Green's functions in Bianchi type-I spaces. Relation between Minkowski and Euclidean approaches

A theory is considered for a free scalar field with a conformal connection in a curved space-time with a Bianchi type-I metric. A representation is obtained for the Green's functionGin<0¦T(x)(x)¦0> _in in the form of an integral of a Schwinger-DeWitt kernel along a contour in a plane of complex-valued proper time. It is shown how a transition may be accomplished from Green's functions in space with the Euclidean signature to Green's functions in space with Minkowski signature and vice versa.Translated from Izvestiya Vyssnikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 20–27, June, 1988.     

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.     

Elastic Green's function of icosahedral quasicrystals

The elastic theory of quasicrystals considers, in addition to the “normal” displacement field, three “phason” degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small. Received: 18 December 1997 / Accepted: 6 March 1998     

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.     

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.     

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.     

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.     

Green's function approach to paraelastic relaxation

The dynamical behavior of the elastic constants of a crystal containing paraelastic defects is investigated theoretically. A two-level model for the paraelastic defect is adopted, and the coupling between the defect and the lattice vibrations is considered to be strong. The imaginary part of the elastic compliance tensor is calculated by the Green's function method using the Feynman graph technique. It is shown that the change of the elastic compliance due to the defects is in general a superposition of the Debye-type relaxation and of resonant absorption of the acoustic waves. Expressions for the linewidth of the resonance and the Debye relaxation time are derived.     

Unified Green's function retrieval by cross correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green's function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green's function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in "remote sensing without a source."     

Relation between vestigial-sideband filtering and pi/2 progressive phase shift

We show that a Gaussian-shaped vestigial-sideband (VSB) return-to-zero (RZ) on-off-keying (OOK) optical signal is essentially a RZ OOK signal with pi/2 progressive phase shift. The reduced intersymbol interference of the VSB signal can be explained as a destructive interference effect. We experimentally demonstrate a method for generating an effective 40-Gbit/s VSB signal without relying on the detuning of an optical filter.     

Computation of Green's function for radiative transfer

In an accompanying paper, we develop the computational expressions for the higher order perturbation of the radiative transfer equation, and present some numerical results for typical cases. In this article, we discuss a number of issues regarding the implementation of the HOP computation: obtaining the Green's function, its expansion as a double series of Legendre polynomials, and obtaining the adjoint radiance of more general sources such as those for the fluxes at arbitrary altitudes. Examples of Green's function and its expansion coefficients are presented.     

Relation between the high density phase and the very-high density phase of amorphous solid water

It has been suggested that high-density amorphous (HDA) ice is a structurally arrested form of high-density liquid (HDL) water, while low-density amorphous ice is a structurally arrested form of low-density liquid (LDL) water. Recent experiments and simulations have been interpreted to support the possibility of a second distinct high-density structural state, named very high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test this interpretation using extensive computer simulations and find that VHDA is a more stable form of HDA and that, in fact, VHDA should be considered as the amorphous ice of the quenched HDL.     

介电函数虚部与电导率的关系

在明确介电函数定义及其虚部意义的基础上,比较分析函数ε'(ω)与复介电函数ε(ω)的不同,建议函数ε'(ω)不要称为"复介电函数"或"复电容率",以免与复介电函数ε(ω)混淆.     

Green's formulation for robust phase unwrapping in digital holography

We present, for the first time to the best of our knowledge, a phase unwrapping method based on an algorithm which makes use of Green's first identity. This method aims at recovering the correct phase information encoded in a fringe pattern after digital holography (DH) numerical processing. DH provides a quantitative measurement of the three-dimensional surface profile of objects. The information about the profile can be obtained in principle from the phase-map. However, the measured phase-map provides the actual phase values wrapped mod.2π so that an unwrapping process is required in order to reconstruct the object profile.     

单边噪声源环境下的格林函数提取

对单边噪声源环境下空间中存在散射体时的格林函数到达时间结构提取展开了实验性研究。通过对位于沙滩上的传声器上记录的海浪噪声进行互相关处理,成功提取出两传声器间的格林函数到达时间结构。到达时间结构中观察到伪散射路径,并且伪散射路径在幅值上远高于散射路径。针对上述现象给出了理论及仿真解释:当传声器对受噪声源单边照射时,广义光学定理失效,伪散射路径将会出现;同时,由于伪散射路径由所有方向噪声源贡献,散射路径仅有稳相点附近声源贡献,因此伪散射路径在幅值上可能高于散射路径。结果表明,在单边噪声源环境下,基于互相关技术可以提取伪散射路径。伪散射路径的短时稳定提取可以为散射体无源成像提供更多信息,在海洋声学、地震学等领域具有潜在应用价值。     

Gauge invariant Green's function in the bloch-nordsieck model

The gauge invariant two-point Fermion Green's function is calculated within the framework of the Bloch-Nordsieck approximation. Its dependence on the contour is investigated. It is shown that in the case of a straight contour the gaugeinvariant fermion propagator is equal to the free one.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 65–70, January, 1985.In conclusion the author thanks V. I. Savrin and N. B. Skachkov for interest in this work and for valuable remarks, and also A. A. Afonin, V. N. Kapshai, and O. P. Solovtsova for useful discussions of the results.