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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Rubinstein, Robert↗
DOE OSTI2025

Operator dynamics in Floquet many-body systems

We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behavior with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterize behavior we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behavior that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. In the simplest models this tail is separated from the initial decay by a minimum, so that the average autocorrelation function has an intermediate-time peak. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behavior at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behavior of OTOCs for Floquet models compared to random-in-time circuits. We show that this difference between averaged autocorrelation functions and OTOCs can be understood in terms of the paths in operator space that contribute to the two quantities: paths for the former retain a limited support at late times, while paths for the latter are dominated by operator spreading. Published by the American Physical Society 2025

Yoshimura, Takato (ORCID:0000000309159846)↗
DOE OSTI2021

Composite fermion nonlinear sigma models

We study particle-hole symmetry at the integer quantum Hall plateau transition using composite fermion mean-field theory. Because this theory implicitly includes some electron-electron interactions, it also has applications to certain fractional quantum Hall plateau transitions. Previous work [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] using this approach showed that the diffusive quantum criticality of this transition is described by a nonlinear sigma model with topological θ = π term. This result, which holds for both the Dirac and Halperin, Lee, and Read composite fermion theories, signifies an emergent particle-hole (reflection) symmetry of the integer (fractional) quantum Hall transition. Here we consider the stability of this result to various particle-hole symmetry-violating perturbations. In the presence of quenched disorder that preserves particle-hole symmetry, we find that finite longitudinal conductivity at this transition requires the vanishing of a symmetry-violating composite fermion effective mass, which if present would generally lead to θ ≠ π and a corresponding violation of particle-hole symmetric electrical transport σ xy ≠ $\frac1{2}$$\frac{e^2}{h}$ . When the disorder does not preserve particle-hole symmetry, we find that θ can vary continuously within the diffusive regime. Our results call for further study of the universality of the quantum Hall plateau transition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1984

Geometric interpretations of the Discrete Fourier Transform (DFT)

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Campbell, C. W.↗
NASA NTRS1993

Model-based automatic generation of grasping regions

The problem of automatically generating stable regions for a robotic end effector on a target object, given a model of the end effector and the object is discussed. In order to generate grasping regions, an initial valid grasp transformation from the end effector to the object is obtained based on form closure requirements, and appropriate rotational and translational symmetries are associated with that transformation in order to construct a valid, continuous grasping region. The main result of this algorithm is a list of specific, valid grasp transformations of the end effector to the target object, and the appropriate combinations of translational and rotational symmetries associated with each specific transformation in order to produce a continuous grasp region.

Bloss, David A.↗
DOE OSTI2022

Hidden Local Symmetry Breaking in Silver Diamondoid Compounds is Root Cause of Ultralow Thermal Conductivity

Typically, conventional structure transitions occur from a low symmetry state to a higher symmetry state upon warming. In this work, an unexpected local symmetry breaking in the tetragonal diamondoid compound AgGaTe 2 is reported, which, upon warming, evolves continuously from an undistorted ground state to a locally distorted state while retaining average crystallographic symmetry. This is a rare phenomenon previously referred to as emphanisis. This distorted state, caused by the weak sd 3 orbital hybridization of tetrahedral Ag atoms, causes their displacement off the tetrahedron center and promotes a global distortion of the crystal structure resulting in strong acoustic–optical phonon scattering and an ultralow lattice thermal conductivity of 0.26 W m –1 K –1 at 850 K in AgGaTe 2 . Here, the findings explain the underlying reason for the unexpectedly low thermal conductivities of silver-based compounds compared to copper-based analogs and provide a guideline to suppressing heat transport in diamondoid and other materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Group-Invariant Quantum Machine Learning

Quantum machine learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries. These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group $\mathfrak{G}$ associated with the dataset. We present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and exemplify their application through several paradigmatic QML classification tasks, including cases when $\mathfrak{G}$ is a continuous Lie group and also when it is a discrete symmetry group. Notably, our framework allows us to recover, in an elegant way, several well-known algorithms for the literature, as well as to discover new ones. Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Very accurate upward continuation to low heights in a test of non-Newtonian theory

