A spectral formalism for computing three‐dimensional deformations due to surface loads: 1. Theory

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green's function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green's function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green's function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green's function approach and other Green's function approaches in the numerical exact limit.

The geocenter variations reflect the global scale mass redistribution and the interaction between the solid Earth and the mass load. Determination of the geocenter variations due to surface mass load from various geophysical sources places constraints on the variations of the origin of terrestrial reference frame, and provides the expected range of variations for space‐geodesy. Our results suggest that on the time scale from 30 days to 10 years the primary variability of geocenter variations from atmosphere, ocean and surface ground water occurs on the annual and semiannual scales. The lumped sum of these surface mass load induced geocenter variations is within 1 cm level.

We present a new charge self-consistent scheme combining Density Functional\nand Dynamical Mean Field Theory, which uses Green's function of multiple\nscattering-type. In this implementation the many-body effects are incorporated\ninto the Kohn-Sham iterative scheme without the need for the numerically\nill-posed analytic continuation of the Green's function and of the self-energy.\nThis is achieved by producing the Kohn-Sham Hamiltonian in the sub-space of\ncorrelated partial waves and allows to formulate the Green's function directly\non the Matsubara axis. The spectral moments of the Matsubara Green's function\nenable us to put together the real space charge density, therefore the charge\nself-consistency can be achieved. Our results for the spectral functions\n(density of states) and equation of state curves for transition metal elements,\nFe, Ni and FeAl compound agree very well with those of Hamiltonian based\nLDA+DMFT implementations. The current implementation improves on numerical\naccuracy, requires a minimal effort besides the multiple scattering formulation\nand can be generalized in several ways that are interesting for applications to\nreal materials.\n

The electronic structure of organic-inorganic interfaces often features resonances originating from discrete molecular orbitals coupled to continuum lead states. An example is molecular junction, individual molecules bridging electrodes, where the shape and peak energy of such resonances dictate junction conductance, thermopower, I-V characteristics, and related transport properties. In molecular junctions where off-resonance coherent tunneling dominates transport, resonance peaks in the transmission function are often assumed to be Lorentzian functions with an energy-independent broadening parameter Γ. Here we define a new energy-dependent resonance broadening function, Γ(E), based on diagonalization of non-Hermitian matrices, which can describe resonances of a more complex, non-Lorentzian nature and can be decomposed into components associated with the left and right leads, respectively. We compute this quantity via an ab initio non-equilibrium Green's function (NEGF) approach based on density functional theory (DFT) for both symmetric and asymmetric molecular junctions, and show that our definition of Γ(E), when combined with Breit-Wigner formula, reproduces the transmission calculated from DFT-NEGF. Through a series of examples, we illustrate how this approach can shed new light on experiments and understanding of junction transport properties in terms of molecular orbitals.

ABSTRACTGreen's functions have been a tool to analyze important reservoir geomechanics effects like subsidence, compaction, well closure, and permeability variation. However, the classical Green's function is related to linear elastic, homogenous, and geometrically simplified media. The use of auxiliary functions that consider heterogeneous media has the potential to simplify the numerical analyses of some complex problems. This research work proposes a new approach to Green's function method based on artificial neural networks (ANNs) to consider stratified media with direct application in reservoir geomechanics. These solutions obtained through ANN have as output the normalized displacement at any point of the stratified massif due to the application of a point load inside the massif. The input data of the proposed ANN are the material properties of the media, the point load, and the point of interest. By using the developed ANN‐based Green's function together with the classical Green's function approach, it is possible to obtain individually the displacement at any point of the massif due to a pore pressure variation within the reservoir, only discretizing the reservoir boundary. This leads to a more efficient method when compared to traditional methods, such as the finite element method. For the points of interest, seafloor, and top and bottom of the reservoir, the numerical example presented was 25 times faster than the classic Green function approach on a computer with 12 threads of 2.6 GHz and 32 GB RAM. This reduction in processing time is crucial for decision‐makers to act in field applications.

Green's function approach is adopted for analyzing the deflection and the transient temperature distribution of a plate made of functionally graded materials (FGMs). The governing equations for the deflection and the transient temperature are formulated into eigenvalue problems by using the eigenfunction expansion theory. Green's functions for solving the deflection and the transient temperature are obtained by using the Galerkin method and the laminate theory, respectively. The eigenfunctions of Green's function for the deflection are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the plate. The eigenfunctions of Green's function for the temperature are determined from the continuity conditions of the temperature and the heat flux at interfaces.

In a previous work [Andrade \textit{et al.}, Phys. Rep. \textbf{647}, 1 (2016)], it was shown that the exact Green's function (GF) for an arbitrarily large (although finite) quantum graph is given as a sum over scattering paths, where local quantum effects are taken into account through the reflection and transmission scattering amplitudes. To deal with general graphs, two simplifying procedures were developed: regrouping of paths into families of paths and the separation of a large graph into subgraphs. However, for less symmetrical graphs with complicated topologies as, for instance, random graphs, it can become cumbersome to choose the subgraphs and the families of paths. In this work, an even more general procedure to construct the energy domain GF for a quantum graph based on its adjacency matrix is presented. This new construction allows us to obtain the secular determinant, unraveling a unitary equivalence between the scattering Schr\"odinger approach and the Green's function approach. It also enables us to write a trace formula based on the Green's function approach. The present construction has the advantage that it can be applied directly for any graph, going from regular to random topologies.

