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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Scattering state and bound state of scalar field in Schwarzschild spacetime: Exact solution

The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-states are presented. Besides the exact solution, we also provide explicit approximate expressions for bound-state eigenvalues and scattering phase shifts. (2) By virtue of the exact solutions, we give a direct calculation for the discontinuous jump on the horizon for massive scalar fields, while in literature such a jump is obtained from an asymptotic solution by an analytic extension treatment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The Connection between Resonances and Bound States in the Presence of a Coulomb Potential

The connection between resonant metastable states and bound states with changing potential strength in the presence of a Coulomb potential is fundamentally different from the case of short-range potentials. This phenomenon is central to the physics of dissociative recombination of electrons with molecular cations. In this paper, it is verified computationally that there is no direct connection between the resonance pole of the S-matrix and any pole in the bound state spectrum. A detailed analysis is presented of the analytic structure of the scattering matrix, in which the resonance pole remains distinct in the complex k-plane while a new state appears in the bound state spectrum. A formulation of quantum-defect theory is developed based on the scattering matrix, which nonetheless exposes a close analytic relation between the resonant and bound state poles and thereby reveals the connection between quantum-defect theory and analytic S-matrix theory in the complex energy and momentum planes. One-channel and multichannel versions of the expressions with numerical examples for simple models are given, and the formalism is applied to give a unified picture of ab initio electronic structure and scattering calculations for e-O 2 + and e-H 2 + scattering.

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

Creating large Fock states and massively squeezed states in optics using systems with nonlinear bound states in the continuum

The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n-photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). In conclusion, we suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n (n > 10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2026

Bound states of Ω baryons in light nuclei

Here, we investigate bound states of light Ω 3⁢𝑥 clusters (𝑥=𝑠,𝑐), motivated by the Ω 3⁢𝑠 ⁢𝑁 potential recently developed by the HAL QCD collaboration. To regularize this potential, we remove the deeply attractive core at 𝑟 < 0.4 fm and parametrize the long-range component (𝑟 > 0.4 fm) using a two-range Gaussian form. This procedure preserves the relevant two-body bound-state energy while having a negligible effect on the Ω 3⁢𝑠⁢ 𝑁⁢𝑁 and Ω 3⁢𝑠⁢ Ω 3⁢𝑠 ⁢𝑁 systems. An effective Ω 3⁢𝑠 ⁢𝛼 potential is then constructed by fitting a two-range Gaussian function to the long-range component of the folding potential, enabling calculations of the bound-state energies of the Ω 3⁢𝑠⁢ 𝛼, Ω 3⁢𝑠⁢ 𝛼⁢𝛼, and Ω 3⁢𝑠 ⁢Ω 3⁢𝑠 ⁢𝛼 systems. The regularization procedure leads to a substantial reduction in bound-state energies compared to those obtained with the original potential. We further extend the analysis to Ω 3⁢𝑐 -cluster systems by introducing an Ω 3⁢𝑐 ⁢𝑁 interaction, derived by comparing the existing Ω 3⁢𝑠⁢ Ω 3⁢𝑠 and Ω 3⁢𝑐 ⁢Ω 3⁢𝑐 potentials. Our results suggest that several parametrizations predict bound states in Ω 3⁢𝑐 -containing clusters. Finally, the Ω 3⁢𝑠 ⁢Ω 3⁢𝑠 interaction is described using a contactlike potential approach, motivated by the effective field theory.

binding energy & masses↗
DOE OSTI2020

Sign changing pairing in single layer FeSe/SrTiO3 revealed by nonmagnetic impurity bound states

