The Green's function of the Poisson equation on the non-concentric annular region

In this article the two-dimensional Poisson equation is considered in the region between two non-concentric circular cylinders. Upon introducing bipolar coordinates the corresponding Green's function is found in form of a simple and rapidly converging series which can be formally summarized as a closed-form. Based on this result we additionally provide the Green's function for the conducting cylinder which is oriented parallel to a ground plane as well as for the case of two conducting cylinders.     

Green's function study of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system

The magnetic properties of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system on a square lattice are investigated by using the double-time temperature-dependent Green's function technique. In order to decouple the higher order Green's functions, Anderson and Callen's decoupling and random phase approximations have been used. The nearest- and next-nearest-neighbor interactions and the single-ion anisotropies are considered and their effects on compensation and critical temperature are studied.     

Exact Green's function for rectangular potentials and its application to quasi-bound states

In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also generalizing and resuming results in the literature. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression. From the poles and residues of the Green's function the bound states eigenenergies and eigenfunctions with the correct normalization constant are obtained. In order to show the versatility of the method, an application of the Green's function approach to extract information of quasi-bound states in rectangular barriers, where the standard analysis of quantum amplitudes fail, is presented.     

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 of confined electrons in an external magnetic field: Analytical formulation

We derive the analytical form of the Green's function of 2-dimensional electrons with lateral confinement in a perpendicular magnetic field. The confinement potentials considered are infinite barriers at radius R (quantum dot) and at r and R (quantum ring).     

Non-equilibrium Green's function approach to the quasiparticle transport and magnetoresistance in hybrid magnetic tunnel junctions

A generalized approach to study quasiparticle transport across hybrid magnetic tunnel junctions (MTJs) is formulated using the non-equilibrium Green's function technique. This formalism allows for arbitrary thicknesses of the electrodes and the central scattering region comprising of materials with multiple electronic bands, and incorporates the many body interactions present in the electrode regions. While the method can be used to study the transport characteristics of various types of MTJs, we have used it to study the tunneling characteristics and magnetoresistance (MR) of MTJs in which s-f interaction is present at the electrode layers. It is also used to study the transport characteristics of MTJs with hybrid electrodes and double barrier. The magnetic correlation present in the electrodes is found to strongly influence the TMR. Eventhough the magnetic correlation in general suppress the TMR, the TMR is found to be enhanced strongly for certain band occupations of the electrodes. We observe a fall of TMR with increase in the number of layers in the insulating region. Band occupation of the metallic layer present at the middle of the insulating layers in the double barrier MTJ is found to be important in deciding its tunnel characteristics. Origin of the different types of behavior of TMR is analyzed in terms of the spin-dependent tunnel currents.     

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.     

Single fermion Green's function in the quantum ordered Fermi-system: Analytic solution

An exact self-consistent solution for a finite temperature quantum-ordered state of correlated electron system found previously (8 and 1) is used to derive the fermionic single-particle Green's function. The quantum order parameter (QOP) found in the form of a periodic (elliptic Jacoby) function of the Matsubara's imaginary time (Mukhin, 2009), plays the role of effective scattering potential seen by electrons. The analytic solution for the Green's function demonstrates the following new features: (1) the pseudo-gap behavior of the single-electron density of states (DOS) near the (shifted) Fermi-level;(2) the side-bands of decreasing intensity away from the Fermi-level; (3) scaling of the quasi-particle energies with the QOP amplitude; (4) fermionic quasi-particles in the QOP state are combined from two confined “odd” and “even” fermions that separately would be unstable. The false-color plot of single-fermion DOS in the limit of a periodic kink-like Matsubara time-dependence of QOP is presented and could be used as prediction for the ARPES experiments. The plot of the DOS transfer between different energies at the “fermi-surface” momentum for a given kink-like QOP is also presented. Some possibly observable consequences of the found finger-prints are discussed.     

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

ABSTRACT

A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm^?1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.     

考虑棱边散射的半空间复杂导体目标高频分析方法

研究了半空间内复杂导体目标棱边散射的高频求解方法.分析半空间电磁波的传播规律和复杂目标棱边的电磁散射特性,将半空间并矢格林函数引入等效电磁流方法中,给出了基于等效电磁流法和物理绕射理论的半空间棱边散射场计算式,同时结合图形电磁学,对半空间复杂目标进行消隐处理,判断目标的棱边像素及获得棱边参数,与半空间目标的面元散射场相叠加,快速有效地计算了半空间复杂目标的雷达散射截面.数值结果证明了方法的有效性和准确性. 关键词： 半空间等效电磁流方法 半空间并矢格林函数 图形电磁学 雷达散射截面     

Quantum Binary and Triplet Distribution Functions of Plasma by using Green's Function

The aim of this paper is to calculate the binary and triplet distribution functions for one and two component Plasmas in terms of Green's function technique. We obtained the triplet distribution function in two form; one of them is based on the Kirkwood Superposition Approximation (KSA) which is consisting of the assumption that the potential in a set of three particles is the sum of the three pair potentials, this is equivalent to assuming that the triplet distribution function is the product of the three binary distribution functions, but the other form is calculated from BBGKY hierarchy. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Many‐body Green's function theory for thin ferromagnetic films: exact treatment of the single‐ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many‐body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second‐ and fourth‐order uniaxial single‐ion anisotropy, and the magnetic dipole‐dipole coupling. The single‐ion anisotropy terms can be treated exactlyby introducing higher‐order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest‐order Green's functions. RPA‐like approximations are used to decouple the exchange interaction terms in both the low‐order and higher‐order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.     

