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DOE OSTI2024

New procedure for evaluation of U(3) coupling and recoupling coefficients

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group–subgroup chains is presented. While the canonical U(3) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and in so doing provides a faster and more accurate determination of any and all required results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(3).

Cross-Coupling Reaction↗

DOE OSTI2020

Gluon field digitization via group space decimation for quantum computers

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of SU(3) up to the third order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Exploring Anomalous Photoelectron Angular Distributions in the Photoelectron Spectra of Gd 3 O 3 – : Study of Gd 3 O 2 – and Gd 3 O 3 – Using Photoelectron Spectroscopy and Density Functional Theory Calculations

Anion photoelectron (PE) spectra of lanthanide oxide clusters obtained previously have exhibited anomalous photoelectron angular distributions which were attributed to strong PE–valence electron (PEVE) interactions. Here, to further explore this effect, we have obtained the PE spectra of Gd 3 O 2 – and Gd 3 O 3 – , two clusters that have similarly complex electronic structures but contrasting symmetries. The spectra exhibit manifolds of detachment transitions at similar binding energies in a 0.5 eV window of energy. The electron affinity of Gd 3 O 2 is measured to be 1.29 ± 0.05 eV, and that of Gd 3 O 3 is 1.31 ± 0.05 eV. As seen in previous studies on lanthanide oxide cluster anions in lower than conventional oxidation states, transitions in spectra obtained lower photon energies are more congested than those obtained with higher photon energy, a signature of strong PEVE interactions. While the detachment transitions have predominantly parallel photoelectron angular distributions (PAD), the PAD varies across the manifold of transitions in the PE spectrum of Gd 3 O 3 – in a way that suggests four different subgroups of transitions. Results of calculations on Gd 3 O 2 – suggest kite or V-shape structures with antiferromagnetic coupling between one of the 4f 7 subshells with the two others. Calculations on Gd 3 O 3 – more definitively point to ring structures with a nearly isoenergetic ferromagnetically coupled high spin (24-tet) state and a dectet state in which one of the 4f 7 subshells is antiferromagnetically coupled with the other two. Taking these results as qualitative, we propose that strong mixing between the unperturbed states predicted computationally leads to overlapping transitions with different PADs.

anions↗

NASA NTRS1998

Squeezed states as representations of symplectic groups

It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon state. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now two-phonon coherent states which may exhibit symmetries not yet observed for photons, including sheared states. Let us note that both SU(1,1) and S(3,2) are isomorphic to the symplectic groups Sp(2) and Sp(4) respectively, and that symplectic transformations consist of rotations and squeeze transformations.

Han, D.↗

DOE OSTI2024

Digitization and subduction of S U ( N ) gauge theories

The simulation of lattice gauge theories on quantum computers necessitates digitizing gauge fields. One approach involves substituting the continuous gauge group with a discrete subgroup, but the implications of this approximation still need to be clarified. To gain insights, we investigate the subduction of S U ( 2 ) and S U ( 3 ) to discrete crystal-like subgroups. Using classical lattice calculations, we show that subduction offers valuable information based on subduced direct sums, helping us identify additional terms to incorporate into the lattice action that can mitigate the effects of digitization. Furthermore, we compute the static potentials of all irreducible representations of Σ ( 360 × 3 ) at a fixed lattice spacing. Our results reveal a percent-level agreement with the Casimir scaling of S U ( 3 ) for irreducible representations that subduce to a single Σ ( 360 × 3 ) irreducible representation. This provides a diagnostic measure of approximation quality, as some irreducible representations closely match the expected results while others exhibit significant deviations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2003

Hindlimb unloading alters ligament healing

We investigated the hypothesis that hindlimb unloading inhibits healing in fibrous connective tissue such as ligament. Male rats were assigned to 3- and 7-wk treatment groups with three subgroups each: sham control, ambulatory healing, and hindlimb-suspended healing. Ambulatory and suspended animals underwent surgical rupture of their medial collateral ligaments, whereas sham surgeries were performed on control animals. After 3 or 7 wk, mechanical and/or morphological properties were measured in ligament, muscle, and bone. During mechanical testing, most suspended ligaments failed in the scar region, indicating the greatest impairment was to ligament and not to bone-ligament insertion. Ligament testing revealed significant reductions in maximum force, ultimate stress, elastic modulus, and low-load properties in suspended animals. In addition, femoral mineral density, femoral strength, gastrocnemius mass, and tibialis anterior mass were significantly reduced. Microscopy revealed abnormal scar formation and cell distribution in suspended ligaments with extracellular matrix discontinuities and voids between misaligned, but well-formed, collagen fiber bundles. Hence, stress levels from ambulation appear unnecessary for formation of fiber bundles yet required for collagen to form structurally competent continuous fibers. Results support our hypothesis that hindlimb unloading impairs healing of fibrous connective tissue. In addition, this study provides compelling morphological evidence explaining the altered structure-function relationship in load-deprived healing connective tissue.

