Nonequilibrium Green＇s function method for quantum thermal transport

This review deals with the nonequilibrium Green＇s function （NEGF） method applied to the problems of energy transport due to atomic vibrations （phonons）, primarily for small jtmction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systerms. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a nmnber of applications of NEGF, not in routine model system calculations, but in a few new aspects showing the power and usefulness of the formalism. In partkaflar, we discuss the problems of multiple leads, coupled left-right-lead system, and system without a center. We also apply the method to the problem of full counting statisties. In the case of nonlinear svstems, we make general comments on the thermal expansion effect. phonon relaxation timv. and a certain class of mean-field approximations. Lastly, we examine the relationship between NEGF. reduced density matrix, and master equation approaches to thermal transport,

Study on Characteristics of 3-D Translating-Pulsating Source Green Function of Deep-Water Havelock Form and Its Fast Integration Method

The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.

Continuum Skyrme Hartree-Fock-Bogoliubov theory with Green’s function method for neutron-rich Ca,Ni,Zr,and Sn isotopes

The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.

Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Electronic Transport Calculations Using Maximally-Localized Wannier Functions

I present a method to calculate the ballistic transport properties of atomic-scale structures under bias. The electronic structure of the system is calculated using the Kohn-Sham scheme of density functionai theory （DFT）. The DFT eigenvectors are then transformed into a set of maximaily localized Wannier functions （MLWFs） [N. Maxzari and D. Vanderbilt, Phys. Rev. B 56 （1997） 12847]. The MLWFs are used as a minimai basis set to obtain the Hamitonian matrices of the scattering region and the adjacent leads, which are needed for transport calculation using the nonequilibrium Green＇s function formalism. The coupling of the scattering region to the semi-infinite leads is described by the self-energies of the leads. Using the nonequilibrium Green＇s function method, one calculates self-consistently the charge distribution of the system under bias and evaluates the transmission and current through the system. To solve the Poisson equation within the scheme of MLWFs I introduce a computationally efficient method. The method is applied to a molecular hydrogen contact in two transition metal monatomic wires （Cu and Pt）. It is found that for Pt the I-V characteristics is approximately linear dependence, however, for Cu the I-V characteristics manifests a linear dependence at low bias voltages and exhibits apparent nonlinearity at higher bias voltages. I have also calculated the transmission in the zero bias voltage limit for a single CO molecule adsorbed on Cu and Pt monatomic wires. While a chemical scissor effect occurs for the Cu monatomic wire with an adsorbed CO molecule, it is absent for the Pt monatomie wire due to the contribution of d-orbitals at the Fermi energy,

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.

沉积层序对谷地场地地震反应的影响-SH波入射

采用一种多域间接边界元方法,求解了层状半空间中多层沉积谷地对平面SH波的放大效应问题。该方法将含有多层沉积的层状半空间分解为开口层状半无限空间域和多个沉积层闭合域,进而通过求解层状半空间中斜线均布荷载动力格林函数来模拟开口域内的散射波场,通过求解全空间中均布荷载动力格林函数来模拟各闭合域的散射波场。方法充分发挥半空间格林函数和全空间格林函数在构造开口半无限空间域和闭合域内散射波场方面的优势,具有灵活性强和精度高的优点。文中验证了方法的正确性,并以正常沉积、软夹层沉积和逆序沉积为例进行了数值计算分析,研究了沉积层序对谷地附近地面运动的影响。数值结果表明,沉积层逆序排列时,低波速层对中高频地震动均有很好的"隔震"效果;沉积层序对地面运动的固有频率和卓越频率均有着显著的影响;沉积序列的改变会导致沉积动力特性的改变,进而会影响到沉积谷地与层状场地的动力相互作用机制。

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

A fast integration method for translating-pulsating source Green＇s function in Bessho form

The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.

Heat Generation by Electric Current in Normal-Metal-Molecular Quantum Dot-Superconductor System

We investigate the heat generation induced by electrical current in a normal-metal-molecular quantum dot-superconductor （NDS） system. By using nonequilibrium Green＇s function method, the heat generation Q is derived and studied in detail. The superconducting lead influences the heat generation significantly. An obvious step appears in Q - eV characteristics and the iocation of this step is related with the phonon frequency ωo. The heat generations exhibit very different behaviour in the condition eV 〈 △ and eV 〉 △ due to different tunneling mechanism. From the study of Q - eVg curves, there is an extra peak as eV 〉 △. The difference in this two cases is also shown in Q - ωo curve, an extra peak emerges as eV 〉 △.