Coordinate transformation and construction of finite element mesh in a diverted tokamak geometry

A coordinate transformation technique between straight magnetic field line coordinate system (Ψ, θ) and Cartesian coordinate system (R, Z) is presented employing a Solov'ev solution of the Grad-Shafranov equation. Employing the equilibrium solution, the poloidal magnetic flux Ψ(R, Z) of a diverted tokamak, magnetic field line equation is solved computationally to find curves of constant poloidal angle θ, which provides us with explicit relations R = R(Ψ, θ) and Z = Z(Ψ, θ). Correspondingly, conversion from one coordinate to the other along particle trajectories in the vicinity of separatrix is demonstrated. Based on the magnetic structure, a finite element mesh is generated in a diverted tokamak geometry to solve Poisson's equation.     

电大开孔箱体屏蔽效能分析解析模型

电磁脉冲武器能够通过"前、后门"耦合效应对箱体内部电子元器件及电路板造成损伤,从而对电气电子设备的安全性构成严重威胁,因此,开展箱体电磁屏蔽效能的分析研究具有重要意义.推导了任意入射波条件下电大开孔箱体屏蔽系数的解析解,并在此基础上对箱体屏蔽效能进行了分析研究.首先通过矢量分解,得出任意入射平面波的坐标分量;再基于Cohn模型,获得了电大开孔的等效电偶、磁偶极子;然后通过镜像原理,计算出总的赫兹电矢量位、磁矢量位;最终求得电大开孔箱体内部任意观测点的电场解析解,用于箱体屏蔽系数计算.设计了5组验证性实验,仿真结果表明:该解析算法相对CST的均方误差为11.565 d B,绝对误差为8.015 d B,相关系数为0.921,从而验证了该算法的准确性;解析算法仿真的平均耗时为0.183 s,仅占CST耗时的1/7530,从而验证了该算法的高效性.     

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为, 如 热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在 一系列低维材料中发现的热-自旋输运现象. 这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.     

广义Helmholtz方程的Green函数及旋波介质色散关系的另一求解方法

运用并矢法求解广义Helmholtz方程,结合Fourier变换、留数定理等数学处理,给出方程的并矢Green函数解析表达式;并进一步就旋波介质给出其中色散关系的另外一种求解方法．     

A diatomic network model for electronic states of bulk,surface and thin films

This paper reports our investigations on an exactly solvable network model of solids. General properties of diatomic lattices, in particular the dispersion relations for the energy levels, the structure of the energy bands and the density of states for bulk, surface and thin films are compared with the corresponding properties of the monatomic lattices which we have previously reported. For a thin film of finite thickness, we present a simple but informative method of analyzing Van Hove singularities in the density of states. Effects due to the inclusion of second neighbor interactions are also studied. Calculations are exact and the method has apparent advantages over other methods of discussing similar problems.     

Electronic and transport properties of zigzag-edge monolayer/bilayer phosphorene nanoribbon junctions under a perpendicular electric field

We study the electronic and transport properties of monolayer/bilayer/bilayer (ML/BL/BL) and monolayer/bilayer/monolayer (ML/BL/ML) zigzag-edge phosphorene nanoribbon (ZPNR) junctions modulated by a perpendicular electric field (PEF). Within the tight-binding model Hamiltonian and by adopting the nonequilibrium Green's function, it is demonstrated that some oscillating conductance plateaus appear for the junctions, and the conductances are suppressed by the applied PEF. Interestingly, the direction of the PEF has different influence on the conductance of both junctions. We further present separately the band structures of the left lead, the central region and right lead, to reveal the reason for different conductance behavior in detail. Our results show that the ML/BL/BL ZPNR junction may be more suitable for the usage of field effect transistor than the ML/BL/ML ZPNR one under a PEF. Moreover, a PEF can be applied to distinguish the bottom−bottom and bottom−up configurations for the ML/BL/ML ZPNR junction.     

Magnetic properties of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system: Green’s function study

The magnetic behaviors of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system on a square lattice are studied by using the double-time temperature-dependent Green’s function technique. In order to decouple the higher order Green’s functions, Anderson and Callen’s decoupling and random phase approximations have been used. The system is described in the presence of an external magnetic field. We illustrate the influences of the nearest- and next-nearest-neighbor interactions and the single-ion anisotropies with an external magnetic field on compensation and critical temperatures. We found that the system that includes only the nearest-neighbor interaction and the single-ion anisotropies does not have a compensation temperature. When the next-nearest-neighbor interactions exceed a certain minimum value, a compensation temperature begins to appear. For some negative values of single-ion anisotropies, there exist first-order phase transitions. The system has first-order phase transition properties when it is under the influence of an external magnetic field.