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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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Green's function methods for multiphysics simulations (Final Report)

Green's functions are important tools for analyzing mathematical properties of partial differential equations (PDEs), and for numerically solving PDEs, especially when equations for the same operator but with multiple right hand sides need to be solved simultaneously. This proposal aims at developing efficient and accurate numerical methods for computing Green's functions, which can be used to tackle a challenging question in multiphysics simulation of DOE-mission science problems: how to couple quantum physics with classical physics. The key mathematical difficulty is properly formulate a "boundary condition" for the region described by quantum physics, and conventional approaches often model such boundary conditions in an empirical way. The proposed Green's function methods use the Dirichlet-to-Neumann map to formulate a boundary condition that is non-empirical and can couple the quantum and classical regions in an in principle exact way. The key ingredient of the new methods is to construct the Dirichlet-to-Neumann map in an efficient, accurate and versatile manner. The new methods have provably low complexity and are ideally suited for massively parallel and emerging many-core computational systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Theory of Green’s Functions of Nambu-Goldstone and Higgs Modes in Superconductors

We examine fundamental properties of Green’s functions of Nambu-Goldstone and Higgs modes in superconductors with multiple order parameters. Nambu-Goldstone and Higgs modes are determined once the symmetry of the system and that of the order parameters are specified. Multiple Nambu-Goldstone modes and Higgs modes exist when we have multiple order parameters. The Nambu-Goldstone Green function D(ω, q) has the form 1/(gN(0)){sup 2}⋅(2Δ){sup 2}/(ω{sup 2}−c{sub s}{sup 2}q{sup 2}) with the coupling constant g and c{sub s}=v{sub F}/√3 for small ω and q, with a pole at ω = 0 and q = 0 indicating the existence of a massless mode. It is shown, based on the Ward-Takahashi identity, that the massless mode remains massless in the presence of intraband scattering due to non-magnetic and magnetic impurities. The pole of D(ω, q), however, disappears as ω increases as large as 2Δ: ω∼2Δ. The Green function H(ω, q) of the Higgs mode is given by H(ω,q)∝(2Δ){sup 2}/((2Δ){sup 2}−(1/3)ω{sup 2}+(1/3)c{sub s}{sup 2}q{sup 2}) for small ω and q, and H(ω, q) is proportional to 1/(gN(0)){sup 2}⋅Δ/√((2Δ){sup 2}+c{sub s}{sup 2}q{sup 2}−ω{sup 2}) for ω∼2Δ with the cut in the interval − ω(q) ≤ z ≡ q{sub 0} ≤ ω(q) where ω(q)=√((2Δ){sup 2}+c{sub s}{sup 2}q{sup 2}). The constant part of the action for the Higgs modes is important since it determines the coherence length of a superconductor. There is the case that it has a large eigenvalue, indicating that the large upper critical field H{sub c2} may be realized in a superconductor with multiple order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as , where is the number of grid points. The cost of the 3D spectral solver scales as , where is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

Computer Science↗
DOE OSTI2024

The Green's Function Model Intercomparison Project (GFMIP) Protocol

The atmospheric Green's function method is a technique for modeling the response of the atmosphere to changes in the spatial field of surface temperature. While early studies applied this method to changes in atmospheric circulation, it has also become an important tool to understand changes in radiative feedbacks due to evolving patterns of warming, a phenomenon called the “pattern effect.” To better study this method, this paper presents a protocol for creating atmospheric Green's functions to serve as the basis for a model intercomparison project, GFMIP. The protocol has been developed using a series of sensitivity tests performed with the HadAM3 atmosphere-only general circulation model, along with existing and new simulations from other models. Our preliminary results have uncovered nonlinearities in the response of the atmosphere to surface temperature changes, including an asymmetrical response to warming versus cooling patch perturbations, and a change in the dependence of the response on the magnitude and size of the patches. These nonlinearities suggest that the pattern effect may depend on the heterogeneity of warming as well as its location. These experiments have also revealed tradeoffs in experimental design between patch size, perturbation strength, and the length of control and patch simulations. The protocol chosen on the basis of these experiments balances scientific utility with the simulation time and setup required by the Green's function approach. Running these simulations will further our understanding of many aspects of atmospheric response, from the pattern effect and radiative feedbacks to changes in circulation, cloudiness, and precipitation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Multiscale Neural Networks for Approximating Green’s Functions

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green’s functions. However, Green’s functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this work, we address these challenges by leveraging multiscale NNs to learn Green’s functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Coupled cluster Green's function: Past, Present, and Future

Coupled cluster Green's function (CCGF) approach has drawn much attention in recent years for targeting the molecular and material electronic structure problems from a many-body perspective in a systematically improvable way. Here, we will present a brief review of the history of how the Green's function method evolved with the wavefunction, early and recent development of CCGF theory, and more recently scalable CCGF software development. We will highlight some of the recent applications of CCGF approach and propose some potential applications that would emerge in the near future.

