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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

Yeon, Kyu Hwang↗
NASA NTRS1949

Lame's Wave Functions of the Ellipsoid of Revolution

It has recently Miss Gertrude Blanch that errors exist in been brought to the attention of the NACA by of the Bureau of Standards, Department of Commerce the tabulated values appearing in tables 11 to 17 of TM 1224. Miss Blanch notes that C. J. Bouwkamp~ from whom Meixner obtained the values presented, subsequently corrected them in tables. appearing in the Journal of Mathematics and Physics, vol. XXVI, no. 2, JULY 1947, pp. 88-91. In spite of the difference in symbols and notation in the two papers, reprints of tables I to IX included in the July 1947 issue of the Journal of Mathematics and Physics are attached for the use of those interested in receiving them. The NACA wishes to express its appreciation to the Journal of Mathematics and Physics for permitting these tables to be reproduced for this purpose.

Meixner, J.↗
NASA NTRS1981

Theoretical studies of solar-pumped lasers

Estimates of the absorption and emission characteristics of molecules required to develop materials for solar-pumped lasers are addressed. These characteristics are described in terms of the Franck Condon factors, which are calculated from the molecular wave functions. Wave functions for vibrational levels in the lower and upper electronic states of I2 and NSe are calculated numerically and methods of checking errors discussed. Errors arise when the vibrational quantum numbers are high; but, using a calculated rather than measured value of the dissociation energy, wave functions up to the fiftieth vibrational level are obtained. A numerical method of evaluating the wave functions is given, which should be more accurate in the region of electronic transitions during absorption. Franck Condon factors, plotted versus the wavelength of the absorbed photons, are shown, and a check on the Franck Condon factors is made using the vibrational sum rule.

Harries, W. L.↗
NASA NTRS1984

A variational method for the calculation of dynamic polarizabilities and two-photon transition moments - The dressed molecule approach

The solution of the time-dependent Schroedinger equation of the molecule + radiation field system is analyzed. A quantized radiation field is used. The relationship between the oscillatory wave function and the dressed state wave function is established, the oscillatory wave function being the solution if the radiation field is turned on at t = 0 and the dressed state being the stationary solution satisfying the boundary condition only if the field is present at t = negative infinity. In general, the oscillatory wave function can be expressed using a complete set of dressed states. However, in the presence of a nonresonant radiation field, the system is well represented by a single dressed state. Molecular properties such as dynamic polarizabilities and two-photon transition moments can be deduced from the dressed state wave function instead of the oscillatory wave function as in previous methods. Because of its stationary character, the dressed state is more amenable to approximate calculations. A CI method is developed for this purpose. The CI matrix is simple in form and can be readily constructed using existing computer codes. The present method can also be adapted to calculate other optical properties.

Huo, W. M.↗
NASA NTRS1987

Ab initio studies of low-lying 3Sigma(-), 3Pi, and 5Sigma(-) states of NH. I - Potential curves and dipole moment functions

Configuration interaction wave functions, potential energy curves, and dipole moment functions have been calculated for the four lowest 3Sigma(-) and the three lowest 3Pi states and 5Sigma(-) states of NH. The electronic wave functions were constructed to give a balanced description of valence-Rydberg interactions. Two repulsive states have been identified as important photodissociation pathways. Spectroscopic constants are presented for the bound states, and results are compared to other theoretical and experimental work. The possible predissociation of the A 3Pi state by the 1 5Sigma(-) state is discussed.

Goldfield, Evelyn M.↗
NASA NTRS1980

Parity-violating electric-dipole transitions in helium

The paper examines parity-violating electric-dipole transitions in He in order to gain insight into the reliability of approximate calculations which are carried out for transitions in many-electron atoms. The contributions of the nearest-lying states are computed with a variety of wave functions, including very simple product wave functions, Hartree-Fock functions and Hylleraas-type wave functions with up to 84 parameters. It is found that values of the matrix elements of the parity-violating interaction can differ considerably from the values obtained from the good wave functions, even when these simple wave functions give accurate values for the matrix elements in question

Hiller, J.↗
DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Quantum Nature of Dielectric Laser Accelerators

Dielectric laser accelerators (DLAs) hold great promise for producing economic and compact on-chip radiation sources. On-chip DLAs benefit from fabrication capabilities of the silicon industry and from breakthroughs in silicon-photonic nanostructures to enhance the interaction between particles and laser fields. Seemingly unrelated recent advances in the quantum interactions of electrons and light have raised interest in the underlying classical-quantum correspondence principle at the foundations of electron acceleration. Here, we present the observation of the underlying quantum nature of DLAs: observing quantized peaks in the electron-energy spectra. Our findings demonstrate quasi-phase-matching between an electron wave function and a light wave, which also demonstrates the role of the quantum wave function in the inverse Smith-Purcell effect. We harness the capabilities of an ultrafast transmission electron microscope (UTEM) to maintain a long electron-light interaction length extending over hundreds of periods of the laser pulse, mediated by a silicon-photonic nanograting DLA. The UTEM is shown as a new platform for characterization of future DLA concepts. The results raise fundamental questions regarding the role of quantum mechanics in DLA design, and more generally about the prospects of manipulating particles’ quantum wave functions in accelerator physics.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Improved energies and local energies with weighted variational Monte Carlo

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of 10 2 –10 4 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Reinforcement Learning Configuration Interaction

Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. Furthermore, we explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Optimization Stability in Excited-State-Specific Variational Monte Carlo

Here, we investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1985

Molecular processes in a high temperature shock layer

The development of techniques for the calculation of electron capture widths, electronic wave functions, cross sections and rates needed for the description of the dissociative recombination (DR) of molecular ions with electrons were described. The cross sections and rates were calculated by using harmonic oscillator wave functions for the ion and a delta function approximation for the continuum vibrational wave function in the repulsive dissociative channel. In order to obtain DR cross sections of quantitative accuracy, a computer program which solves the one dimensional nuclear motion wave equation was revised to calculate the cross sections and rates. The program and the new results are described. Included is a discussion of large windows found in the dissociative recombination cross sections from excited ion vibrational levels. These windows have not been previously reported in the literature. The magnitude of the DR cross sections for several dissociative routes are sensitive to the location of the crossing of the neutral and ion potential curves. Studies of the effects of basis set and CI wave function size on vertical excitation energies are described. Preliminary studies on N2 and O2 using large scale wave functions are also reported.

Guberman, S. L.↗
DOE OSTI2021

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1999

A Critical Examination of Wind-Wave Spectral Functional Form

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous energy and frequency as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Among the main conceptual innovations is the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need of spurious harmonics to represent nonlinear and nonstationary signals. The spectral forms of the ocean waves are very different. This new method offers the first physical meaningful view of the wave spectrum. Data from laboratory and field will be presented to illustrate the differences.

Huang, Norden E.↗