Analytic continuation-free Green's function approach to correlated electronic structure calculations

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.

We outline a complete spectral formalism for computing high spatial resolution three‐dimensional deformations arising from the surface mass loading of a spherically symmetric planet. The main advantages of the formalism are that all surface mass loads are always described using a consistent mathematical representation (expansions using spherical harmonic basis functions) and that calculations of deformation fields for various spatial resolutions can be performed by simply altering the spherical harmonic degree truncation level of the procedure. The latter may be important when incorporating improved observational constraints on a particular surface mass load, when considering potential errors in the computed field associated with mass loading having a spatial scale unresolved by the observational constraints, or when treating a number of global surface mass loads constrained with different spatial resolutions. These advantages do not extend to traditional “Green's function” approaches which involve surface element discretizations of the global mass loads. In the practical application of the Green's function approach the discretization is subjective and dependent on the particular surface mass load being considered. Furthermore, treatment of mass loads with higher spatial resolutions can require tedious rediscretization of the surface elements. Another advantage of the spectral formalism, over the Green's function approach, is that a posteriori analyses of the computed deformation fields, such as degree correlations, power spectra, and filtering analyses, are easily performed. In developing the spectral formalism, we consider specific cases where the Earth's mantle is assumed to respond as an elastic, slightly anelastic, or linear viscoelastic medium. In the case of an elastic or slightly anelastic mantle rheology the spectral response equations incorporate frequency dependent Love numbers. The formalism can therefore be used, for example, to compute the potentially resonant deformational response associated with the free core nutation and Chandler wobble eigenfunctions. For completeness, the spectral response equations include both body forces, as arise from the gravitational attraction of the Sun and the Moon, and surface mass loads. In either case, and for both elastic and anelastic mantle rheologies, we outline a pseudo‐spectral technique for computing the ocean adjustment associated with the total gravitational perturbation induced by the external forcing. Three‐dimensional deformations computed using the usual Love number approach are generally referenced to an origin located at the center of mass of the undeformed planet. We derive a spectral technique for transforming the results to an origin located at the center of mass of the deformed planet.

Matsubara Green's Function and its Analytic Continuation using Flat Histogram Quantum Monte Carlo Simulation

Pseudo Jahn–Teller origin of ferroelectric instability in BaTiO3 type perovskites: The Green's function approach and beyond

We consider a Hubbard model (HM) with occupation dependent hopping integrals. Using the Hartree–Fock (H–F) approximation and the new Green's function approach with inter‐site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k‐dependent spectral weights is included. In addition, we obtain the shift of the spin bands, which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model, the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT‐Quantum Monte Carlo calculations and with the Hubbard III approximation, which includes the correlated hopping effect.

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.

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.

We present an analytical and experimental study of the scattering parameters in a one dimensional (1D) symmetric photonic crystal and their relation to the density of states (DOS). The 1D photonic crystal is constituted by $N$ alternating wires and loops that are either inserted horizontally or attached vertically between the source and load on a transmission line. The complete knowledge of the scattering matrix coefficients (${S}_{ij}$) allows us to access the DOS and eigenvalues of the finite periodic structure as well as the DOS and dispersion curves of an infinite periodic system. We show the usefulness of the transmission and reflection delay times and highlight their similarities and differences with respect to the DOS, in particular as a function of the absorption strength in the system. For both horizontal and vertical geometries, we show analytically that in a lossless structure, the DOS is proportional to the Friedel phase, namely the derivative of the argument of the determinant of the scattering matrix S. For a low loss system, this proportionality remains still valid with a good approximation and can be used as a practical tool to derive the DOS and therefore the dispersion curves from experimental data. Also, the absorption can be accurately extracted from the measurement of the modulus of the determinant of $S$. However, for increasing strength of dissipation, we show how and why these relationships cease to be valid. Still, the transmission delay time can remain an efficient tool to derive DOS even at relatively high dissipation strength. Additionally, we show that in the vertical geometry the transmission and reflection delay times exhibit negative delta peaks which are related directly to the eigenmodes of the finite system with different boundary conditions on its extremities. Our theoretical results are obtained by means of the Green's function approach, whereas the experimental demonstrations are performed using standard coaxial cables in the radio-frequency domain.

A new type of Green function approach is introduced for time-domain scattering for a stratified dissipative slab. The new Green functions are defined as mappings from the transmitted field to the split fields (i.e., the right-moving and left-moving fields) at any point within the stratified slab. Unlike the usual Green functions, the present Green functions have compact support in the time variable. The new technique is illustrated for the case of normally incident electromagnetic waves on a stratified slab where the permittivity, permeability, and conductivity vary with the depth. The linear and homogeneous partial differential equations (PDEs) for these ‘‘compact Green functions’’ are derived. The PDEs together with the initial and boundary conditions are well suited for a numerical treatment. Numerical results for the compact Green functions are presented in the direct problem, while in the inverse problem the permittivity and conductivity (or the permeability and conductivity) are reconstructed simultaneously using the reflection and transmission data for the first round trip. The present method is useful and attractive for both the direct and inverse problems due to its simplicity, high speed, and high accuracy in numerical computations.

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.

Seismic oceanography can provide a two- or three-dimensional view of the water column thermocline structure at a vertical and horizontal resolution from the multi-channel seismic dataset. Several seismic imaging methods and techniques for seismic oceanography have been presented in previous research. In this study, we suggest a new formulation of the frequency-domain reverse-time migration method for seismic oceanography based on the analytic Green's function. For imaging thermocline structures in the water column from the seismic data, our proposed seismic reverse-time migration method uses the analytic Green's function for numerically calculating the forward- and backward-modeled wavefield rather than the wave propagation modeling in the conventional algorithm. The frequency-domain reverse-time migration with analytic Green's function does not require significant computational memory, resources, or a multifrontal direct solver to calculate the migration seismic images as like conventional reverse-time migration. The analytic Green's function in our reverse-time method makes it possible to provide a high-resolution seismic water column image with a meter-scale grid size, consisting of full-band frequency components for a modest cost and in a low-memory environment for computation. Our method was applied to multi-channel seismic data acquired in the Arctic Ocean and successfully constructed water column seismic images containing the oceanographic reflections caused by thermocline structures of the water mass. From the numerical test, we note that the oceanographic reflections of the migrated seismic images reflected the distribution of Arctic waters in a shallow depth and showed good correspondence with the anomalies of measured temperatures and calculated reflection coefficients from each XCDT profile. Our proposed method has been verified for field data application and accuracy of imaging performance.

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.

A detailed theoretical study of the density of states (DOS) is presented for free electrons in terahertz- (THz-) driven three-dimensional electron gases (3DEGs) in the presence of static magnetic fields. Applying the Green's function approach to a specific sample configuration where the electron - photon interactions can be included exactly, we have derived the steady-state DOS for electrons in a THz-driven 3DEG. The results obtained show that the presence of intense THz electromagnetic radiations will result in a reduction of the DOS in the low-energy regime in a 3DEG in quantizing magnetic fields. A photon-modified electron DOS will lead to the lifting of the Fermi level in a 3DEG system and, consequently, to the occupation of higher Landau levels at a fixed magnetic field. A more pronounced effect can be observed for relatively low-frequency and/or high-intensity radiations.

Ab initio green's function calculations on highly conducting polymers: Effects of electron correlation and aperiodicity