NASA Discipline Musculoskeletal↗

NASA NTRS1990

Compositions of large metal nodules in mesosiderites - Links to iron meteorite group IIIAB and the origin of mesosiderite subgroups

The compositions of large metal nodules in 12 mesosiderites, ranging from 3 mm to 4 cm in minimum dimensions and from 10 to 200 mg/g in silicate content, were analyzed by neutron activation; also analyzed were two additional samples (Pennyweight Point and Murchison Downs) which were originally designated iron meteorites but were later classified as Mes nodules. It was found that mesosiderites subgroups classified on the basis of metal composition are virtually the same as those based on silicate composition. The general covariation of the silicate and the metal compositional characteristics suggests that these features were established in the same process or in linked processes. A mesosiderite formation model is proposed.

Hassanzadeh, Jamshid↗

DOE OSTI2021

Dimensionality-Induced Change in Topological Order in Multiferroic Oxide Superlattices

We construct ferroelectric (LuFeO 3 ) m /(LuFe 2 O 4 ) superlattices with varying index m to study the effect of confinement on topological defects. We observe a thickness-dependent transition from neutral to charged domain walls and the emergence of fractional vortices. In thin LuFeO 3 layers, the volume fraction of domain walls grows, lowering the symmetry from P6 3 cm to P3c1 before reaching the nonpolar P6 3 /mmc state, analogous to the group-subgroup sequence observed at the high-temperature ferroelectric to paraelectric transition. Our study shows how dimensional confinement stabilizes textures beyond those in bulk ferroelectric systems.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Classification of mafic clasts from mesosiderites - Implications for endogenous igneous processes

Results are presented from an analysis of 13 igneous pebbles from the Vaca Muerta, EET87500, and Bondoc mesosiderites, using electron microprobe and instrumental neutron activation techniques. These data, combined with literature data on compositions of 43 mesosiderite clasts were used to compile a classification scheme for the various types of mafic silicate clasts that occur in mesosiderites. These clasts were classified into five principal groups: (1) polygenic and monogenic cumulates (30 percent); (2) polygenic basalts (30 percent); (3) quench-textured rocks, comprising two compositional subgroups (those which resemble basaltic eucrites (5 percent), and those which resemble cumulate eucrites (2 percent)); (4) monogenic basalts (11 percent); and (5) ultramafic rocks, consisting mainly of large crystals of orthopyroxene (9 percent) or olivine (4 percent). The conditions under which these clasts were formed are discussed.

Rubin, Alan E.↗

DOE OSTI2024

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical U(4) > U(3) > U(2) > U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) > SU S (2) Ⓧ SU T (2) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N) . It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Cross-Coupling Reaction↗

DOE OSTI2023

Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles

Abstract We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO (2), SO (3), and SO (4), and of the Lorentz group S O ( 1 , 3 ) . Other examples include squeeze mapping, piecewise discontinuous labels, and SO (10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Conformal wave expansions for flat space amplitudes

The extended BMS algebra contains a conformal subgroup that acts on the celestial sphere as SO(1, 3). It is of interest to perform mode expansions of free fields in Minkowski spacetime that realize this symmetry in a simple way. In the present work we perform such a mode expansion for massive scalar fields using the unitary principal series representations of SO(1, 3) with a view to developing a holographic approach to gravity in asymptotically flat spacetime. These mode expansions are also of use in studying holography in three-dimensional de Sitter spacetime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2002

Range Information Systems Management (RISM) Phase 1 Report

RISM investigated alternative approaches, technologies, and communication network architectures to facilitate building the Spaceports and Ranges of the future. RISM started by document most existing US ranges and their capabilities. In parallel, RISM obtained inputs from the following: 1) NASA and NASA-contractor engineers and managers, and; 2) Aerospace leaders from Government, Academia, and Industry, participating through the Space Based Range Distributed System Working Group (SBRDSWG), many of whom are also; 3) Members of the Advanced Range Technology Working Group (ARTWG) subgroups, and; 4) Members of the Advanced Spaceport Technology Working Group (ASTWG). These diverse inputs helped to envision advanced technologies for implementing future Ranges and Range systems that builds on today s cabled and wireless legacy infrastructures while seamlessly integrating both today s emerging and tomorrow s building-block communication techniques. The fundamental key is to envision a transition to a Space Based Range Distributed Subsystem. The enabling concept is to identify the specific needs of Range users that can be solved through applying emerging communication tech