Recently, gravity measurements were made on a tall, very stable television transmitting tower in order to detect a non-Newtonian gravitational force. This experiment required the upward continuation of gravity from the Earth's surface to points as high as only 600 m above ground. The upward continuation was based on a set of gravity anomalies in the vicinity of the tower whose data distribution exhibits essential circular symmetry and appropriate radial attenuation. Two methods were applied to perform the upward continuation - least-squares solution of a local harmonic expansion and least-squares collocation. Both methods yield comparable results, and have estimated accuracies on the order of 50 microGal or better (1 microGal = 10(exp -8) m/sq s). This order of accuracy is commensurate with the tower gravity measurments (which have an estimated accuracy of 20 microGal), and enabled a definitive detection of non-Newtonian gravity. As expected, such precise upward continuations require very dense data near the tower. Less expected was the requirement of data (though sparse) up to 220 km away from the tower (in the case that only an ellipsoidal reference gravity is applied).

Romaides, Anestis J.↗
DOE OSTI2020

One Structure, Two Elements—LuGe 2 Superconductor vs Ordinary Metallic Conductor LuSn 2 . A Case Study on How Site-Selective Germanium for Tin Atom Substitution Leads to Modulating of the Charge Distribution

The substitution of chemically similar elements in a given crystal structure is an effective way to enhance physical properties, but the understanding on such improvements is usually impeded because the substitutions are random, and the roles of the different atoms cannot be distinguished by crystallographic symmetry. Herein, we provide a detailed crystallographic analysis and property measurements for the continuous solid solutions LuGe x Sn 2–x (0 < x < 2). The results show that there is no apparent change of the global symmetry, with the end-members LuGe 2 and LuSn 2 , as well as the intermediate LuGe x Sn 2–x compositions adopting the ZrSi 2 type structure (space group Cmcm, Pearson index oC12). Yet, the refinements of the crystal structures from single-crystal X-ray diffraction data show that Ge–Sn atom substitutions are not random, but occur preferentially at the zig-zag chain. The patterned distribution of two group 14 elements leads to a significant variation in chemical bonding and charge ordering within the other structural fragment, the 2D square nets, thereby resulting in tuned electron transport. The enhancement is greater than the typical Bloch-Gruneisen model, and more akin to the parallel-resistor model. Magnetization measurements on single crystals show bulk superconductivity in all LuGe x Sn 2–x samples with shielding fractions as high as 90%. Specific heat data confirm the effect to originate from residual metallic tin in the material, indicating that Sn atom substitutions in the 2D square nets cause disruptions of the hypervalent bonding and local anisotropy, which ultimately leads to vanishing of the superconducting state in the end-member LuGe 2 . This work sheds light on how the complexity in chemical interactions by two different carbon congeners leads to changes in the physical properties and how they can be correlated with the induced charge distribution. Furthermore, these studies also provide a general approach to modulation of charge density, and thus, of emerging physical properties in other classes of intermetallic systems based on the main-group elements of groups 13 to 15.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Chemical Control of Symmetry and Bandgap in Tungsten Oxyhalide van der Waals Semiconductors

Tunability in solid-state materials is essential for testing theory, discovering quantum phases, and enabling functionality. Layered van der Waals (vdW) semiconductors offer a unique platform, providing new degrees of freedom at the two-dimensional (2D) limit through exfoliation and external controls. Here, in this study, we demonstrate tunability of symmetry and electronic structure via halogen substitution in a family of layered vdW tungsten oxyhalides. Substituting the halogens in WO 2 X 2 (X = I, Br, Cl) tunes the bandgap across a broad energy range and modifies the structural symmetry from centrosymmetric to noncentrosymmetric. By alloying WO 2 I 2– y Br y , we continuously tune the polar distortion and optical gap across the visible range. These insights into halogen substitution effects on symmetry and electronic structure lay the foundation for new tunable vdW semiconductors for optoelectronics and nonlinear optics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Winding θ and destructive interference of instantons

While the θ dependence of field theories is 2π periodic, the ground-state wavefunctions at θ and θ + 2π often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the θ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the 2d CP N-1 sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small S1 compactification with nonzero winding θ parameter and a suitable symmetry-twisted boundary condition. This system has N classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have N-fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, in sharp contrast to what happens when the θ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the N perturbative vacua acquire different charges under the global symmetry with the activation of the winding θ angle. We also demonstrate a similar destructive interference between instanton effects in the CP N-1 quantum mechanics with the Berry phase.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Rotational symmetry relation for efficient response function generation in the coarse mesh transport method COMET

