐Carlo Method for Warm Electrons in a High‐Frequency Electric Field

AbstractA two‐particle Monte‐Carlo method for the numerical simulation of the nonhomogeneous kinetic equations useful for the treatment of warm electron properties in the case of ac fields is given. The method is based on the solution of the Green function equation by the Monte‐Carlo technique. The electric field time dependence is taken into account by the simulation of the motion of particles with variable weights. Making use of the proposed method the frequency dependence of the non‐linearity coefficient for p‐Ge is calculated.

A two-particle Monte Carlo method for warm electrons with application to covalent semiconductors

A two-particle Monte Carlo method for solving non-homogeneous kinetic equations in the warm-electron case is developed. The method is based on the solution of the Green function equation describing the electron reaction to the instantaneous particle generation arising from the non-homogeneous term of the equation. When the simultaneous motion of two particles (positive and negative) is simulated, the particles annihilate. This enables the authors to perform repeated particle generations and to calculate the averaged electron reaction to the non-homogeneous term, i.e. to solve the non-homogeneous equation. To illustrate the efficiency of the proposed method the results obtained are compared with those obtained by other methods and also with experimental results for p-Ge.

Equations for Green functions with the use of the exact Hamiltonian in the quasiparticle-phonon nuclear model

A set of equations for Green functions based on the exact Hamiltonian of the Quasiparticle-Phonon Model (QPM) for spherical even-even nuclei is obtained. The relation between this new set and the usual equations employed so far in the QPM is discussed. In particular a comparison between the obtained secular equation for excited state energy and the one used so far in the QPM for the case, when the excited state wave function consists of one- and two-phonon components, is made. The numerical evaluation performed in the schematic two level model showed that the difference between the results given by the calculation with the exact Hamiltonian and those based on the approximated Hamiltonian was remarkable in nonmagic nuclei.

Correlated random walk on a bcc lattice with next-nearest-neighbor hops: Self-consistent decoupling approximation.

The self-consistent decoupling scheme recently introduced to improve the theory of Tahir-Kheli and Elliott for tracer diffusion on a lattice, in the limit of a static background, is extended here to include next-nearest-neighbor hops on a bcc lattice. Results for ${f}^{\mathrm{tr}}$, previously conjectured by Tahir-Kheli, are obtained through the new, approximate Green's-function equations. It is shown that the method applies generally to nth-neighbor hopping on any hypercubic lattice.

Dimension shifting operators and null states in 2D conformally invariant field theories

We discuss the existence and properties of differential operators which transform covariant operators into covariant operators of different weights in two-dimensional conformally invariant field theories. We relate them to null states and the vanishing of the Kac determinant in representations of the conformal algebra, and to the existence of differential equations for Green functions of covariant operators. In this framework, we rederive the essential features of our earlier work on dual models with shifted intercept, which in euclidean space-time gives explicit solutions of the conformal bootstrap equations where all operators are marginal.

The electron specific heat of a two-dimensional crystal

The electronic specific heat of a two-dimensional, square lattice crystal is determined by considering only electron-ion core interactions represented by a sinusoidal-like potential. Two electrons per lattice site are assumed to be under the influence of the potential. The Green's function equation of motion technique is employed in the second quantized formulation, with the approximation that the allowed linear momenta are restricted to two Brillouin zones. The result shows a specific heat variation with temperature, characteristics of an intrinsic semi-conductor or metal, dependent upon the well-depth of the potential.

Binding energies of electrons by nitrogen pairs in GaP.

Theoretical calculations of binding energies of electrons by nitrogen pairs in GaP are reported. The calculations are based on the Koster-Slater Green's-function equation and the central-cell defect-potential approximation of Hjalmarson et al. [Phys. Rev. Lett. 44, 810 (1980)]. The defect-potential parameters ${V}_{s}$ and ${V}_{p}$ are adjusted to fit the experimental binding energies of electrons by single N impurity and seven (NN${)}_{1}$ (x=1,2,...,7) pairs. The results are in general agreement for the first time with experiments for either range or ordering of binding energies, and thus strongly support the Hopfield-Thomas-Lynch model for isoelectronic traps. Besides, excited electronic states of (NN${)}_{1}$, (NN${)}_{3}$, (NN${)}_{5}$, and (NN${)}_{6}$ are reported. The energy value of the (NN${)}_{1}$ excited state supports the speculation of Cohen et al.

Optimal basis sets for deep levels. II. Defect-molecule approximation.

