Search NASA⌕ Search

SEARCH · Search NASA

Results for “Wave Functions”

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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Decomposition of the configuration-interaction coefficients in the multiconfiguration time-dependent Hartree-Fock method

An approximate implementation of the multiconfiguration time-dependent Hartree-Fock method is proposed, in which the matrix of configuration-interaction coefficients is decomposed into a product of matrices of smaller dimension. The applicability of this method in which all the configurations are kept in the expansion of the wave function, while the configuration-interaction coefficients are approximately calculated, is discussed by showing the results on three model systems: a one-dimensional model of a beryllium atom, a one-dimensional model of a carbon atom, and a one-dimensional model of a chain of four hydrogen atoms. The time-dependent electronic dynamics induced by a few-cycle, long-wavelength laser pulse is found to be well described at a lower computational cost compared to the standard multiconfiguration time-dependent Hartree-Fock treatment. Drawbacks of the method are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Schematic way to find solution of the outcoupled matter wave with a source term

We propose a schematic way to obtain solution of the outcoupled atom laser beam wave function in the presence of a source term where the beam is influenced by gravity. In this case, we only focus on the external potentials inside the region of Bose-Einstein condensate that are generated by electromagnetic source and gravity. Since the evolution of the atom laser beam can be portrayed through the ordinary Schrödinger equation with a source, we are allowed to express the general solution as the superposition of the homogeneous solution and particular solution. With the given external potentials and ansatz solutions, we attain that the obtained energy depends on the parameter constituting to the ratio between the longitudinal frequency and transverse frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen–Cooper–Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. Here, the method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree–Fock based electronic structure methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Sulfur vacancies in photorefractive Sn{sub 2}P{sub 2}S{sub 6} crystals

A photoinduced electron paramagnetic resonance (EPR) spectrum in single crystals of Sn{sub 2}P{sub 2}S{sub 6} (SPS) is assigned to an electron trapped at a sulfur vacancy. These vacancies are unintentionally present in undoped SPS crystals and are expected to play an important role in the photorefractive behavior of the material. Nonparamagnetic sulfur vacancies are formed during the initial growth of the crystal. Subsequent illumination below 100 K with 442 nm laser light easily converts these vacancies to EPR-active defects. The resulting S = 1/2 spectrum shows well-resolved and nearly isotropic hyperfine interactions with two P ions and two Sn ions. Partially resolved interactions with four additional neighboring Sn ions are also observed. Principal values of the g matrix are 1.9700, 1.8946, and 1.9006, with the corresponding principal axes along the a, b, and c directions in the crystal. The isotropic parts of the two primary {sup 31}P hyperfine interactions are 19.5 and 32.6 MHz and the isotropic parts of the two primary Sn hyperfine interactions are 860 and 1320 MHz (the latter values are each an average for {sup 117}Sn and {sup 119}Sn). These hyperfine results suggest that singly ionized sulfur vacancies have a diffuse wave function in SPS crystals, and thus are shallow donors. Before illumination, sulfur vacancies are in the doubly ionized charge state because of compensation by unidentified acceptors. They then trap an electron during illumination. The EPR spectrum from the sulfur vacancy is destroyed when a crystal is heated above 120 K in the dark and reappears when the crystal is illuminated again at low temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Microscopic study of {sup 6}He elastic scattering around the Coulomb barrier

We investigate {sup 6}He scattering on {sup 27}Al, {sup 58}Ni, {sup 120}Sn, and {sup 208}Pb in a microscopic version of the Continuum Discretized Coupled Channel (CDCC) method. We essentially focus on energies around the Coulomb barrier. The {sup 6}He nucleus is described by an antisymmetric 6-nucleon wave function, defined in the Resonating Group Method. The {sup 6}He continuum is simulated by square-integrable positive-energy states. The model does not depend on any adjustable parameter as it is based only on well known nucleon-target potentials. We show that experimental elastic cross sections are fairly well reproduced. The calculation suggests that breakup effects increase for high target masses. For a light system such as {sup 6}He+{sup 27}Al, breakup effects are small, and a single-channel approximation provides fair results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