Abstract The discovery of high-temperature superconductivity in single layer FeSe epitaxially grown on SrTiO 3 (001) substrates has instigated extensive debate over whether its pairing symmetry is conventional sign-preserving s -wave or unconventional sign-changing. Here, we probe the pairing state for single layer FeSe/SrTiO 3 grown by molecular beam epitaxy using scanning tunneling microscopy/spectroscopy. We observe robust in-gap bound states induced by non-magnetic Fe-vacancy defects within the Fe-plane, which exhibit strong spatial electron-hole asymmetry with two-fold symmetry in hole states and four-fold in electron states. The bound states exhibit no energy shift or splitting under an applied magnetic field, consistent with a sign-changing order parameter. This is further confirmed by defect bound state quasiparticle interference that shows a sign-changing behavior with a pair of corresponding peaks at the positive and negative energies near the impurity bound states. Our findings provide unambiguous evidence for a sign-changing pairing symmetry for single layer FeSe/SrTiO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Bound states of pseudo-Dirac dark matter

We study here the bound-state spectrum in a simple model of pseudo-Dirac dark matter, and examine how the rate of bound-state formation through radiative capture compares to Sommerfeld-enhanced annihilation. We use this model as an example to delineate the new features induced by the presence of a mass splitting between the dark matter and a nearly-degenerate partner, compared to the case where only a single dark-matter-like state is present. We provide a simple analytic prescription for estimating the spectrum of bound states in systems containing a mass splitting, which in turn allows characterization of the resonances due to near-zero-energy bound states, and validate this estimate both for pseudo-Dirac dark matter and for the more complex case of wino dark matter. Furthermore, we demonstrate that for pseudo-Dirac dark matter the capture rate into deeply bound states is, to a good approximation, simply related to the Sommerfeld enhancement factor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Metastable Bound States of the Two-Dimensional Bimagnetoexcitons in the Lowest Landau Levels Approximation

The possible existence of the bound states of the interacting two-dimensional (2D) magnetoexcitons in the lowest Landau levels (LLLs) approximation was investigated using the Landau gauge description. The magnetoexcitons taking part in the formation of the bound state with resultant wave vector k=0 have opposite in-plane wave vectors k and −k and look as two electric dipoles with the arms oriented in-plane perpendicularly to the corresponding wave vectors. The bound state of two antiparallel dipoles moving with equal probability in any direction of the plane with equal but antiparallel wave vectors is characterized by the variational wave function of the relative motion φ{sub n}(k) depending on the modulus |k|. The spins of two electrons and the effective spins of two holes forming the bound states were combined separately in the symmetric or in the antisymmetric forms (↑↓ +η ↓↑) with the same parameter η=±1 for electrons and holes. In the case of the variational wave function φ{sub 2}(k)=(8α{sup 3}){sup 1/2}k{sup 2}l{sub 0}{sup 2}exp [−αk{sup 2}l{sub 0}{sup 2}] the maximum density of the magnetoexcitons in the momentum space representation is concentrated on the in-plane ring with the radius k{sub r}=1/(√αl{sub 0}). The stable bound states of the bimagnetoexciton molecule do not exist for both spin orientations. Instead of them, a deep metastable bound state with the activation barrier comparable with the ionization potential I{sub l} of the magnetoexciton with k=0 was revealed in the case η=1 and α=0.5. In the case η=−1 and α=3.4 only a shallow metastable bound state can appear.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

White paper: from bound states to the continuum

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program 'From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory'. One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. Here, the many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Probing the Critical Dipole Moment To Support Excited Dipole-Bound States in Valence-Bound Anions

We report, in this paper, photodetachment spectroscopy and high-resolution photoelectron imaging of para -halogen substituted phenoxide anions, p -XC 6 H 4 O – (X = F, Cl, Br, I). The dipole moments of the p -XC 6 H 4 O neutral radicals increase from 2.56 to 3.19 D for X = F to I, providing a series of similar molecules to allow the examination of charge-dipole interactions by minimizing molecule-dependent effects. Excited DBSs ([XC 6 H 4 O]* – ) are observed for the four anions with binding energies of 8, 11, 24, and 53 cm –1 , respectively, for X = F to I, below their respective detachment thresholds. The binding energies exhibit a linear correlation with the dipole moments of the neutral radicals, extrapolating to a critical dipole moment of 2.5 D for zero binding energy. Because of the small binding energy of the excited DBS of [FC 6 H 4 O]* – , rotational autodetachment is observed to compete with vibrational autodetachment in the resonant photoelectron spectra, resulting in electrons with near zero kinetic energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Bound states and electromagnetic radiation of relativistically rotating cylindrical wells