We test the ``defect-molecule'' model of Coulson and Kearsley by calculating s- and p-type bound-state energies in silicon for attractive and repulsive Gaussian substitutional impurity potentials with exponential coefficients \ensuremath{\alpha}=0.2 and 1 a.u. The model is shown to work surprisingly well, which justifies its widespread use in the interpretation of experimental and computational results. The leading correction is found to be a d-state wave function on the impurity site. This enters for p states only and is much more important for repulsive than for attractive potentials. The basis set of the wave functions is much smaller than the nonorthogonal basis of the Green's function. In order to treat this problem properly we have developed a least-squares method of approximating the Green's-function equation. The method should be applicable to other problems also.

Self-consistent scattering theoretical method for surfaces: Application to Si(100)

We have developed a method for solving self-consistently the Green's-function equations describing a semiinfinite crystal within local density functional formalism. Based on scattering theory, it yields the potential, charge density, wavevector-resolved layer state densities and the energy spectrum of the surface. A detailed study of the ideal Si(100) surface illustrates the approach and sheds light on differences in previous self-consistent results of matching and supercell calculations for this very surface.

Green's function equations of motion for driven two-level atoms

Using a diagram technique, equations of motion for N coherently driven two-level atoms are obtained from Green's functions. The longitudinal (Coulomb) dipole–dipole interaction is neglected. Three approximations (Born approximation, extended Born approximation, and screened interaction approximation) are considered. The existing theories are shown to be equivalent to the extended Born approximation. For a small sample, the equations of motion exhibit S conservation in this case. The screened interaction model predicts a different behaviour; in particular, S-breaking terms appear in the equations of motion for a small sample.

Magnetic Excitons in a Spin‐Cluster System

AbstractMagnetic properties are calculated in the effective‐field approximation for a four‐level (singlet‐triplet) spin‐cluster system. Furthermore the spectrum of magnetic excitons propagating in this interacting system having in zero order discrete energy levels is studied. For the treatment of the magnetic spin‐cluster crystal the standard‐basis operator (SBO) formalism is applied. The model Hamiltonian used by Heber, Nara, and Freudenhammer is transformed in terms of the SBO's; and the eigen‐values are determined. The thermodynamic properties are obtained from the SBO Green's function equations of motion developing in the random‐phase approximation (RPA). A formula for the magnetization and susceptibility is derived.

A reexamination of the Green function treatment of the Mollow problem

The application of the Green function method to the Mollow problem is reconsidered. This problem consists of an intense monochromatic electromagnetic field in resonance with a two-level atom. We obtain a solution to the infinite hierarchy of Green function equations of motion instead of decoupling the equations of motion. This solution gives an excitation spectrum in agreement with Mollow's results. We conclude that earlier discrepancies in the excitation spectrum were artifacts of the decoupling procedure. Finally, we comment upon the physical ideas associated with the present and previous Green function treatments of the Mollow problem.

Renormalisation-group block-decimation method for the disordered one-dimensional system

Using a block-decimation scheme the authors have derived a recursion relation to renormalise the Green's function equation of motion for disordered one-dimensional systems. The short-range correlation and the cluster states can be well treated by this method.

Green Function Theory and its Global Structure

The Green function theory is successful in many fields of theoretical physics and the Bogoliubov-Gor'kov theory system is its important branch that involves many theoretical methods. In the last twenty years many papers have been published, but as all the equations of motion are coupled and their number is infinite, its global structure problem has not been investigated as yet. This paper is devoted to the study of its global structure, the exact decoupling problem, and the uniqueness and completeness problems. Some higher order spectral representation theorems and exact relationships between higher and lower order Green functions are obtained. Thus the equations of motion are decoupled exactly.In this paper it is proved that after cutting off the equations of motion are decoupled exactly and the solution of these equation systems may not be unique. It is also proved that if there is one solution satisfying all the Green function's equations, then there must be a solution set, all of them satisfy all the equations and its number is infinite and the differences between them are arbitrary.By adding some limitations to ImG(x) at the real axis a uniqueness theorem is proved.

Quantum theory of nonequilibrium processes, I

Green's function techniques for studying nonequilibrium quantum processes are discussed. Perturbation expansions and Green's function equations of motion are developed for noncorrelated and correlated initial states of a system. A transition, from the Kadanoff-Baym Green's function equations of motion to the Boltzmann equation, and specifications of the respective limit, are examined in detail.

Renormalization group treatment for spin waves in the randomly disordered Heisenberg chain

We calculate local densities of states in the randomly disordered binary quantum Heisenberg chain using a generalization of a recently developed approach based on renormalization group ideas. It involves decimating alternate spins along the chain in such a way as to obtain recursion relations to describe the renormalized set of Green's function equations of motion. The densities of states are richly structured, indicating that the method takes into account compositional fluctuations of arbitrary range.