Properties of advanced coupled-cluster Green's function

ABSTRACT

We present an extension of the analysis previously applied to the retarded part of the coupled cluster (CC) Green's function to its advanced part. In analogy to our earlier studies for the retarded part, we demonstrate that the advanced CC Green's function is expressed in terms of connected diagrams only, which is a direct consequence of algebraic form of equations satisfied by CC amplitudes. We also demonstrate that ω-derivatives of the advanced CC Green's function can be calculated analytically and can be expressed in terms of connected diagrams only. We analyse the structure of connected diagrams and the role of intermediate operators which satisfy electron affinity equation-of-motion CC-type conditions.     

The Green's function moment method

This paper develops a modified moment method for the numerical solution of two “Pocklington Type” integral equations. The first equation arises from the problem of scalar diffraction through a slot; the second from scattering by a straight, thin-wire. Numerical results and comparison with a more conventional method are given.     

Green's function method for nonequilibrium systems

The causality principle formulated in the paper is offered as a boundary condition for the Schwinger equation. This approach allows study of, in particular, the dynamics of closed, finite systems. An approximate method for solving the equation is offered. A generalization of the Boltzmann equation is obtained for the presence of particle attenuation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 75–80, April, 1973.The author is very grateful to V. L. Bonch-Bruevich for discussion of the work.     

Green's function method in classical electrodynamics

A perturbation theory for solution of the Vlasov and Klimontovich equations is formulated on the basis of the method of Green's functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 85–89, February, 1991.     

Ionization potentials of HCN and HNC by a Green's function method

The vertical valence ionization potentials of HCN and HNC have been calculated by a many-body Green's function method using extended basis sets including polarization functions. For HCN the agreement of the computed ionization potentials with experiment is very satisfactory. The ordering is 1π, 3σ, 2σ. The ionization potentials of HNC have not been measured yet. The calculated ordering is 3σ, 1π, 2σ. The electronic structure of the two molecules is seen to differ.     

Application of the Green's function method to ferrimagnetism

The Green function theory, which has been used hitherto for ferro- and antiferromagnetism, has been extended for the case of a two-sublattice ferrimagnet. Two parametrized Green functions are used corresponding to the two sublattices. The equations of motion are set up and the higher order Green functions are decoupled according toCallen's approximation. The functions are obtained by solving the simultaneous equations. The quasi-particle energies are evaluated from the singularities of the Green functions and the magnetization at low temperatures is found to obey theT ^3/2-law. These results obtained for the energy and magnetization agree well with those obtained by the conventional spin wave method.     

Green's function of a dressed particle

We present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of self-energy diagrams (e.g., the noncrossed ones, in the self-consistent Born approximation), we sum all the diagrams, but with each diagram averaged over its free propagators' momenta. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Possible generalizations to other models are also discussed.     

A method of measuring the Green's function in an enclosure

The acoustic Green's function can be measured using a device with two matched microphones mounted in a tube driven by a loudspeaker combined with another microphone that represents the observation point. Good agreement is obtained between the measured and theoretical Green's function in a rectangular room below 320 Hz. At higher frequencies the agreement is less good because of the imperfect geometry of the room.     

Emergence of the acoustic Green's function from thermal noise

The fluctuation-dissipation theorem is used to show how acoustic Green's functions corresponding to sound propagation in opposite directions between any two given points can be extracted from time series of thermal noise recorded at these points. The result applies to arbitrarily inhomogeneous, moving or motionless fluids with time-independent parameters, and demonstrates that the two-point correlation function of thermal noise contains as much information about the environment as can be obtained acoustically by placing transceivers at the two points.     

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.     

Second-order Green's function theory of a Heisenberg paramagnet

The Heisenberg paramagnet in one, two, and three dimensions is analyzed by a second-order Green's function theory similar to that used by Knapp and ter Haar. This theory, which incorporates the exact values for the zero, first, and second moments of the relaxation function as boundary conditions, yields results satisfying the rotational symmetry of the paramagnetic region as well as the principle of detailed balance. We find that our predictions for equal time properties in the classical limit are identical with the RPA Green's function theory of Liu as well as the spherical model results of Lax. The quantum limit is analyzed, and our predictions for the 1/T series coefficients for both internal energy and susceptibility are compared with exact results.Supported by National Science Foundation.     

Green's function probe of a static granular piling

We present an experiment which aims to investigate the mechanical properties of a static granular assembly. The piling is a horizontal 3D granular layer confined in a box. We apply a localized extra force at the surface and the spatial distribution of stresses at the bottom is obtained (the mechanical Green's function). For different types of granular media, we observe a linear pressure response whose profile shows one peak centered at the vertical of the point of application. The peak's width increases linearly with increasing depth. This Green's function seems to be in at least qualitative agreement with predictions of elastic theory.     

Excited-state forces within a first-principles Green's function formalism

We present a new first-principles formalism for calculating forces for optically excited electronic states using the interacting Green's function approach with the GW Bethe-Salpeter-equation method. This advance allows for efficient computation of gradients of the excited-state Born-Oppenheimer energy, allowing for the study of relaxation, molecular dynamics, and photoluminescence of excited states. The approach is tested on photoexcited carbon dioxide and ammonia molecules, and the calculations accurately describe the excitation energies and photoinduced structural deformations.     

A recursive color image edge detection method using Green's function approach

In this paper, an extended version of image edge detector using Green's function approach is proposed for detection of edges in the color vector space field. In the proposed method, the relationship between the Red, Green and Blue components is considered to design a differential operator for detection of edges in color images. By using the proposed operator, partial derivatives of all components of color image can simultaneously affect on the edge detection process. Therefore the proposed method can preserve the vector nature of color images during the edge processing stages. Also, the proposed method is compared both quantitatively and qualitatively with other color edge detectors. Experimental results show that the proposed method can efficiently preserve the edges even when the color images corrupted with different levels of noise.     

Resonances with triaxial deformation in the complex scaled Green's function method

We extend the complex scaled Green's function(CGF) method to describe resonances with triaxial deformation and present a theoretical formalism. Taking ~(43)S as an example, we elaborate numerical details and demonstrate how to determine the resonance parameters. With changes in the deformation parameters, we study the influence of the triaxial deformation parameter γ on single-particle levels. In particular, the present scheme focuses on the advantages of the complex scaling method(CSM) and the Green's function method, and is suitable for the exploration of resonances.     

Extracting the Green's function from measurements of the energy flux

Existing methods for Green's function extraction give the Green's function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green's function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green's function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green's function can be retrieved from measurement of the flux of scattered particles through a closed surface.     

Application of a complex band structure to compute the surface states by the Green's function method

By using the analytical properties of the band energies and wave functions in the complex quasi-momentum domain, a procedure is constructed for the calculation of the Green's function \(G_{k_\parallel }\) . The function \(G_{k_\parallel }\) is represented as the sum of components dependent on complex wave vectors. If such a representation is used for \(G_{k_\parallel }\) in the calculation of the surface Green's function [2], then the equation to determine the surface state spectrum in a model with a potential jump agrees with that obtained in [3] by the method of merging the wave functions.     

A Green's function method for surface acoustic waves in functionally graded materials

Acoustic wave propagation in anisotropic media with one-dimensional inhomogeneity is discussed. Using a Green's function approach, the wave equation with inhomogeneous variation of elastic property and mass density is transformed into an integral equation, which is then solved numerically. The method is applied to find the dispersion relation of surface acoustic waves for a medium with continuously or discontinuously varying elastic property and mass density profiles.