The coarse mesh transport code COMET is a continuous energy hybrid stochastic-deterministic neutronics solver with high fidelity and formidable computation speed in solving reactor core problems. Its method is based on the incident flux expansion theory. In this work, we take advantage of the local geometric symmetry in many reactor cores lattices (e.g., fuel lattices and reflector blocks) to develop relations among the flux response expansion coefficients for symmetric surfaces to further improve the computational efficiency of the COMET response function generation tool (method). This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle. The relations for the response coefficients for the symmetric surfaces can be then written as the Kronecker product of those transformation matrices. The method is implemented into COMET and tested on two advanced high temperature reactor (AHTR) full-length single assembly benchmark problems. The COMET results using the response function library based on the symmetry relations were compared to those using the library directly generated by continuous energy Monte Carlo for all surfaces. It was found that the eigenvalues and stripe-wise fission densities using the two libraries are in statistical agreement as expected. This indicates that the new method maintains the high fidelity of the original COMET method while improving the computational efficiency in the response function generation by 270% to 400%, depending on the local geometric symmetry. This method also reduces the size of the response function library by the same magnitude (270% to 400%). (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Nematic antiferromagnetism and deconfined criticality from the interplay between electron-phonon and electron-electron interactions

Systems with strong electron-phonon couplings typically exhibit various forms of charge order, while strong electron-electron interactions lead to magnetism. In this work, we use determinant quantum Monte Carlo calculations to solve a model on a square lattice with a caricature of these interactions. In the limit where electron-electron interactions dominate it has antiferromagnetic order, while where electron-phonon coupling dominates there is columnar valence-bond-solid (VBS) order. We find an intervening phase that hosts coexisting nematic and antiferromagnetic orders. We have also found evidence of a Landau-forbidden continuous quantum phase transition with an emergent O(4) symmetry between the VBS and the nematic antiferromagnetic phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Mass loss

Observational evidence for mass loss from cool stars is reviewed. Spectra line profiles are used for the derivation of mass-loss rates with the aid of the equation of continuity. This equation implies steady mass loss with spherical symmetry. Data from binary stars, Mira variables, and red giants in globular clusters are examined. Silicate emission is discussed as a useful indicator of mass loss in the middle infrared spectra. The use of thermal millimeter-wave radiation, Very Large Array (VLA) measurement of radio emission, and OH/IR masers are discussed as a tool for mass loss measurement. Evidence for nonsteady mass loss is also reviewed.

Goldberg, Leo↗
DOE OSTI2023

Interactions of particles with “continuous spin” fields

Powerful general arguments allow only a few families of long-range interactions, exemplified by gauge field theories of electromagnetism and gravity. However, all of these arguments presuppose that massless fields have zero spin scale (Casimir invariant) and hence exactly boost invariant helicity. This misses the most general behavior compatible with Lorentz symmetry. We present a Lagrangian formalism describing interactions of matter particles with bosonic “continuous spin” fields with arbitrary spin scale ρ. Remarkably, physical observables are well approximated by familiar theories at frequencies larger than ρ, with calculable deviations at low frequencies and long distances. For example, we predict specific ρ-dependent modifications to the Lorentz force law and the Larmor formula, which lay the foundation for experimental tests of the photon’s spin scale. We also reproduce known soft radiation emission amplitudes for nonzero ρ. The particles’ effective matter currents are not fully localized to their worldlines when ρ ≠ 0, which motivates investigation of manifestly local completions of our theory. Our results also motivate the development of continuous spin analogues of gravity and non-Abelian gauge theories. Given the correspondence with familiar gauge theory in the small ρ limit, we conjecture that continuous spin particles may in fact mediate known long-range forces, with testable consequences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Higgs-confinement transitions in QCD from symmetry protected topological phases

In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity P and time reversal T. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial P- and T-invariant theta-angles θ f , θ g = π for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite U(1) B baryon-number chemical potential μ B , which preserves P and T. At very large μ B , three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks U(1) B . We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle θ g = π that safely co-exists with the U(1) B Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Krishnan, Hariharan↗
DOE OSTI2022

Entanglement between two gravitating universes

Abstract We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard ‘island formula’ for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2 n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Z n replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a ‘swap wormhole’, a geometry in which the boundaries of the two universes are glued together by a ‘swaperator’. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes—a realization of the ER = EPR idea. The new wormhole restores unitarity of quantum information.

79 ASTRONOMY AND ASTROPHYSICS↗