Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix Theory”

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 307 records · Page 17

Proton spin structure and generalized polarizabilities in the strong quantum chromodynamics regime

The strong interaction is not well understood at low energies or for interactions with low momentum transfer. Chiral perturbation theory gives testable predictions for the nucleonic generalized polarizabilities, which are fundamental quantities describing the nucleon’s response to an external field. We report a measurement of the proton’s generalized spin polarizabilities extracted with a polarized electron beam and a polarized solid ammonia target in the region where chiral perturbation theory is expected to be valid. The investigated structure function g2 characterizes the internal spin structure of the proton. From its moments, we extract the longitudinal–transverse spin polarizability δLT and twist-3 matrix element and polarizability d2¯. Our results provide discriminating power between existing chiral perturbation theory calculations and will help provide a better understanding of this strong quantum chromodynamics regime.

Ruth, D↗

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improving inference with matrix elements and machine learning

Particle physics processes bring together a high-energy amplitude described by quantum field theory and nonperturbative effects and detector interactions described by complex computer simulations. We review some recently developed multivariate inference techniques that leverage this structure and combine matrix-element information with machine learning. Automated by the MadMiner package, the new techniques have been applied to multiple problems in particle physics, allowing for stronger limits than traditional analysis methods and showing their potential to improve the sensitivity of the LHC legacy measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Effective field theories for collective excitations of atomic nuclei

Collective modes emerge as the relevant degrees of freedom that govern low-energy excitations of atomic nuclei. These modes—rotations, pairing rotations, and vibrations—are separated in energy from non-collective excitations, making it possible to describe them in the framework of effective field theory. Rotations and pairing rotations are the remnants of Nambu–Goldstone modes from the emergent breaking of rotational symmetry and phase symmetries in finite deformed and finite superfluid nuclei, respectively. The symmetry breaking severely constrains the structure of low-energy Lagrangians and thereby clarifies what is essential and simplifies the description. The approach via effective field theories exposes the essence of nuclear collective excitations and is defined with a breakdown scale in mind. This permits one to make systematic improvements and to estimate and quantify uncertainties. Effective field theories of collective excitations have been used to compute spectra, transition rates, and other matrix elements of interest. In particular, predictions of the nuclear matrix element for neutrinoless double beta decay then come with quantified uncertainties. This review summarizes these results and also compares the approach via effective field theories to well-known models and ab initio computations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Field Theories for type-II fractons

We derive an effective field theory for a type-II fracton starting from the Haah code on the lattice. The effective topological theory is not given exclusively in terms of an action; it must be supplemented with a condition that selects physical states. Without the constraint, the action only describes a type-I fracton. The constraint emerges from a condition that cube operators multiply to the identity, and it cannot be consistently implemented in the continuum theory at the operator level, but only in a weaker form, in terms of matrix elements of physical states. Informed by these studies and starting from the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory that does not need a constraint or projector, and yet has no mobile excitations. Whether this continuum theory admits a lattice counterpart remains unanswered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Measurements and interpretations of W ± Z production cross-sections in pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Measurements of integrated and differential cross-sections for W ± Z production in proton-proton collisions are presented. The data collected by the ATLAS detector at the Large Hadron Collider from 2015 to 2018 at a centre-of-mass energy of $\sqrt{s}=13$ TeV are used, corresponding to an integrated luminosity of 140 fb −1 . The W ± Z candidate events are reconstructed using leptonic decay modes of the gauge bosons into electrons or muons. The integrated cross-section per lepton flavour for the production of W ± Z is measured in the detector fiducial region with a relative precision of 4%. The measured value is compared with the Standard Model prediction at a precision of up to next-to-next-to-leading-order in QCD and next-to-leading-order in electroweak. Cross-sections for W + Z and W − Z production and their ratio are presented. The W ± Z production is also measured differentially as functions of various kinematic variables, including new observables sensitive to CP-violation effects. All measurements are compared with state-of-the-art Standard Model predictions from fixed-order calculations or Monte Carlo generators based on next-to-leading-order matrix elements interfaced with parton showers. An effective field theory interpretation of the measurements is performed, considering both CP-conserving and CP-violating dimension-6 operators modifying the W ± Z production. In the absence of observed deviations from the Standard Model, limits on CP-conserving Wilson coefficients are extracted using the transverse mass of the W ± Z system. For CP-violating coefficients a machine learning approach is used to construct an observable with enhanced sensitivity to CP-violation effects.

