Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Dyson equation”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Analytical continuation of matrix-valued functions: Carathéodory formalism

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multiorbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation, and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. Here we derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the truncation of the off-diagonal self-energy elements leads to considerable approximation artifacts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Ab initio self-consistent many-body theory of polarons at all couplings

We present a theoretical framework to describe polarons from first principles within a many-body Green’s function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the phonon-mediated self-energy is composed by two distinct terms. One term is the Fan-Migdal self-energy and describes dynamic electron-phonon processes, the other term is a contribution to the self-energy originating from the static displacements of the atomic nuclei in the polaronic ground state. The lowest-order approximation to the present theory yields the standard many-body perturbation theory approach to electron-phonon interactions in the limit of large polarons, and the ab initio polaron equations introduced in the limit of small polarons. Here, a practical recipe to implement the present unifying formalism in first-principles calculations is outlined. We apply our method to the Fröhlich model, and obtain remarkably accurate polaron energies at all couplings, in line with Feynman’s polaron theory and diagrammatic Monte Carlo calculations. We also recover the well-known results of Fröhlich and Pekar at weak and strong coupling, respectively. The present approach enables predictive many-body calculations of polarons in real materials at all couplings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Green's functions applied to the theory of spectroscopy

Green’s functions are a powerful analytical and computational tool for ab initio calculations of X-ray spectra. For example, Green’s functions provide an efficient means for calculations over broad energy ranges since many-body effects can be incorporated naturally in terms of the electron self-energy. Here, their role in the theory of X-ray absorption and related spectroscopies is discussed, with particular focus on many-body effects such as quasi-particle energy shifts and lifetimes, core-hole interactions and electron–phonon interactions. Additionally, the cumulant expansion for the Green’s function is reviewed and compared with the usual GW Dyson equation approach for including multielectron excitations that produce satellite features in X-ray spectra.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Light neutrino masses from gravitational condensation: the Schwinger–Dyson approach

In this work we demonstrate that non-zero neutrino masses can be generated from gravitational interactions. We solve the Schwinger–Dyson equations to find a non-trivial vacuum thereby determining the neutrino condensate scale and the number of new particle degrees of freedom required for gravitationally induced dynamical chiral symmetry breaking. We show for minimal beyond the Standard Model particle content, the scale of the condensation occurs close to the Planck scale.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

SDE_quark

This program provides a fixed-grid quadrature algorithm to compute integrals in the self-energy of the quark propagator within the Maris-Tandy model. The quark propagator both on t he spacelike real axis and at complex-valued momenta is determined from its Schwinger-Dyson equation (SDE). We first apply an iterative solver to find the quark propagator on the spacelike real axis. The propagator at complex-valued momenta is then computed from its self-energy based on this solution, where demanding integrals are encountered. In order to compute of these integrals, we apply customized variable transformations for the radial integral after subtracting the asymptotics. We subsequently apply an optional compound of quadrature rules for the angular integral.

Jia, Shaoyang↗
NASA NTRS1976

Microwave remote sensing of a two-layer random medium

A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.

Tsang, L.↗
NASA NTRS1979

Wave theory for microwave remote sensing of a half-space random medium with three-dimensional variations

The two-variable expansion technique is used to solve for the mean Green's functions from the Dyson equation under the nonlinear approximation for a half-space random medium with three-dimensional correlation functions. The Bethe-Salpeter equations are then solved under the ladder approximation. The radiative transfer equations, which have been applied extensively in the study of microwave remote sensing problems, are derived under these approximations. The limiting cases of large and small horizontal correlation lengths are discussed. It is found that there is only one propagation constant except for the case of large horizontal correlation lengths, in which there are two propagation constants. It is shown that boundary layer appears in first-order solutions and does not appear in zeroth-order solutions.

Tsang, L.↗
NASA NTRS1981

Mean dyadic Green's function for a two layer random medium

The mean dyadic Green's function for a two-layer random medium with arbitrary three-dimensional correlation functions has been obtained with the zeroth-order solution to the Dyson equation by applying the nonlinear approximation. The propagation of the coherent wave in the random medium is similar to that in an anisotropic medium with different propagation constants for the characteristic transverse electric and transverse magnetic polarizations. In the limit of a laminar structure, two propagation constants for each polarization are found to exist.

Zuniga, M. A.↗
DOE OSTI2021

Nucleon off-shell structure and the free neutron valence structure from A=3 inclusive electron scattering measurements

Understanding the differences between the distribution of quarks bound in protons and neutrons is key for constraining the mechanisms of SU(6) spin-flavor symmetry breaking in Quantum Chromodynamics (QCD). While vast amounts of proton structure measurements were done, data on the structure of the neutron is much more spars as experiments typically extract the structure of neutrons from measurements of light atomic nuclei using model-dependent corrections for nuclear effects. Recently the MARATHON collaboration performed such an extraction by measuring inclusive deep-inelastic electron-scattering on helium-3 and tritium mirror nuclei where nuclear effects are expected to be similar and thus be suppressed in the helium-3 to tritium ratio. Here we evaluate the model dependence of this extraction by examining a wide range of models including the effect of using instant-form and light-cone nuclear wave functions and several different parameterizations of nucleon modification effects, including those with and without isospin dependence. We find that, while the data cannot differentiate among the different models of nuclear structure and nucleon modification, they consistently prefer a neutron-to-proton structure function ratio of at $x_B \rightarrow 1$ of $\sim 0.4$ with a typical uncertainty ($1\sigma$) of $\sim0.05$ and $\sim0.10$ for isospin-independent and isospin-dependent modification models, respectively. While strongly favoring SU(6) symmetry breaking models based on perturbative QCD and the Schwinger-Dyson equation calculation, the MARATHON data do not completely rule out the scalar di-quark models if an isospin-dependent modification exist.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model

