Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Green function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Hybrid quantum-classical approach for coupled-cluster Green's function theory

The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of T gates that grows as O ( N 5 ) per time step to calculate the impurity Green's function in the time domain, where N is the total number of energy levels in the AIM. Since the number of T gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requires O ( N 6 ) computational resources per time step.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green’s function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(N e 3 ), where N e is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Space charge fields in azimuthally symmetric beams: Integrated Green's function approach

Electromagnetic fields induced by the space charge in relativistic beams play an important role in Accelerator Physics. They lead to emittance growth, slice energy change, and the microbunching instability. Typically, these effects are modeled numerically since simple description exists only inthe limits of large- or small-scale current variations. In this paper we consider an axially symmetric charged beam inside a round pipe and find the solution of the space charge problem that is valid in the full range of current variations. We express the solution for the field components in terms of Green’s functions, which are fully determined by just a single function. We then find that this function is an on-axis potential from a charged disk in a round pipe, with transverse charge density ρ⊥(r), and it has a compact analythical expression. We finally provide an integrated Green’s function based approach for efficient numerical evaluation in the case when the transverse charge density stays the same along the beam

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Topological Green’s Function Zeros in an Exactly Solved Model and Beyond

The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we here study an exactly integrable, local model for a fractionalized topological insulator. Using a controlled perturbation theory about this limit, we demonstrate the existence of topological bands of zeros in the exact fermionic Green’s function and show that in this model they do affect the topological invariant of the system, but not the quantized transport response. Close to (but prior to) the Higgs transition signaling the breakdown of fractionalization, the topological bands of zeros acquire a finite “lifetime.” We also discuss the appearance of edge states and edge zeros at real space domain walls separating different phases of the system. This model provides a fertile ground for controlled studies of the phenomenology of Green’s function zeros and the underlying exactly solvable lattice gauge theory illustrates the synergetic cross pollination between solid-state theory, high-energy physics, and quantum information science.

Bollmann, Steffen↗
DOE OSTI2021

Green’s functions on a renormalized lattice: An improved method for the integer quantum Hall transition

Highlights: • Speed up of numerical calculations by exact renormalization group steps. • Practical approach to handle delicate scaling analysis. • Absence of evidence to prefer marginal corrections over power-law corrections. We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green’s function method. We apply this framework to investigate the critical behavior of the integer quantum Hall transition of a tight-binding Hamiltonian defined on a simple square lattice. In addition, we employ an improved scaling analysis that includes two irrelevant exponents to characterize the shift of the critical energy as well as the corrections to the dimensionless Lyapunov exponent. We compare our findings with the results of a conventional implementation of the recursive Green’s function method, and we put them into broader perspective in view of recent development in this field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Triple Excitations in Green’s Function Coupled Cluster Solver for Studies of Strongly Correlated Systems in the Framework of Self-Energy Embedding Theory

Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handling a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green’s function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green’s function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO 3 solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Excited-state electronic structure of molecules using many-body Green’s functions: Quasiparticles and electron–hole excitations with VOTCA-XTP

Here, we present the open-source VOTCA-XTP software for the calculation of the excited-state electronic structure of molecules using many-body Green’s function theory in the GW approximation with the Bethe–Salpeter equation (BSE). This work provides a summary of the underlying theory and discusses the details of its implementation based on Gaussian orbitals, including resolution-of-identity techniques and different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using graphics processing units in a hybrid OpenMP/Cuda scheme. A distinctive feature of VOTCA–XTP is the capability to couple the calculation of electronic excitations to a classical polarizable environment on an atomistic level in a coupled quantum- and molecular-mechanics (QM/MM) scheme, where a complex morphology can be imported from Molecular Dynamics simulations. The capabilities and limitations of the GW–BSE implementation are illustrated with two examples. First, we study the dependence of optically active electron–hole excitations in a series of diketopyrrolopyrrole-based oligomers on molecular-architecture modifications and the number of repeat units. Second, we use the GW–BSE/MM setup to investigate the effect of polarization on localized and intermolecular charge-transfer excited states in morphologies of low-donor content rubrene–fullerene mixtures. These showcases demonstrate that our implementation currently allows us to treat systems with up to 2500 basis functions on regular shared-memory workstations, providing accurate descriptions of quasiparticle and coupled electron–hole excited states of various characters on an equal footing.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