单层含硫空位MoS2光伏效应的第一性原理研究

基于非平衡态格林函数--密度泛函理论,采用第一性原理研究方法,对单层含硫空位MoS2的光伏效应进行了研究.利用能带图和联合态密度分析单层含硫空位MoS2的光响应函数.结果表明:对于单层含硫空位的MoS2,线偏光电流效应不明显,而圆偏光电流效应比较明显.计算模拟了随偏振角(相位角)变化的光响应函数,计算结果符合唯象理论.单层含硫空位的MoS2可被应用于新型电子和光电子器件中,为进一步认识单层硫空位MoS2的光电流效应提供了新的理论基础.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization （II）： Solution of Equation

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Theoretical Investigation of Exchange Bias in Compensated Cases

The exchange bias （EB） of the ferromagnetic （FM）/antiferromagnetic （AFM） bilayers in a compensated case is studied by use of the many-body Green＇s function method of quantum statistical theory. The so-called compensated case is that there is no net magnetization on the AFM side of the interface. Our conclusion is that the EB in this case is primarily from the asymmetry of the interracial exchange coupling strengths between the FM and the two sublattices of the AFM. The effects of the layer thickness, temperature and the interracial coupling strength oi2 the exchange bias HE are investigated. The dependence of HE on the FM layer thickness and temperature is qualitatively in agreement with experimental results. HE is nearly inversely proportional to FM thickness. When temperature varies, both HE and He decrease with temperature increasing. The anisotropy of the FM layer only slightly influence He, but does not influence HE.

Simulation of strong earthquake characteristics of a scenario earthquake(M_(S)7.5)based on the enlightenment of 2022 M_(S)6.9 earthquake in Menyuan

The Menyuan area is an important transportation hub in the Hexi Corridor.The Menyuan M_(S)6.9 earthquake that occurred on January 8,2022 had a major impact on the local infrastructure and transportation of this region.Due to the high possibility of similar strong earthquakes occurring in this area in the future,preliminary assessment of the seismic intensity characteristics of destructive earthquakes in this region is essential for effective disaster control.This paper uses the empirical Green′s function(EGF)method as a numerical simulation tool to predict the ground motion intensity of Datong Autonomous County under the action of the scenario earthquake(M_(S)7.5).Seismic records of aftershocks of the 2016 Menyuan M_(S)6.4 earthquake were used as Green’s functions for this simulation.The uncertainties associated with various source parameters were considered,and 36possible earthquake scenarios were simulated to obtain 72 sets of horizontal ground motions in Datong County.The obtained peak ground acceleration(PGA)vs.time histories of the horizontal ground motion were screened using the attenuation relationships provided by the fifth-edition of China’s Seismic Ground Motion Parameter Zoning Map and the NGA-West2dataset.Ultimately,32 possible acceleration-time histories were selected for further analysis.The screened PGA values ranged from 78.8 to 153 cm/s^(2).The uncertainty associated with the initial rupture point was found to greatly affect the results of the earthquake simulation.The average acceleration spectrum of the selected acceleration-time history exceeded the expected spectrum of a intermediate earthquake,which means that buildings in Datong County might sustain some damage should the scenario earthquake occur.This research can provide reliable ground motion input for urban earthquake damage simulation and seismic design in Datong County.Growing the dataset of small earthquakes recorded in this region will facilitate the large-scale simulation of ground motions under different earthquake scenarios.

半无限长导线端面Green函数严格形式的一个新推导

为得到半无限长理想导线端面上的单体Green函数,应用介观问题中求解Green函数常用的代数迭代方法,利用端面处的自洽关系,推导出任意截面的半无限长链端面上Green函数的严格形式.该结果克服了多数文献中通常采用的直接积分法计算而忽略虚纵向波矢态的贡献,具有更强的严格性和更广的适用范围.

A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach

With the rapidly increasing integration density and power density in nanoscale electronic devices,the thermal management concerning heat generation and energy harvesting becomes quite crucial.Since phonon is the major heat carrier in semiconductors,thermal transport due to phonons in mesoscopic systems has attracted much attention.In quantum transport studies,the nonequilibrium Green’s function(NEGF)method is a versatile and powerful tool that has been developed for several decades.In this review,we will discuss theoretical investigations of thermal transport using the NEGF approach from two aspects.For the aspect of phonon transport,the phonon NEGF method is briefly introduced and its applications on thermal transport in mesoscopic systems including one-dimensional atomic chains,multi-terminal systems,and transient phonon transport are discussed.For the aspect of thermoelectric transport,the caloritronic effects in which the charge,spin,and valley degrees of freedom are manipulated by the temperature gradient are discussed.The time-dependent thermoelectric behavior is also presented in the transient regime within the partitioned scheme based on the NEGF method.

GLOBAL EXISTENCE AND POINTWISE ESTIMATES OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS

The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.

Theoretical design of single-molecule NOR and XNOR logic gates by using transition metal dibenzotetraaza[14]annulenes

The idea of replacing traditional silicon-based electronic components with the ones assembled by organic molecules to further scale down the electric circuits has been attracting extensive research focuses.Among the molecularly assembled components,the design of molecular logic gates with simple structure and high Boolean computing speed remains a great challenge.Here,by using the state-of-the-art nonequilibrium Green’s function theory in conjugation with first-principles method,the spin transport properties of single-molecule junctions comprised of two serially connected transition metal dibenzotetraaza[14]annulenes(TM(DBTAA),TM=Fe,Co)sandwiched between two single-walled carbon nanotube electrodes are theoretically investigated.The numerical results show a close dependence of the spin-resolved current-voltage characteristics on spin configurations between the left and right molecular kernels and the kind of TM atom in TM(DBTAA)molecule.By taking advantage of spin degree of freedom of electrons,NOR or XNOR Boolean logic gates can be realized in Fe(DBTAA)and Co(DBTAA)junctions depending on the definitions of input and output signals.This work proposes a new kind of molecular logic gates and hence is helpful for further miniaturization of the electric circuits.