Here in order to solve the Bethe-Salpeter equation (BSE) in the Minkowski space, we first introduce the Nakanishi integral representations of the Bethe-Salpeter amplitude and the Bethe-Salpeter wave function. We then derive the explicit integral equations for the corresponding spectral functions from the BSE for states of two scalar particles bound by a scalar-particle exchange interaction, where the propagators of constituents are allowed to be fully dressed. These integral equations are subsequently solved numerically in the variation of the Wick-Cutkosky model with massive exchange particles, where an algorithm of adaptive mash grid is proposed. The equations and algorithm we develop here serve as the foundation of Minkowski-space formulation of BSE for bound states of fermions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

In polar semiconductors and insulators, the Fröhlich interaction between electrons and long-wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearance of characteristic phonon sidebands in the spectral function, commonly dubbed “polaron satellites.” The simplest model that captures these effects is the Fröhlich model, whereby electrons in a parabolic band interact with a dispersionless longitudinal optical phonon. The Fröhlich model has been employed in a number of seminal papers, from early perturbation-theory approaches to modern diagrammatic Monte Carlo calculations. One limitation of this model is that it focuses on undoped systems, thus ignoring carrier screening and Pauli blocking effects that are present in real experiments on doped samples. Here, to overcome this limitation, we extend the Fröhlich model to the case of doped systems, and we provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. We perform the analysis using two approaches, namely, Dyson’s equation with the Fan-Migdal self-energy, and the second-order cumulant expansion. We find that these two approaches provide qualitatively different results. In particular, Dyson’s approach yields better quasiparticle masses and worse satellites, while the cumulant approach provides better satellite structures, at the price of worse quasiparticle masses. Both approaches yield an anomalous enhancement of the electron effective mass at finite doping levels, which in turn leads to a breakdown of the quasiparticle picture in a significant portion of the phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

A note on chiral trace relations from qq-characters

We study chiral operators in four-dimensional N = 2 supersymmetric gauge theories. We provide a general procedure to derive the exact relations among the vacuum expectation values of chiral operators in the Ω-background using the non-perturbative Dyson-Schwinger equations of qq-characters. We demonstrate our procedure using several examples. For pure SU(N) gauge theory and SU(N) gauge theory with 2N fundamental hypermultiplets, we verify the relations conjectured previously in the literature. We also briefly discuss the relations in SU(N) linear superconformal quiver gauge theories.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Spontaneous breaking of U(1) symmetry in coupled complex SYK models

As shown in [1], two copies of the large N Majorana SYK model can produce spontaneous breaking of a Z 2 symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the U(1) x U(1) symmetry. We also present a tensor counterpart of this coupled model. When the coefficient α of the quartic term lies in a certain range, the coupled large N theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of α. We show that the operator c$^†_{1i}$c 2i , which is charged under the axial U(1) symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large N Dyson-Schwinger equations and show that, outside the fixed line, this U(1) symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large N.

1/N expansion↗
DOE OSTI2023

QCD running couplings and effective charges

Here we discuss our present knowledge of $\alpha_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $\alpha_s(Q^2) $ at high momentum transfer, $Q$, is necessary for any perturbative QCD calculation. Equally important, the behavior of $\alpha_s$} at low $Q^2$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of $\alpha_s(Q^2)$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of $\alpha_s(Q^2)$ from both the Dyson-Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to $\alpha_s$. We conclude by highlighting how the nonperturbative knowledge of $\alpha_s$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Kaon gluon parton distribution and momentum fraction from 2+1+1 lattice QCD with high statistics

We present a high-statistics lattice-QCD determination of the kaon gluon parton distribution function and gluon momentum fraction. We use clover valence fermion action to take 1,296,640 kaon-correlator measurements on a highly improved staggered quark ensemble with 𝑎 ≈ 0.12 fm and 310-MeV pion mass generated by the MILC Collaboration. A detailed investigation into the impact of gauge-link smearing on the gluonic matrix elements indicates that five steps of hypercubic smearing offer an effective balance between signal quality and preservation of long-distance physics. We report a nonperturbatively renormalized kaon gluon momentum fraction of Math output error at 𝜇 = 2 GeV in the Math output error scheme. Using reduced pseudo-Ioffe-time-distribution matrix elements and pseudo-parton-distribution-function (PDF) matching, we extract the kaon gluon PDF and compare with the prediction from the Dyson-Schwinger equation and with the pion PDF obtained from the same ensemble.

First-principles calculations↗
DOE OSTI2023

Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F 2 n F 2 p for mirror nuclei He 3 and H 3

A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions x B → 0 and x B → 1. The extrapolated F 2 ratio as quark momentum fraction x B → 1 is $\frac{F^n_2}{F^p_2}$ → 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio when x B → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high- x B , the proton quark distribution function ratio d/u is derived from the F 2 ratio and found to be d/u → 1/6. Our extrapolated values for both the $\frac{F^n_2}{F^p_2}$ ratio and the d/u parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. Finally, one such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated F 2 ratio at x B = 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Spatial and momentum imaging of the pion and kaon

We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multidimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: ( b T 2 ) u π = 0.11 fm 2 , ( b T 2 ) s K = 0.08 fm 2 , and ( b T 2 ) u K = 0.13 fm 2 , and therefore the s quark in the kaon is much closer to the center of transverse momentum than the u quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full Dyson-Schwinger equations calculation (containing an infinite tower of Fock states) for the pion form factor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