Bastin, Gary L.↗

NASA NTRS1982

Low energy, left-right symmetry restoration in SO(N) GUTS

A general n step symmetry breaking pattern of SO(4K+2) down to SU sub C (3)xSU sub L (2)xU sub Y (1), which uses regular subgroups only, does not allow low energy left right symmetry restoration. In these theories, the smallest mass scale at which such restoration is possible is approximately one billion GeV as in the SO(10) case. The unification mass in SO(4K+2) GUTS must be at least as large as that in SU(5). These results assumed standard values of the Weinberg angle and strong coupling constant.

Holman, R.↗

DOE OSTI2024

Block encodings of discrete subgroups on a quantum computer

We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. This method is applicable to general discrete groups, including crystal-like subgroups such as BI of S U ( 2 ) and V of S U ( 3 ) . We detail the construction of primitive gates—the inversion gate, the group multiplication gate, the trace gate, and the group Fourier gate—utilizing this encoding method for BT and for the first time BI group. We also provide resource estimations to extract the gluon viscosity. The inversion gates for BT and BI are benchmarked on the quantum computer with estimated fidelities of 40 − 4 + 5 % and 4 − 3 + 5 % , respectively. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Symmetry progression and band vs Mott character of CdPS 3 under pressure

Complex chalcogenides are renowned for their tunable electronic, magnetic, and optical properties under external stimuli. The MPX 3 family (M = Mn, Ni, Co, V; X = S, Se) is a platform for many exciting discoveries—especially under compression—although CdPS3 is thought to be different because the Cd center possesses a filled 4d shell, which precludes Mottness. Here, we combine synchrotron-based infrared absorbance and Raman scattering spectroscopies with diamond anvil cell techniques, complementary lattice dynamics calculations, and an analysis of the energy landscape to reveal a series of structural phase transitions in CdPS 3 . We find four distinct pressure-driven transitions, with low frequency modes detectable over the full 35 GPa range of our investigation. A group–subgroup analysis along with our first-principles calculations allows us to partially unravel the space group sequence. For instance, the first critical pressure is a monoclinic C2/m to trigonal $\overline{R}$3 transition at 10 GPa. Despite the softness and overall sensitivity to pressure, we do not locate an insulator-to-metal transition in this pressure range, indicating that the energy scale for gap closure is significantly higher than expected. We discuss these findings in terms of force-induced color change and Mott vs band character in this system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1980

On the chemical composition of L-chondrites

Radiochemical neutron activation analysis of Ag, As, Au, Bi, Co, Cs, Ga, In, Rb, Sb, Te, Tl, and Zn and major element data in 14 L4-6 and 3 LL5 chondrites indicates that the L group is unusually variable and may represent at least 2 subgroups differing in formation history. Chemical trends in the S/Fe rich subgroup support textural evidence indicating late loss of a shock formed Fe-Ni-S melt; the S/Fe poor subgroup seemingly reflects nebular fractionation only. Highly mobile In and Zn apparently reflect shock induced loss from L chondrites. However, contrasting chemical trends in several L chondrite sample sets indicate that these meteorites constitute a more irregular sampling of, or more heterogeneous parent material than do carbonaceous or enstatite chondrites. Data for 15 chondrites suggest higher formation temperatures and/or degrees of shock than for LL5 chondrites.

Neal, C. W.↗

NASA NTRS1976

The use of LANDSAT-1 imagery in mapping and managing soil and range resources in the Sand Hills region of Nebraska

The author has identified the following significant results. Evaluation of ERTS-1 imagery for the Sand Hills region of Nebraska has shown that the data can be used to effectively measure several parameters of inventory needs. (1) Vegetative biomass can be estimated with a high degree of confidence using computer compatable tape data. (2) Soils can be mapped to the subgroup level with high altitude aircraft color infrared photography and to the association level with multitemporal ERTS-1 imagery. (3) Water quality in Sand Hills lakes can be estimated utilizing computer compatable tape data. (4) Center pivot irrigation can be inventoried from satellite data and can be monitored regarding site selection and relative success of establishment from high altitude aircraft color infrared photography. (5) ERTS-1 data is of exceptional value in wide-area inventory of natural resource data in the Sand Hills region of Nebraska.

Seevers, P. M.↗