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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 NTRS1993

Quantum wormholes and harmonic oscillators

The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.

Garay, Luis J.↗
DOE OSTI2025

Control-Affine Schrödinger Bridge and Generalized Bohm Potential

From a stochastic control perspective, the Schrödinger bridge is a density-valued continuous curve parameterized by time that connects a given pair of initial and terminal probability densities via minimum effort controlled Brownian motion. The control-affine Schrödinger bridge extends this idea to a generic control-affine Itô diffusion, possibly with an additive state cost. Here, in this letter, we recast the necessary conditions of optimality for the control-affine Schrödinger bridge problem as a two point boundary value problem for a quantum mechanical Schrödinger PDE with complex potential. This complex-valued potential is a generalization of the real-valued Bohm potential in quantum mechanics. Our derived potential is akin to the optical potential in nuclear physics where the real part of the potential encodes elastic scattering (transmission of wave function), and the imaginary part encodes inelastic scattering (absorption of wave function). The key takeaway is that the process noise that drives the evolution of probability densities induces an absorbing medium in the evolution of wave function. These results make new connections between control theory and non-equilibrium statistical mechanics through the lens of quantum mechanics.

Markov processes↗
NASA NTRS1972

On optimizing the treatment of exchange perturbations.

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Hirschfelder, J. O.↗
DOE OSTI2020

Entanglement and the double copy

We construct entangled states of gluons that scatter exactly as if they were gravitons. Operationally, these objects implement the double copy at the level of the wave function. Our analysis begins with a general ansatz for a wave function characterizing gluons in two copies of SU(N ) gauge theory. Given relatively minimal assumptions following from permutation invariance and dimensional analysis, the three- and four-particle wave functions generate scattering amplitudes that automatically coincide exactly with gravity, modulo normalization. For five-particle scattering the match is not automatic but imposing certain known selection rules on the amplitude is sufficient to uniquely reproduce gravity. The resulting amplitudes exhibit a color-dressed and permutation-invariant form of the usual double copy relations. We compute the entanglement entropy between the two gauge theory copies and learn that these states are maximally-entangled at large N. Moreover, this approach extends immediately to effective field theories, where Born-Infeld photons and Galileons can be similarly recast as entangled gluons and pions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Effect of Linker Structure and Functionalization on Secondary Gas Formation in Metal–Organic Frameworks

Rare-earth terephthalic acid (BDC)-based metal–organic frameworks (MOFs) are promising candidate materials for acid gas separation and adsorption from flue gas streams. However, previous simulations have shown that acid gases (H 2 O, NO 2 , and SO 2 ) react with the hydroxyl on the BDC linkers to form protonated acid gases as a potential degradation mechanism. Herein, gas-phase computational approaches were used to identify the formation energies of these secondary protonated acid gases across multiple BDC linker molecules. Formation energies for secondary protonated acid gases were evaluated using both density functional theory (DFT) and correlated wave function methods for varying BDC–gas reaction mechanisms. Upon validation of DFT to reproduce wave function calculation results, rotated conformational linkers and chemically functionalized BDC linkers with -OH, -NH 2 , and -SH were investigated. Furthermore, the calculations show that the rotational conformation affects the molecule stability. Double-functionalized BDC linkers, where two functional groups are substituted onto BDC, showed varied reaction energies depending on whether the functional groups donate or withdraw electrons from the aromatic system. Based on these results, BDC linker design must balance adsorption performance with degradation via linker dehydrogenation for the design of stable MOFs for acid gas separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Scalar field in Reissner–Nordström spacetime: Bound state and scattering state (with appendix on eliminating oscillation in partial sum approximation of periodic function)

Highlights: • Bound-state and scattering-state solutions of massive scalar fields in R-N spacetime. • Bound-state wave functions and eigenvalues of massive scalar fields in R-N spacetime. • Solving explicit expressions of scattering phase shifts by integral equation methods. • Introducing tortoise coordinates for R-N spacetime. • Eliminating oscillations in the partial sum approximation of periodic functions. In this paper, we solve the massive scalar field in the Reissner–Nordström spacetime. The scalar field in the Reissner–Nordström spacetime has both bound states and scattering states. For bound states, we solve the bound-state wave function and the eigenvalue spectrum. For scattering states, we solve the scattering wave function and give an explicit expression for scattering phase shift by the integral equation method. Especially, we introduce the tortoise coordinate for the Reissner–Nordström spacetime. Moreover, in the calculation of scattering cross sections, we encounter a difficulty in partial sum approximation. If the sum of partial waves cannot be performed exactly, one has to turn to the partial sum approximation which approximates a function by the first several terms of the series. However, in the partial sum approximation there exists an incorrect oscillation which cannot be eliminated by keeping more terms. In the appendix we suggest an approach for eliminating such oscillations in the partial sum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Composite anyons on a torus