Here, we compute the effect of rigid rotation on the non-relativistic bound states. The energy levels of the bound states increase with the angular velocity of rotation until at certain value of the angular velocity they are completely pushed out into the continuum which corresponds to dissociation of the bound states. When the angular velocity exceeds the critical value at which the ground state disappears into the continuum, no bound state is possible. This effect should have important consequences for the phenomenology of the quark-gluon plasma. One of the ways to study it experimentally is to observe the electromagnetic radiation emitted by a rotating bound state. We compute the corresponding intensity of electromagnetic radiation and show that it strongly depends on the angular velocity of rotation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material

Recently, log-periodic quantum oscillations have been detected in the topological materials zirconium pentatelluride (ZrTe 5 ) and hafnium pentatelluride (HfTe 5 ), displaying an intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe 5 can host the geometric quasi-bound states with a DSI feature, resembling an artificial supercritical atom collapse. The density of states of these quasi-bound states is enhanced, and the quasi-bound states are spatially distributed in the “orbitals” surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy. By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible; meanwhile, the energies of quasi-bound states move gradually toward the Fermi energy (E F ). These features are consistent with the theoretical prediction of a magnetic field–induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Magnetically brightened dark electron-phonon bound states in a van der Waals antiferromagnet

In van der Waals (vdW) materials, strong coupling between different degrees of freedom can hybridize elementary excitations into bound states with mixed character. Correctly identifying the nature and composition of these bound states is key to understanding their ground state properties and excitation spectra. Here, we use ultrafast spectroscopy to reveal bound states of d-orbitals and phonons in 2D vdW antiferromagnet NiPS 3 . These bound states manifest themselves through equally spaced phonon replicas in frequency domain. These states are optically dark above the Néel temperature and become accessible with magnetic order. By launching this phonon and spectrally tracking its amplitude, we establish the electronic origin of bound states as localized d–d excitations. Our data directly yield electron-phonon coupling strength which exceeds the highest known value in 2D systems. These results demonstrate NiPS 3 as a platform to study strong interactions between spins, orbitals and lattice, and open pathways to coherent control of 2D magnets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Realizing symmetry-guaranteed pairs of bound states in the continuum in metasurfaces

Abstract Bound states in the continuum (BICs) have received significant attention for their ability to enhance light-matter interactions across a wide range of systems, including lasers, sensors, and frequency mixers. However, many applications require degenerate or nearly degenerate high-quality factor ( Q ) modes, such as spontaneous parametric down conversion, non-linear four-wave mixing, and intra-cavity difference frequency mixing for terahertz generation. Previously, degenerate pairs of bound states in the continuum (BICs) have been created by fine-tuning the structure to engineer the degeneracy, yielding BICs that respond unpredictably to structure imperfections and material variations. Instead, using a group theoretic approach, we present a design paradigm based on six-fold rotational symmetry ( C 6 ) for creating degenerate pairs of symmetry-protected BICs, whose frequency splitting and Q -factors can be independently and predictably controlled, yielding a complete design phase space. Using a combination of resonator and lattice deformations in silicon metasurfaces, we experimentally demonstrate the ability to tune mode spacing from 2 nm to 110 nm while simultaneously controlling Q -factor.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
NASA NTRS1972

Bounded state variables and the calculus of variations

An optimal control problem with bounded state variables is transformed into a Lagrange problem by means of differentiable mappings which take some Euclidean space onto the control and state regions. Whereas all such mappings lead to a Lagrange problem, it is shown that only those which are defined as acceptable pairs of transformations are suitable in the sense that solutions to the transformed Lagrange problem will lead to solutions to the original bounded state problem and vice versa. In particular, an acceptable pair of transformations is exhibited for the case when the control and state regions are right parallelepipeds. Finally, a description of the necessary conditions for the bounded state problem which were obtained by this method is given.

Hanafy, L. M.↗
NASA NTRS1972

Bounded state space

This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented.

Eyman, E. D.↗
DOE OSTI2024

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