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Green function approach to R-matrix theory and applications to light nuclear reactions [Slides]
Abstract not provided.
Numerical algorithms developed for carrier transport in nanoelectronic devices: recursive green functions, NEGF, and multiple sequential scattering
Quantitative simulations of carrier transport in physical systems that are of the size of a few nanometers require the use of quantum mechanical models at a very fundamental level.
Greens Functions for Prediction of Noise From Non-Axisymmetric Jets
No abstract available
On the Landau Background Gauge Fixing and the IR Properties of YM Green Functions
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Green Functions for the Radial Electric Component of the Monopole Wake Field in a Round Resistive Chamber
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Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function
In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CC self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.
Electromagnetic scaling functions within the Green's function Monte Carlo approach
We have studied the scaling properties of the electromagnetic response functions of 4 He and 12 C nuclei computed by the Green's function Monte Carlo approach, retaining only the one-body current contribution. Longitudinal and transverse scaling functions have been obtained in the relativistic and nonrelativistic cases and compared to experiment for various kinematics. The characteristic asymmetric shape of the scaling function exhibited by data emerges in the calculations in spite of the nonrelativistic nature of the model. The results are mostly consistent with scaling of zeroth, first, and second kinds. Our analysis reveals a direct correspondence between the scaling and the nucleon-density response functions. In conclusion, the scaling function obtained from the proton-density response displays scaling of the first kind, even more evidently than the longitudinal and transverse scaling functions
The Determination of the Large-Scale Circulation of the Pacific Ocean from Satellite Altimetry using Model Green's Functions
A Green's function method for obtaining an estimate of the ocean circulation using both a general circulation model and altimetric data is demonstrated. The fundamental assumption is that the model is so accurate that the differences between the observations and the model-estimated fields obey a linear dynamics. In the present case, the calculations are demonstrated for model/data differences occurring on very a large scale, where the linearization hypothesis appears to be a good one. A semi-automatic linearization of the Bryan/Cox general circulation model is effected by calculating the model response to a series of isolated (in both space and time) geostrophically balanced vortices. These resulting impulse responses or 'Green's functions' then provide the kernels for a linear inverse problem. The method is first demonstrated with a set of 'twin experiments' and then with real data spanning the entire model domain and a year of TOPEX/POSEIDON observations. Our present focus is on the estimate of the time-mean and annual cycle of the model. Residuals of the inversion/assimilation are largest in the western tropical Pacific, and are believed to reflect primarily geoid error. Vertical resolution diminishes with depth with 1 year of data. The model mean is modified such that the subtropical gyre is weakened by about 1 cm/s and the center of the gyre shifted southward by about 10 deg. Corrections to the flow field at the annual cycle suggest that the dynamical response is weak except in the tropics, where the estimated seasonal cycle of the low-latitude current system is of the order of 2 cm/s. The underestimation of observed fluctuations can be related to the inversion on the coarse spatial grid, which does not permit full resolution of the tropical physics. The methodology is easily extended to higher resolution, to use of spatially correlated errors, and to other data types.
Optical spectroscopy of molecular junctions: Nonequilibrium Green’s functions perspective
We consider optical spectroscopy of molecular junctions from the quantum transport perspective when radiation field is quantized and optical response of the system is simulated as photon flux. Using exact expressions for photon and electronic fluxes derived within the nonequilibrium Green function (NEGF) methodology and utilizing fourth order diagrammatic perturbation theory (PT) in molecular coupling to radiation field, we perform simulations employing realistic parameters. Results of the simulations are compared to the bare PT which is usually employed in studies on nonlinear optical spectroscopy to classify optical processes. We show that the bare PT violates conservation laws, while flux conserving NEGF formulation mixes optical processes.
Response Functions of Correlated Systems within Green's Function Theory
Why use Green's functions as the fundamental variable? Wave-function (Psi) methods are king for high-fidelity and Density-functional (Rho) methods are very efficient (Kohn-Sham). Goldilocks principle: Green's function (G) methods straddle the Rho and Psi methods, intermediate in both accuracy and efficiency. Also, when interest lies in excitations & 2-particle properties: G-methods are natural - intrinsic to the theory.
Approximate Green’s Function Coupled Cluster A Method Employing Effective Dimension Reduction
The Green’s function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structures of molecular structures and periodic systems, especially when electrons are strongly correlated. However, in order for the GFCC method to become an approach that can be routinely used in the electronic structure calculations, more robust linear algebraic techniques and approximations need to be employed to reduce its extremely high computational overhead. In our recent studies, we showed that the GFCC equation can be numerically solved by seeking solutions of multiple linear systems in the frequency regime of interest, which can be easily distributed in a massively parallel environment, and broaden the avenue for more state-of-the-art numerical linear algebraic tools associated with multiple linear systems to be kicked in to this field. In the present pursuit of this practice, we show a successful application of model order reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires a high resolution of spectral function, instead of solving GFCC linear equation in the original dimension for every single frequency point, an easily-solvable linear system model with reduced dimension can be built upon projecting the original GFCC linear system into a subspace, from which the interpolation and extrapolation can give a reasonable approximation to the results of the original GFCC linear equations. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some select frequencies inside the frequency regime. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The approach is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems including carbon monoxide, 1,3-butadiene, benzene, and adenine molecules. As a byproduct, the high quality linear system model is also found to be able to provide high quality initial guess for the existing linear solver to improve the convergence performance.
Self-consistent second-order Green’s function perturbation theory for periodic systems
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green’s function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear as promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green’s function (GF2) method, where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in k-space are the key components of a computationally feasible algorithm. We apply this technique to the one-dimensional hydrogen lattice — a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.
Generalized quadrature for finite temperature Green’s function methods
Not provided.
Direct Reconstruction of Ablative Thermal Protection System Aeroheating Using A Green's Function Approach
A Green’s function inverse heat transfer (IHT) approach is used to reconstruct the surface heating conditions on ablative thermal protection system (TPS) materials from embedded heat flux sensor and temperature probe measurements. The approach models the temperature time-history at the measurement location as a discrete linear system, allowing for the heat flux boundary condition to be recovered directly without the need for time-marching schemes. The effects of material decomposition and pyrolysis gas transport are modeled using an energy source/sink analogue. The performance of the reconstruction approach is analyzed on a 1D test case representative of an atmospheric entry heating scenario. The approach can recover the TPS surface heat flux to within 4% of the input heating condition with a computation time of 2-3 seconds (>3 orders of magnitude faster than current time-marching IHT methods). As a byproduct of the surface heating reconstruction, the algorithm also captures the surface pyrolysis gas mass flux and solid decomposition at multiple through-thickness locations within the TPS.