An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same “effective” integer filling factor. We consider such anyons on a torus, and construct representative wave functions for their ground as well as excited states. These wave functions involve higher Landau levels in general, but can be explicitly projected into the lowest Landau level for many parameters. We calculate the variational energy gap between the first excited state and ground state and find that it remains open as the statistical phase is varied. Lastly, we obtain from these wave functions, both analytically and numerically, various topological quantities, such as ground-state degeneracy, the Chern number, and the Hall viscosity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Quasimolecular 𝐽 tet = 3/2 Moments in the Cluster Mott Insulator GaTa 4 ⁢Se 8

Quasimolecular orbitals in cluster Mott insulators provide a route to tailor exchange interactions, which may yield novel quantum phases of matter. Here, we demonstrate the cluster Mott character of the lacunar spinel GaTa 4 Se 8 using resonant inelastic x-ray scattering (RIXS) at the Ta L 3 edge. Electrons are fully delocalized over Ta 4 tetrahedra, forming quasimolecular J tet = 3/2 moments. The modulation of the RIXS intensity as function of the transferred momentum q allows us to determine the cluster wave function, which depends on competing intracluster hopping terms that mix states with different character. This mixed wave function is decisive for the macroscopic properties since it affects intercluster hopping and exchange interactions and furthermore renormalizes the effective spin-orbit coupling constant. The versatile wave function, tunable via intracluster hopping, opens a new perspective on the large family of lacunar spinels and cluster Mott insulators in general.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Five-point functions and the permutation group 𝑆 5

Five-point functions and five-body wave functions play an important role in many areas of nuclear and particle physics, e.g., in 2 →3 scattering processes, in the five-gluon vertex, or in the study of pentaquarks. In this work we consider the permutation group 𝑆 5 to facilitate the description of such objects. We work out the multiplets transforming under irreducible representations of 𝑆 5 and provide compact formulas allowing one to cast the permutations of an object 𝑓 12345 into combinations with definite permutation symmetry. We also give the explicit expressions for the irreducible multiplet products. We consider several practical applications as examples: We arrange the four-momenta and Lorentz invariants of a five-point function into the multiplet structure, we work out the color tensors of the five-gluon vertex in the multiplet notation, and we discuss applications for five-body wave functions like those of pentaquarks.

Bethe-Salpeter equation↗
DOE OSTI2023

Feasibility of a Novel Density Functional Method Outside the Kohn-Sham Framework for Modeling Global Potential Energy Surfaces of Molecular Chemical Reactions (Final Technical Report)

The project aimed towards the construction of computational methods capable of modeling the global potential energy surface (PES) of small molecules, molecular ions, and radicals — including the parts of the PES which correspond to chemical reactions, and the reaction paths connecting reactants, intermediates, and reaction products. This goal may seem humble at first glance, but for chemical systems with more than about six atoms in total, at the time the project was proposed, there were no established theoretical methods capable of simulating such systems reliably, not even for small molecules in the gas phase which are electronically benign. This restriction severely hampers our ability to model and control chemical processes under harsh conditions. With the goal of constructing a method capable of modeling such chemical systems, we proposed to pursue a novel approach towards a Multi-Configuration (MC) DFT outside the traditional frameworks of Kohn-Sham theory and other methods of coupling wave function theory with DFT. Rather than being a complete active space (CAS) method, the proposed DOCI-DFT would employ a special restricted form of the active space wave function, called Doubly-Occupied CI (DOCI)—this wave function form is sufficient to describe not only heterolytic, but also homolytic bond dissociation processes at the zeroth order (i.e., as active space wave function). There are no other standard mean field methods which can do so. In the original proposal, we also outlined strong formal and practical arguments speaking for this method. The project proposal was accepted by the Department of Energy and provided two years of seed funding for one graduate student, as well as two years of two weeks PI summer-salary for the PI. However, ultimately the project could not be effectively pursued due to severe interferences outside the context scientific problems and was cancelled. Apart from two weeks of PI salary (and associated fringe & overhead costs issues by the performing institution), no costs were charged against the award, with the entire rest of funding returned to the Department of Energy. This report reiterates the primary background information regarding the project, its original goals, and outlines the preliminary work performed during the two weeks of DOE funding charged.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2009

