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.     

Green's function approach to the impurity state in the Lieb lattice

Wavefunction of an impurity attached to the Lieb lattice is considered by directly computing the Green's function (GF) for the nearest-neighbor tight-binding model. By replacing the lattice GF with a GF array including all the nine GFs defining on the three-atom unit cell of the Lieb lattice, an accurate and efficient numerical technique is developed. Agreement of both the real and imaginary components of the GF between numerical simulation of the lattice GF and continuum-space Fourier transformation is achieved in the whole resonant-energy range. Both results demonstrate that the wavefunction amplitude decays in a power-law pattern while the resonant energy is small and it decays in a pattern stronger than the power law and weaker than exponentially while the resonant energy is large. The decaying exponents depend on the adatom type and location in the unit cell, which directly modifies the temperature-dependent conductance under the variable-range hopping theory.     

The quasienergy spectrum of semiconductors with direct band gaps in the laser field

Explicit analytical expressions are derived for Floquet states and the quasienergy spectrum of semiconductors with zinc-blende structure and direct band gaps, taking into account the real symmetry properties of the degenerate valence bands.The author would like to thank Academician professor Nguyen Van Hieu for suggesting the problem and for valuable discussions.     

Defect modes due to substitutional impurities in FCC lattice: Green's function approach

Lattice dynamical study of monoatomic fcc crystals containing substitutional impurities has been made by the Green's function technique, using group theory. The impurity and its 12 nearest neighbors constitute an XY₁₂ impurity space having O_h symmetry. The phonon Green function matrix is analyzed according to the irreducible representations of the point group pertaining to the substitutional impurity in the fcc lattice. The effects due to change in mass at the impurity site and the change in nearest neighbor force constants for the impurity-host atom interactions are taken into account. Analytical expressions for the various modes of vibrations pertaining to the defect space have been obtained. Local mode frequencies due to various substitutional impurities, corresponding to F_1u mode (defect atom moving) have been computed. A special model is chosen for the defecthost force and it is assumed that there are no distortions of the lattice structure due to the defect. A Kihara hardcore potential with parameters fitted to neutron data has been used to compute lattice dynamics and Green functions of the host lattices. Our theoretical results have been compared with available experimental and theoretical results. Our results show reasonably good agreement with experimental results.     

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.     

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.     

Quasiclassical Green’s function approach to mesoscopic superconductivity

Recent experiments on mesoscopic normal metal/superconductor heterostructures resolve properties on length scales and at low temperatures such that the temperature is below the Thouless energyk_BT ≤ E_Th. We describe the properties of these systems within the framework of quasiclassical many-body techniques. Diffusive and ballistic systems are covered, both in equilibrium and nonequilibrium situations. Thereby we demonstrate the common physical basis of various subtopics.     

Application of the Green's function method to lattice vibrations in thin films

The Green's function method is used to investigate the lattice vibrations in a simple cubic thin film with nearest neighbour interactions. Appropriate Green's functions for the study of the surface waves for (001) and (011) orientations of the surface are determined. For a thin film with two parallel (001) free surfaces the atomic force tensors at the surface are modified in order to satisfy the rotational invariance condition. The surface waves are determined and a detailed discussion is made for the long wave-length limit k_y = 0 and k_x ? 1. For a given k_x there is a critical thickness below which only an antisymmetrical solution can exist. For the (011) orientation only the case of a single free surface is discussed.     

Pressure coefficients of band gaps in semiconductors

A first principles pseudopotential method within the local density approximation is used to calculate the pressure coefficients for band gaps in several diamond and zincblende semiconductors. Despite the underestimation of the band gaps found in almost all local density calculations, the predictions for the linear pressure coefficients and the critical pressures for conduction band inversion are consistent with experiment for all cases considered.     

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.     

Polariton-mediated Raman scattering in microcavities: A Green’s function approach

We present calculations of the intensity of polariton-mediated inelastic light scattering in semiconductor microcavities within a Green’s function framework. In addition to reproducing the strong coupling of light and matter, this method also enables the inclusion of damping mechanisms in a consistent way. Our results show excellent agreement with recent Raman scattering experiments.     

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.     

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.     

Green's function formulae for the internal intensity in radiative transfer computations by matrix-vector methods

In radiative transfer computations, Green's functions are particularly useful and have a straightforward physical interpretation, as discussed by Cogley and co-workers. By recognizing that, in thermal emission problems, the angular distribution of emission is prescribed a priori, one can obtain a more rapid computational procedure in which most computations are in discrete formalism one-dimensional or vector formulae.     

Dynamical pictures and causality in finite temperature Green's functions

Real-time finite temperature Green's functions are discussed on the basis of the definition of new dynamical pictures. Causality appears explicitly. Feynman diagrams are formally identical to the ones of zero temperature. The vanishing of disconnected diagrams follows naturally.     

Quantized Dirac field in curved Riemann-Cartan background. I. Symmetry properties,Green's function

In the present series of papers, we study the properties of quantized Dirac field in curved Riemann-Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann-Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann-Cartan background, using the Schwinger-DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background.