On the motion of a quantum particle in the spinning cosmic string space–time

We analyze the energy spectrum and the wave function of a particle subjected to magnetic field in the spinning cosmic string space–time and investigate the influence of the spinning reference frame and topological defect on the system. To do this we solve Schrödinger equation in the spinning cosmic string background. In our work, instead of using an approximation in the calculations, we use the quasi-exact ansatz approach which gives the exact solutions for some primary levels. - Highlights: • Solving the Schrödinger equation in the spinning cosmic string space time. • Proposing a quasi-exact analytical solution to the general form of the corresponding equation. • Generalizing the previous works.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Coulomb Problem for Z > Z{sub cr} in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z{sub cr}(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z{sub cr} (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z{sub cr} (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε{sub 0} and widths γ of quasistationary states as a function of supercriticality. The values of ε{sub 0}* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z{sub cr}. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations

A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Derivation of the Time Dependent Two Dimensional Focusing NLS Equation

We present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schrödinger equation starting from an interacting N-particle system of Bosons. The interaction potential we consider is given by W{sub β}(x)=N{sup −1+2β}W(N{sup β}x) for some spherically symmetric and compactly supported potential W∈L{sup ∞}(ℝ{sup 2},ℝ). The class of initial wave functions is chosen such that the variance in energy is small. Furthermore, we assume that the Hamiltonian H{sub W{sub β,t}}=−∑{sub j=1}{sup N}Δ{sub j}+∑{sub 1≤j 2, or in trace norm, for more general external potentials. For trapping potentials of the form A(x)=C|x|{sup s} ,C>0, the condition H{sub W{sub β,t}}≥− CN can be fulfilled for a certain class of interactions W{sub β}, for all 0<β<((s+1)/(s+2)), see Lewin et al. (Proc Am Math Soc 145:2441–2454, 2017).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Crystallization and collapse in relativistically degenerate matter

In this paper, it is shown that a mass density limit exists beyond which the relativistically degenerate matter would crystallize. The mass density limit, found here, is quite analogous to the mass limit predicted by Chandrasekhar for a type of compact stars called white dwarfs (M{sub Ch} Asymptotically-Equal-To 1.43 Solar Mass). In this study, the old problem of white dwarf core collapse, which has been previously investigated by Chandrasekhar using hydrostatic stability criteria, is revisited in the framework of the quantum hydrodynamics model by inspection of the charge screening at atomic scales in the relativistic degeneracy plasma regime taking into account the relativistic Fermi-Dirac statistics and electron interaction features such as the quantum statistical pressure, Coulomb attraction, electron exchange-correlation, and quantum recoil effects. It is revealed that the existence of ion correlation and crystallization of matter in the relativistically degenerate plasma puts a critical mass density limit on white dwarf core region. It is shown that a white dwarf star with a core mass density beyond this critical limit can undergo the spontaneous core collapse (SCC). The SCC phenomenon, which is dominantly caused by the electron quantum recoil effect (interference and localization of the electron wave function), leads to a new exotic state of matter. In such exotic state, the relativistic electron degeneracy can lead the white dwarf crystallized core to undergo the nuclear fusion and an ultimate supernova by means of the volume reduction (due to the enhanced compressibility) and huge energy release (due to the increase in cohesive energy), under the stars huge inward gravitational pressure. Moreover, it is found that the SCC phenomenon is significantly affected by the core composition (it is more probable for heavier plasmas). The critical mass density found here is consistent with the values calculated for core density of typical white dwarf stars.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application

We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Conjugate Fermi holes and its manifestation in He-like systems

The structure of genuine and conjugate Fermi holes in two-electron atomic systems, namely He and He-like atomic ions, has been studied relying on accurate full configuration interaction wave functions. The standard Fermi hole exists in the vicinity of region in the two-electron coordinate space satisfying the well-known condition, r{sub 1} = r{sub 2}, while the conjugate Fermi hole exists in the vicinity of region close to this genuine Fermi hole but satisfying r{sub 1} ≠ r{sub 2} instead of r{sub 1} = r{sub 2}. Existence of these holes has shown to give an insightful interpretation of the origin of the first Hund rule and of the anomalously strong angular correlation manifested in the series of the singlet-triplet pair of singly-excited states of the aforementioned systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Tables Of Gaussian-Type Orbital Basis Functions

NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium through neon and potassium through krypton. Sets contain optimized Gaussian-type orbital exponents and coefficients, and near Hartree-Fock quality. Orbital exponents optimized by minimizing restricted Hartree-Fock energy via scaled Newton-Raphson scheme in which Hessian evaluated numerically by use of analytically determined gradients.

Partridge, Harry↗
DOE OSTI2016

Calculation of the static and dynamical correlation energy of pseudo-one-dimensional beryllium systems via a many-body expansion

Due to the importance of both static and dynamical correlation in the bond formation, low-dimensional beryllium systems constitute interesting case studies to test correlation methods. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. To gain insight into the main characteristics of the wave function, we started by focusing on the description of small Be chains using standard quantum chemical methods. In a next step we applied the MoI to larger beryllium systems, starting from the Be{sub 6} ring. The complete active space formalism was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Although this is a well-established approach for systems with limited multireference character, its application regarding the description of whole dissociation curves requires further testing. Subsequent to the discussion of the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Contribution of higher multiplicity collisions to elastic p{sup 6,8}He and p{sup 8,9}Li scattering within Glauber theory

Differential cross sections for elastic p{sup 6,8}He and p{sup 8,9}Li scattering at energies between 60 and 70 MeV per nucleon and at the energy of 700 MeV per nucleon were calculated. The calculations in question were performed with the wave functions found on the basis of the α–n–n (for {sup 6}He), α–t–n (for {sup 8}Li), and α–t–2n (for {sup 9}Li) three-body models and with the density from the large-scale shell model for the {sup 8}He nucleus. The respective matrix elements were derived either upon taking fully into account the multiple-scattering operator or in the optical-limit approximation. A comparison of the results of the precise and approximate calculations made it possible to estimate reliably the contribution of higher multiplicity collisions to the differential cross sections.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Hadronic form factor models and spectroscopy within the gauge/gravity correspondence

We show that the nonperturbative light-front dynamics of relativistic hadronic bound states has a dual semiclassical gravity description on a higher dimensional warped AdS space in the limit of zero quark masses. This mapping of AdS gravity theory to the boundary quantum field theory, quantized at fixed light-front time, allows one to establish a precise relation between holographic wave functions in AdS space and the light-front wavefunctions describing the internal structure of hadrons. The resulting AdS/QCD model gives a remarkably good accounting of the spectrum, elastic and transition form factors of the light-quark hadrons in terms of one parameter, the QCD gap scale. The light-front holographic approach described here thus provides a frame-independent first approximation to the light-front Hamiltonian problem for QCD. This article is based on lectures at the Niccolo Cabeo International School of Hadronic Physics, Ferrara, Italy, May 2011.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The total position-spread tensor: Spin partition

The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H{sub n} (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

General, Rigorous Approach for the Treatment of Interfragment Covalent Bonds

Here, a generalized, projection-based transformation of the method-agnostic Fock operator in various ab initio fragment-based quantum chemistry methods has been developed for the treatment of interfragment covalent bonds. This transformation freezes the relevant localized molecular orbital associated with each interfragment bond, thereby restricting the variational subspace of the fragment wave functions, in order to maintain the proper physical characteristics of the involved covalent bonds. In addition, sets of orbitals that would lead to multiple occupancy of certain orbitals are explicitly removed from the variational space. The transformation is developed for the specific case of mutually orthonormal frozen and unfrozen orbitals within each fragment. The newly developed approach is then used to study model systems with two popular ab initio fragment-based methods, and the results of these calculations are compared to those obtained by existing methodologies. Analysis is focused on both quantitative and qualitative accuracy as well as computational scalability and stability. Other methods for which the developed formalisms are appropriate are outlined, and future extensions of the methods are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