Peng, Bo↗
DOE OSTI2021

An efficient method to estimate the probability density of seismic Green's functions

We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.

58 GEOSCIENCES↗
DOE OSTI2016

Spectral properties of four-time fermionic Green's functions

The spectral relations for the four-time fermionic Green's functions are derived in the most general case. The terms which correspond to the zero-frequency anomalies, known before only for the bosonic Green's functions, are separated and their connection with the second cumulants of the Boltzmann distribution function is elucidated. Furthermore, the high-frequency expansions of the four-time fermionic Green's functions are provided for different directions in the frequency space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green’s function methods: Theory and application to GW and GF2

One-particle Green’s function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green’s functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as $\langle$S 2 $\rangle$ and $\langle$N 2 $\rangle$, can be challenging because they require a solution of the computationally expensive Bethe–Salpeter equation to find two-particle Green’s functions. We demonstrate that the solution of the Bethe–Salpeter equation can be completely avoided. Applying the thermodynamic Hellmann–Feynman theorem to self-consistent one-particle Green’s function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of $\langle$S 2 $\rangle$ and $\langle$N 2 $\rangle$ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Natively Periodic Fast Multipole Method: Approximating the Optimal Green’s Function

The fast multipole method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green's function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green's function for such a method that results in the numerical solution that converges to the equivalent particle-mesh (PM) solution in the limit of sufficiently high order of multipoles. A discrete functional equation for the optimal Green's function can be derived, but is not practically useful as methods for its solution are not known. Instead, this paper presents an approximation for the optimal Green's function that is accurate to better than 10 -3 in ${L}_{\mathrm{MAX}}$ norm and 10 -4 in L 2 norm for practically useful multipole counts. Such an approximately optimal Green's function offers a practical way for implementing the FMM with periodic boundary conditions natively, without the need to compute lattice sums or to rely on hybrid FMM-PM approaches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

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.

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

Horizon constraints on holographic Green’s functions

We explore a new class of general properties of thermal holographic Green’s functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green’s functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these ‘pole-skipping’ points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green’s function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales ω ~ T are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved U(1) current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of poleskipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Green’s function coupled cluster formulations utilizing extended inner excitations

Here, we analyze new approximations of the Green’s function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i( n, m ) method, where the excitation level of the inner auxiliary operators ( m ) used to describe the ionization potential and electron affinity effects in the N-1 and N+1 particle spaces is higher than the excitation level ( n ) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called “n + 1” rule in this category [or the GFCC-i( n, n + 1) method], which states that in order to maintain size-extensivity of the Green’s function matrix elements, the excitation level of inner auxiliary operators X p (ω) and Y q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N 2 and CO molecules in the inner and outer valence regimes. Lastly, in comparison with the Green’s function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin–Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

Density Functional Theory↗
DOE OSTI2022

Real-space Green’s function approach to photoelectron diffraction

We discuss the real-space Green’s function (RSGF) approach for core-level photoelectron diffraction (PD) and its comparison to x-ray absorption spectra (XAS). We focus especially on the separable Green’s function formalism for efficient calculations of high-order multiple scattering. Computational details such as scattering potentials, self-energy effects, Debye–Waller factors, and inelastic losses are discussed. Finally, we consider prospects for improving ab initio PD calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green’s function

Computing the numerical solution of the Kadanoff–Baym equations, a set of nonlinear integral differential equations satisfied by the two-time Green's functions derived from many-body perturbation theory for a quantum many-body system away from equilibrium, is a challenging task. Recently, we have successfully applied dynamic mode decomposition (DMD) to construct a data driven reduced order model that can be used to extrapolate the time-diagonal of a two-time Green's function from numerical solutions of the KBE within a small time window. In this paper, we extend the previous work and use DMD to predict off-diagonal elements of the two-time Green's function. We partition the two-time Green's function into a number of one-time functions along the diagonal and subdiagonals of the two-time window as well as in horizontal and vertical directions. We use DMD to construct separate reduced order models to predict the dynamics of these one-time functions in a two-step procedure. We extrapolate along diagonal and several subdiagonals within a subdiagonal band of a two-time window in the first step. In the second step, we use DMD to extrapolate the Green's function outside of the sub-diagonal band. In conclusion, we demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.

97 MATHEMATICS AND COMPUTING↗