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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

An Overview of the Null-Field Method. II: Convergence and Numerical Stability

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

Null-field method↗
DOE OSTI2023

Thermofield Theory for Finite-Temperature Electronic Structure

Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task. Besides, excited-state theories are generally not as well studied as ground-state ones. In this mini-review, we present an overview of a finite-temperature wave function formalism based on thermofield dynamics to overcome these difficulties. Thermofield dynamics allows us to map the equilibrium thermal density matrix to a pure state, i.e., a single wave function, albeit in an expanded Hilbert space. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we have developed a procedure to generalize ground-state wave function theories to finite temperatures. As explicit examples, we highlight formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of Fermions in the grand-canonical ensemble. To assess the quality of these approximations, we also show benchmark studies for the one-dimensional Hubbard model, while comparing against exact results. We will see that the thermal methods perform similarly to their ground-state counterparts, while merely adding a prefactor to the asymptotic computational cost. Furthermore, they also inherit all the properties, good or bad, from the ground-state methods, signifying the robustness of our formalism and the scope for future development.

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

Coherent γ *-nucleus scattering and coherent nuclear states

In the context of a McLerran-Venugopalan (MV) model for a large nucleus, coherent scattering of a virtual photon on that nucleus is evaluated in the A − = 0 gauge, the gauge appropriate for the target nucleus. The evaluation of the scattering in A − = 0 gauge is very intricate compared to the usual A + = 0 gauge evaluation natural for the scattering process, but has the advantage of directly giving the scattering in terms of a partonic description of the nucleus. In the limit where a tagged forward jet puts the dipole-nucleus scattering in the saturation regime the coherent reactions are equal to the inelastic reactions. In terms of the nuclear wave function the coherent reactions come from color singlet and zero total transverse momentum quark-antiquark pairs in the wave function and in the saturation regime the nuclear wave function is a coherent state for these pairs. In the saturation region half of all quarks (or antiquarks) come from zero momentum and color charge pairs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

Jensen, R. V.↗
NASA NTRS2003

Approximating the Helium Wavefunction in Positronium-Helium Scattering

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph↗
NASA NTRS2012

Theoretical Studies of N2-broadened Half-widths of H2O Lines Involving High j States

Based on the properties of the energy levels and wave functions of H2O states, one can categorize H2O lines into individually defined groups such that within the same group, the energy levels and the wave functions associated with two paired lines have an identity property while those associated with different pairs have a similarity property. Meanwhile, by thoroughly analyzing processes used to calculate N2-broadened half-widths, it was found that the 'Fourier series' of W(sup a)(sub L(sub 1))(sub K(sub 1))(sub K(sub 1)) (t; j(sub f) T(sub f) and W(sup a)(sub L(sub 1))(sub K(sub 1))(sub K(sub 1)) (t; j(sub i) T(sub i), and a factor P(sub 222) (j(sub f) T(sub f) j(sub i) T(sub i)) are the key items in the Robert-Bonamy formalism to distinguish contributions to ReS2(r(sub c)) among different transitions of j(sub f) T(sub f) - j(sub i). However, these items are completely determined by the energy levels and the wave functions associated with their initial and final states and they must bear the latter's features as well. Thus, it becomes obvious that for two paired lines in the same group, their calculated half-widths must be almost identical and the values associated with different pairs must vary smoothly as their ji values vary. Thus, the pair identity and the smooth variation rules are established within individual groups of lines. One can use these rules to screen half-width data listed in HITRAN and to improve the data accuracies.

water↗
DOE OSTI2021

Extremely Slow Trap-Mediated Hole Relaxation in Room-Temperature InP/ZnSe/ZnS Quantum Dots

Time-resolved photoluminescence (PL) and transient absorption (TA) spectroscopy have been used to elucidate the hole relaxation dynamics in high-quality InP/ZnSe/ZnS quantum dots (QDs) at room temperature. In QDs having an In/P ratio close to 1:1, hole cooling is fast compared to the ~40 ps time-correlated photon-counting instrument response. However, in QDs that luminesce at wavelengths greater than around 600 nm and have excess indium, a significant fraction of the PL exhibits a slower rise time. In this case, the PL rises over a range of timescales varying from close to the instrument response to approximately 300–400 ps. The time constant of the slowest component increases with increasing InP core size and the fraction of the PL that has the slow rise time increases with excess indium in the particle. In all cases, a slow rise time and any spectral evolution on that timescale are absent in the TA results, indicating that the slow dynamics may be assigned to relaxation in the valence band. QDs emitting at wavelengths below 560 nm show very different dynamics, exhibiting a barely detectable <50 ps rise time. Based on these results and measured elemental compositions, the slow hole relaxation is assigned to the transient population of indium-based traps in the ZnSe shell that are above the valence band edge only for the larger, red-emitting QDs. Here, the relative trap to band edge relaxation rates can be understood in terms of effective mass approximation hole wave function calculations, which show that the relaxation rate is largely determined by the extent to which the hole wave function in the lowest exciton penetrates into the ZnSe shell, overlapping the trapped-hole wave functions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Localized Active Space Pair-Density Functional Theory

Accurate quantum chemical methods for the prediction of spin-state energy gaps for strongly correlated systems are computationally expensive and scale poorly with the size of the system. This makes calculations for many experimentally interesting molecules impractical even with abundant computational resources. Previous work has shown that the localized active space (LAS) self-consistent field (SCF) method can be an efficient way to obtain multiconfiguration SCF wave functions of comparable quality to the corresponding complete active space (CAS) ones. To obtain quantitative results, a post-SCF method is needed to estimate the complete correlation energy. One such method is multiconfiguration pair-density functional theory (PDFT), which calculates the energy based on the density and on-top pair density obtained from a multiconfiguration wave function. In this work, we introduce localized-active-space PDFT, which uses a LAS wave function for subsequent PDFT calculations. The method is tested by computing spin-state energies and gaps in conjugated organic molecules and a bimetallic compound and comparing to the corresponding CAS-PDFT values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1980

Two-photon excitation cross-section in light and intermediate atoms

The method of explicit summation over the intermediate states is used along with LS coupling to derive an expression for two-photon absorption cross section in light and intermediate atoms in terms of integrals over radial wave functions. Two selection rules, one exact and one approximate, are also derived. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum defect method are used. A relationship between the cross section and the oscillator strengths is derived. Cross sections due to selected transitions in nitrogen, oxygen, and chlorine are given. The expression for the cross section is useful in calculating the two-photon absorption in light and intermediate atoms.