We develop a formalism for studying the motion of nondegenerate electrons in semiconductors, which allows a nonperturbative description of the effects of an external high electric field on electron-phonon scattering within the Kadanoff-Baym-Keldysh nonequilibrium Green's-function approach. Based on the exact solutions of Schr\odinger's equation, we solve Dyson's equation for the single-particle retarded Green's function ${G}^{r}$${(\mathrm{k}}_{\ensuremath{\perp}}$,z,z',\ensuremath{\omega}). Recognizing that high fields break the translational symmetry of the system and that momentum is no longer a good quantum number, we use Airy transforms to handle the position dependence parallel to the applied high field. From this we are able to derive a model for the spectral density function A${(\mathrm{k}}_{\ensuremath{\perp}}$,s,\ensuremath{\omega}) through which we can account for quantum effects such as collisional broadening and the intracollisional field effect in a simple and rigorous way. We demonstrate the theory by considering only weak scattering with nonpolar optical phonons and restrict ourselves to fields that are constant in space and time. Our formulation suggests the presence of a novel quantum effect induced by the simultaneous presence of scattering and electric field which produces a discontinuous trajectory of the electron path along the field direction.

This paper presents a Green's function approach to the calculation of the pi-electronic states of molecules. The Green's functions are written in terms of the molecular orbital. Physical quantities are more easily treated in this approach than the previous method using the AO scheme. Formulae for the excitation and the ground state energies are obtained by RPA. Using the semi-empirical parameters, several examples are calculated. However, the well-known instability in RPA appears when the excitation and the ground state energies are calculated with the non-empirical parameters. From the viewpoint of diagramatic method, we discuss how this instability can be removed by introducing doubly excited configurations are renormalization of orbital energies.

A combined variational–Green's function approach to the determination of the capacitance of various useful three-dimensional geometries is developed. This formalism leads to general, exact expressions for the capacitance, which can be used with all geometries provided the spatial distribution of the charge can be determined. In particular, the theory takes into account the finite thickness and unequal areas of the capacitor plates. Specific applications of the theory include circular capacitors with disc and ring-shaped charged plate geometries. Such geometries are commonly encountered in experimental set-ups for capacitive measurements of thin film thicknesses in the field of microelectronics. Numerical results indicate that the values of thin film thicknesses calculated via simplified one-dimensional formulae for the capacitance may be incorrect by more than 10%

Simulation of wheel–rail impact load and sleeper–ballast contact pressure in railway crossings using a Green's function approach

In this paper, we take advantage of using a Green's function approach as an analytical tool to study linear and nonlinear aspects of thermoacoustic systems.Green's function is defined as the impulse response of a system; it has a clear physical meaning in combustion systems, and it provides a fast and flexible tool to predict thermoacoustic instabilities in both time and frequency domains.In this study, we consider a tube, which houses two sources: a heat source and an external noise source.The heat source is modelled by an amplitude-dependent n-law, the noise source is assumed to emit two types of noise (pink noise or white noise).We use the Green's function approach to derive an integral equation for the acoustic field in the Rijke tube, and we also derive an algebraic equation for the thermoacoustic eigenfrequency.Both equations are validated.The results that we found, show that the presence of noise (whether pink or white noise) results in "triggering" an instability and in accelerating the growth of the amplitude.These effects become more pronounced as the level of noise increases.The influence of pink noise is stronger than that of white noise.We also studied how the hysteresis behavior (a nonlinear effect in dynamical systems) is affected by the noise, using the heater power as bifurcation parameter.Our study reveals that the width of the bistable region decreases as the strength of noise increases.

The Green's-function approach to transient-hot-electron transport of Xing and Ting [Phys. Rev. B 35, 3971 (1987)] is applied to a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterojunction. Scattering mechanisms, such as remote and background ionized impurity scattering as well as acoustic (via deformation potential and piezoelectric coupling) and polar-optical-phonon contributions, have been included in the force and energy transient state equations. The effect of screening on the ionized impurities by the free carriers has been taken into account approximately. Our results for the transient velocity are in reasonable agreement with available Monte Carlo simulations. Theoretical calculations for the transient velocity and electron temperature have been carried out for electrons with and without electron-electron interactions.

ABSTRACTThe central ideas and the advantages of the difference equation Green's function approach for layered systems with 2D-periodicity are presented. The tight-binding linear muffin-tin orbital and other practical aspects of the implementation are discussed. Preliminary test results are presented.

A nonequilibrium Green's function approach is employed to investigate the spin-Hall effect in diffusive two-dimensional electron systems with Rashba spin-orbit interaction. Considering a long-range electron-impurity scattering potential in the self-consistent Born approximation, we find that the spin-Hall effect arises from two distinct interband polarizations in helicity basis: a disorder-unrelated polarization directly induced by the electric field and a polarization mediated by electron-impurity scattering. The disorder-unrelated polarization is associated with all electron states below the Fermi surface and produces the original intrinsic spin-Hall current, while the disorder-mediated polarization emerges with contribution from the electron states near the Fermi surface and gives rise to an additional contribution to the spin-Hall current. Within the diffusive regime, the total spin-Hall conductivity vanishes in infinitely large samples, independently of temperature, of the spin-orbit coupling constant, of the impurity density, and of the specific form of the electron-impurity scattering potential. However, in a finite-size Rashba two-dimensional semiconductor, the spin-Hall conductivity no longer always vanishes. Depending on the sample size in the micrometer range, it can be positive, zero or negative with a maximum absolute value reaching as large as $e∕8\ensuremath{\pi}$ order of magnitude at low temperatures. As the sample size increases, the total spin-Hall conductivity oscillates with a decreasing amplitude. We also discuss the temperature dependence of the spin-Hall conductivity for different sample sizes.