A superconfiguration calculation of opacity with consistent bound and continuum electron treatments using green’s functions

One of the challenges in calculating the opacity of dense plasmas is the difficulty in consistently modeling electrons bound to nuclei and those that exist within the continuum of free states in electronic structure models. We address this issue by adapting the green's function approach, originally developed for use in average atom calculations, to the determination of superconfiguration (SC) electronic structure. The spectra created using these SCs indicate that a consistent treatment of continuum electronic structure is important for phenomena involving electrons near ionization thresholds, such as the pressure ionization of bound states and the opacity due to transitions near bound-free edges. Though important for dense plasmas, the detailed incorporation of continuum electrons into structure calculations does not have significant impact on the recent discrepancies between the predicted and measured opacity of hot, dense iron (Bailey et al 2015 Nature517 56). Here we find that the inclusion of plasma effects through an ion-sphere model along with our treatment of continuum electronic states gives a description of pressure ionization in hot, dense aluminum that is in better agreement with experiment than methods that rely on perturbative descriptions of the plasma environment (Hoarty et al 2013 Phys. Rev. Lett.110 265003).

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Note on the Green’s function formalism and topological invariants

It has been discovered previously that the topological order parameter could be identified from the topological data of the Green's function, namely the (generalized) TKNN invariant in general dimensions, for both non-interacting and interacting systems. In this note, we show that this phenomenon has a clear geometric derivation. In conclusion, this proposal could be regarded as an alternative proof for the identification of the corresponding topological invariant and the topological order parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Global anomalies of Green's function zeros.

We study global anomalies of nonlocal effective theories proposed to describe symmetry-preserving Luttinger surfaces, i.e., the momentum-space manifolds of Green’s function zeros (GFZs) at zero energy, in strongly interacting fermionic systems. In particular, we focus on the simplest possible cases associated with a gapless Dirac zero, which is the counterpart of the gapless Dirac quasiparticle in weakly interacting systems. These theories may be derived by integrating out low-energy degrees of freedom that do not couple to the relevant gauge field. We discuss the global anomaly, the bulk-boundary correspondence, and the constraint on phases consistent with the anomaly, such as non-Fermi liquids and emergent gapless quasiparticles on Luttinger surfaces. Failing to avoid spontaneous symmetry breaking in the thermodynamical limit inevitably leads to unstable GFZs. We also provide some perspective on why the related nonlocal fermionic effective theory studied recently is not a suitable starting point for a symmetrically gapped phase

Su, Lei↗
DOE OSTI2021

Real-space Green's function approach for x-ray spectra at high temperature

There has been considerable interest in properties of condensed matter at high temperature, including nonequilibrium behavior and extreme conditions up to the warm dense matter regime. Such behavior is encountered, e.g., in experimental time-resolved x-ray absorption spectroscopy in the presence of intense laser fields. In an effort to simulate such behavior, we present an approach for calculations of high-temperature x-ray absorption spectra in arbitrary materials, using a generalization of the real-space Green's function formalism. Here, the method is incorporated as an option in the core-level x-ray spectroscopy code FEFF10. To illustrate the approach, we present calculations for several materials together with comparisons to experiment and with other methods.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Augmenting machine learning of Grad–Shafranov equilibrium reconstruction with Green's functions

This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using principal component analysis of plasma toroidal current densities (J t ) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for the poloidal flux (ψ) and diagnostics generated from the toroidal current (J t ). Similar to the idea of a physics-informed neural network (NN), this physically enforces consistency between ψ, J t , and the synthetic diagnostics. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. The results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J t with median R 2 = 0.9993 and R 2 = 0.978, respectively. A comprehensive NN using a network architecture search is also employed to predict the coefficients of the basis functions. The NN demonstrates significantly better performance compared to the least squares method with median R 2 = 0.9997 and 0.9916 for J t and ψ, respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Evaluating the exfoliation of two-dimensional materials with a Green's function surface model