Omidvar, K.↗
DOE OSTI2026

Fokker-Planck Equation Governing the Distribution of Walkers in Auxiliary-Field Quantum Monte Carlo

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. Here, in this Letter, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wave function actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wave function in constrained path AFQMC, contrary to the common assumption, the wave function sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this Letter.

Monte Carlo methods↗
NASA NTRS1978

Electron impact excitation of highly charged sodium-like ions

Optical transition probabilities and electron collision strengths for Ca X, Fe XVI, Zn XX, Kr XXVI and Mo XXXII are calculated for transitions between n equal to 3 and n equal to 4 levels. The calculations neglect relativistic effects on the radial functions. A semi-empirical approach provides wave functions of the excited states; a distorted wave function without exchange is employed to obtain the excitation cross sections. The density dependence of the relative intensities of certain emission lines in the sodium isoelectronic sequence is also discussed.

Blaha, M.↗
DOE OSTI2025

Anti-symmetric barron functions and their approximation with sums of determinants

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants.

Abrahamsen, Nilin↗
DOE OSTI2021

Machine learning the dynamics of quantum kicked rotor

Highlights: • Quantum kicked rotor. • Quantum phase transition. • Machine learning. • LSTM network. • Convolutional neural network. Using the multilayer convolutional neural network (CNN), we can detect the quantum phases in random electron systems, and phase diagrams of two and higher dimensional Anderson transitions and quantum percolations as well as disordered topological systems have been obtained. Here, instead of using CNN to analyze the wave functions, we analyze the dynamics of wave packets via long short-term memory network (LSTM). We adopt the quasi-periodic quantum kicked rotors, which simulate the three and four dimensional Anderson transitions. By supervised training, we let LSTM extract the features of the time series of wave packet displacements in localized and delocalized phases. We then simulate the wave packets in unknown phases and let LSTM classify the time series to localized and delocalized phases. We compare the phase diagrams obtained by LSTM and those obtained by CNN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Interference in nonlinear Compton scattering using a Schrödinger-equation approach

The interference between Compton scattering and nonlinear Compton scattering from a two-color field in the X-ray regime is theoretically examined for bound electrons. Here, the underlying phase shifts are analyzed using a perturbative approach in the incoming classical field. The perturbative approach is bench marked with a non-perturbative approach in the classical field. The interference for different combinations of linear polarization of the two fields is examined when the Compton and the nonlinear Compton scattered waves have the same wave vector and polarization. Only two cases exhibit interference. When there is interference, the calculations reveal an intrinsic phase difference between the Compton scattered wave function and the nonlinear Compton scattered wave function of either 0 or pi depending on the scattering angle.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1974

Radiative transitions involving the (2p2)(3 Pe) metastable autodetaching of H(-)

The absorption coefficient for the free-bound transition H (ls) + e(-)+ h omega yields H(-)(2 sq p,(3)P(e)) is calculated (together with the differential emission rate for the inverse process) using ls - 2s - 2p close coupling continuum wave functions and a Hylleraas bound state wave function. A maximum in the absorption and emission spectra is found to occur at a photon wavelength of 1219.5 A, which is 2 A closer to the Lyman alpha line than predicted by the calculations of Drake, and is in closer agreement with the stellar absorption feature identified by Heap and Stecher. The free-bound absorption process appears to be a significant source of continuous ultraviolet opacity.

Jacobs, V. L.↗
NASA NTRS1994

Parabolized stability equations

The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.

Herbert, Thorwald↗
NASA NTRS1980

Two-photon excitation cross section in light and intermediate atoms in frozen-core LS-coupling approximation

Using the method of explicit summation over the intermediate states two-photon absorption cross sections in light and intermediate atoms based on the simplistic frozen-core approximation and LS coupling have been formulated. Formulas for the cross section in terms of integrals over radial wave functions are given. Two selection rules, one exact and one approximate, valid within the stated approximations are derived. The formulas are applied to two-photon absorptions in nitrogen, oxygen, and chlorine. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum-defect method have been used. A relationship between the cross section and the oscillator strengths is derived.

Omidvar, K.↗
DOE OSTI2022

Comparison of the canonical transformation and energy functional formalisms for ab initio calculations of self-localized polarons

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. We recently developed an ab initio approach based on canonical transformations to efficiently compute the formation and energetics of small polarons A different approach based on a Landau-Pekar energy functional has been proposed in the recent literature. Here in this work, we analyze and compare these two methods in detail. We show that the small polaron energy is identical in the two formalisms when using the same polaron wave function. We also show that our canonical transformation formalism can predict polaron band structures and can properly treat zero- and finite-temperature lattice vibration effects, although at present using a fixed polaron wave function. Conversely, the energy functional approach can compute the polaron wave function, but as we show here, it neglects lattice vibrations and cannot address polaron self-localization and thermal band narrowing. Taken together, this work relates two different methods developed recently to study polarons from first-principles, highlighting their merits and shortcomings and discussing them both in a unified formalism.

36 MATERIALS SCIENCE↗