Free-Free Transitions in the Presence of Laser Fields at Very Low Incident Electron Energy

We study the free-free transition in electron-hydrogenic systems in ground state in presence of an external laser field at very low incident energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The laser field is chosen to be monochromatic, linearly polarized and homogeneous. The incident electron is considered to be dressed by the laser in a nonperturbative manner by choosing a Volkov wave function for it The scattering wave function for the electron is solved numerically by taking into account the effect of the electron exchange, short-range as well as of the long-range interactions to get the S and P wave phase shifts while for the higher angular momentum phase shifts, the exchange approximation has only been considered. We calculate the laser-assisted differential cross sections (LADCS) for the aforesaid free-free transition process for single photon absorption/emission. The laser intensity is chosen to be much less than the atomic field intensity. A strong suppression is noted in the LADCS as compared to the field free (FF) cross sections. Unlike the FF ones, the LADCS exhibit some oscillations having a distinct maximum at a low value of the scattering angle depending on the laser parameters as well as on the incident energies.

Bhatia, Anand K.↗
DOE OSTI2021

Quantum information approach to high energy interactions

High energy hadron interactions are commonly described by using a probabilistic parton model that ignores quantum entanglement present in the light-cone wave functions. Here, we argue that since a high energy interaction samples an instant snapshot of the hadron wave function, the phases of different Fock state wave functions cannot be measured—therefore the light-cone density matrix has to be traced over these unobservable phases. Performing this trace with the corresponding U(1) Haar integration measure leads to ‘Haar scrambling’ of the density matrix, and to the emergence of entanglement entropy. This entanglement entropy is determined by the Fock state probability distribution, and is thus directly related to the parton structure functions. As proposed earlier, at large rapidity η the hadron state becomes maximally entangled, and the entanglement entropy is S E ~η according to QCD evolution equations. When the phases of Fock state components are controlled, for example in spin asymmetry measurements, the Haar average cannot be performed, and the probabilistic parton description breaks down.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1973

Degenerate R-S perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.

Hirschfelder, J. O.↗
NASA NTRS1974

Degenerate RS perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Hirschfelder, J. O.↗
DOE OSTI2020

A cautionary tale: Problems in the valence-CASSCF description of the ground state (X1Σ+) of BF

In the full optimized reaction space and valence-complete active space self-consistent field (vCAS) methods, a set of active orbitals is defined as the union of the valence orbitals on the atoms, all possible configurations involving the active orbitals are generated, and the orbitals and configuration coefficients are self-consistently optimized. Such wave functions have tremendous flexibility, which makes these methods incredibly powerful but can also lead to inconsistencies in the description of the electronic structure of molecules. In this paper, the problems that can arise in vCAS calculations are illustrated by calculations on the BH and BF molecules. BH is well described by the full vCAS wave function, which accounts for molecular dissociation and 2s–2p near-degeneracy in the boron atom. The same is not true for the full vCAS wave function for BF. There is mixing of core and active orbitals at short internuclear distances and swapping of core and active orbitals at large internuclear distances. In addition, the virtual 2π orbitals, which were included in the active space to account for the 2s–2p near degeneracy effect, are used instead to describe radial correlation of the electrons in the F2pπ-like pairs. Although the above changes lead to lower vCAS energies, they lead to higher vCAS+1+2 energies as well as irregularities and/or discontinuities in the potential energy curves. All of the above problems can be addressed by using the spin-coupled generalized valence bond-inspired vCAS wave function for BF, which includes only a subset of the atomic valence orbitals in the active space.

Xu, Lu T. (ORCID:0000000182064902)↗
NASA NTRS2012

Free-Free Transitions in the Presence of Laser Fields and Debye Potential at Very Low Incident Electron Energies

We study the free-free transition in electron-helium ion in the ground state and embedded in a Debye potential in the presence of an external laser field at very low incident electron energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The laser field is chosen as monochromatic, linearly polarized and homogeneous. The incident electron is considered to be dressed by the laser field in a nonperturbative manner by choosing Volkov wave function for it. The scattering wave function for the incident electron on the target embedded in a Debye potential is solved numerically by taking into account the effect of electron exchange. We calculate the laser-assisted differential and total cross sections for free-free transition for absorption/emission of a single photon or no photon exchange. The results will be presented at the conference.

Bhatia, Anand↗
NASA NTRS1993

Covariant harmonic oscillators: 1973 revisited

Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.

Noz, M. E.↗