Previous methods for the evaluation of the exfoliation of two-dimensional (2D) layered materials have drawbacks in computational efficiency and are unable to describe cases with semi-infinite substrates. Based on a Green's function surface (GFS) model, here we develop an approach to efficiently determine the tendency of exfoliation of 2D materials from their bulk crystals or semi-infinite substrates. By constructing appropriate surface configurations, we may calculate the exfoliation energy more precisely and quickly than the traditional way with the slab model. Furthermore, the GFS approach can provide angle-resolved photoemission spectroscopy of surface systems for direct comparison with experimental data. In this work, our findings indicate that the GFS approach is powerful for studies of 2D materials and various surface problems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Effect of Time Window and Spectral Measurement Options on Empirical Green’s Function Analysis Using DAS Array and Seismic Stations

The recorded seismic waveform is a convolution of event source term, path term, and station term. Removing high-frequency attenuation due to path effect is a challenging problem. Empirical Green’s function (EGF) method uses nearly collocated small earthquakes to correct the path and station terms for larger events recorded at the same station. However, this method is subject to variability due to many factors. Here, we focus on three events that were well recorded by the seismic network and a rapid response distributed acoustic sensing (DAS) array. Using a suite of high-quality EGF events, we assess the influence of time window, spectral measurement options, and types of data on the spectral ratio and relative source time function (RSTF) results. Increased number of tapers (from 2 to 16) tends to increase the measured corner frequency and reduce the source complexity. Extended long time window (e.g., 30 s) tends to produce larger variability of corner frequency. The multitaper algorithm that simultaneously optimizes both target and EGF spectra produces the most stable corner-frequency measurements. The stacked spectral ratio and RSTF from the DAS array are more stable than two nearby seismic stations, and are comparable to stacked results from the seismic network, suggesting that DAS array has strong potential in source characterization.

58 GEOSCIENCES↗
DOE OSTI2022

Real-time equation-of-motion CC cumulant and CC Green’s function simulations of photoemission spectra of water and water dimer

Newly developed coupled-cluster (CC) methods enable simulations of ionization potentials and spectral functions of molecular systems in a wide range of energy scales ranging from core-binding to valence. This paper discusses the results obtained with the real-time equation-of-motion CC cumulant (RT-EOM-CC) approach and CC Green’s function (CCGF) approaches in applications to the water and water dimer molecules. Here, we compare the ionization potentials obtained with these methods for the valence region with the results obtained with the coupled-cluster with singles, doubles, and perturbative triples formulation as a difference of energies for N and N – 1 electron systems. All methods show good agreement with each other. They also agree well with the experiment with errors usually below 0.1 eV for the ionization potentials. We also analyze unique features of the spectral functions, associated with the position of satellite peaks, obtained with the RT-EOM-CC and CCGF methods employing single and double excitations, as a function of the monomer OH bond length and the proton transfer coordinate in the dimer. Finally, we analyze the impact of the basis set effects on the quality of calculated ionization potentials and find that the basis set effects are less pronounced for the augmented-type sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Relativistic effects in Green's function Monte Carlo calculations of neutrino-nucleus scattering

Here, microscopic calculations of neutrino-nucleus scattering cross sections are critical for the success of the neutrino-oscillation program. In addition to retaining nuclear correlations in the initial and final state of the reaction, they are based on consistent nuclear interactions and transition current operators, thereby enabling robust uncertainty quantification. In this work, we address a significant limitation of these microscopic methods, which arises from their nonrelativistic nature. By performing the calculations in a reference frame that minimizes nucleon momenta and utilizing the so-called two-fragment model, we extend the applicability of Green's function Monte Carlo calculations of neutrino-nucleus scattering to higher momenta than currently possible. To validate this approach, we compare our theoretical predictions against inclusive data measured by the MiniBooNE, T2K, and MINER ν A experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