hadron-hadron scattering↗

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental identification of the T = 1 , J π = 6 + state of Co 54 and isospin symmetry in A = 54 studied via one-nucleon knockout reactions

In this paper, new experimental data obtained from γ-ray tagged one-neutron and one-proton knockout from 55 Co are presented. A candidate for the sought-after T = 1, T z = 0, J π = 6 + state in 54 Co is proposed based on a comparison to the new data on 54 Fe, the corresponding observables predicted by large-scale-shell-model (LSSM) calculations in the full fp-model space employing charge-dependent contributions, and isospin-symmetry arguments. Furthermore, possible isospin-symmetry breaking in the A = 54, T = 1 triplet is studied by calculating the experimental c coefficients of the isobaric mass multiplet equation (IMME) up to the maximum possible spin J = 6 expected for the (1f 7/2 ) -2 two-hole configuration relative to the doubly magic nucleus 56 Ni. Lastly, the experimental quantities are compared to the theoretically predicted c coefficients from LSSM calculations using two-body matrix elements obtained from a realistic chiral effective field theory potential at next-to-next-to-next-to-leading order (N 3 LO).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Applications of flow models to the generation of correlated lattice QCD ensembles

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman–Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Probabilistic Error Bounds for Low-Rank Tensor Decompositions Used in Large-Scale Data Analysis Applications (LDRD Final Report)

This report documents a research project on analyzing low-rank tensor models for data analysis that took place at Sandia National Laboratories from October 2023–September 2025. The focus of this work was to extend theoretical frameworks from statistics and probability theory for use with models for scalar, vector, and matrix data to models with tensor, or general multi-dimensional array, data. Through this work, we have provided a new set of tools for bounding errors on low-rank tensor models of both complete and sampled data. The remainder of this report is organized as follows. In Section 1, we describe the proposed work at the start of the project. Section 2 describes the research advances made as part of the project. Other research contributions in the form of conference presentations and software development is provided in Section 3. Workforce development at Sandia and Florida Atlantic University (via a subcontract on this project) is provided in Section 4.

97 MATHEMATICS AND COMPUTING↗

Understanding surfaces and interfaces in nanocomposites of silicone and barium titanate through experiments and modeling

Barium titanate (BTO) is a ferroelectric perovskite used in electronics and energy storage systems because of its high dielectric constant. Decreasing the BTO particle size was shown to increase the dielectric constant of the perovskite, which is an intriguing but contested result. We investigated this result by fabricating silicone-matrix nanocomposite specimens containing BTO particles of decreasing diameter. Furthermore, density functional theory modeling was used to understand the interactions at the BTO particle surface. Combining results from experiments and modeling indicated that polymer type, particle surface interactions, and particle surface structure can influence the dielectric properties of polymer-matrix nanocomposites containing BTO.

composite↗

Bootstrapping 2d ϕ 4 theory with Hamiltonian truncation data

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d Φ 4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the Φ 4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

97 MATHEMATICS AND COMPUTING↗

Sharp boundaries for the swampland

We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the S-matrix. Higher derivative couplings are expected to be of order one in the units of the UV cutoff. Our approach justifies this expectation and allows to prove precise bounds on the order one coefficients. Our main tool are dispersive sum rules for the S-matrix. We overcome the difficulties presented by the graviton pole by measuring couplings at small impact parameter, rather than in the forward limit. We illustrate the method in theories containing a massless scalar coupled to gravity, and in theories with maximal supersymmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Subleading corrections in $ \mathcal{N} $ = 3 Gaiotto-Tomasiello theory

We study subleading corrections to the genus-zero free energy of the N = 3 Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar resolvent, up to exponentially suppressed corrections. In the particular case that the two gauge groups in the quiver are of equal rank, we find an explicit (perturbative) expansion for the free energy. If, additionally, both groups have equal levels, then we find the full expression for the genus-zero free energy, modulo exponentially suppressed corrections. We also verify our results numerically.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the Stability of Power Transmission Systems Under Persistent Inverter Attacks: A Bi-Linear Matrix Approach

We investigate the stability and robustness properties of a power transmission system under persistent deceiving attacks on inverter-interfaced energy resources. The attacks can corrupt the damping coefficients in the inverters' controllers and measurements of the frequency at the points of coupling. Leveraging tools from hybrid dynamical systems theory, we characterize a broad family of persistent (and not necessarily periodic) attacks acting on the inverters, under which the stability properties of the transmission system can be shown to not be compromised. To address potentially conservative conditions identified through conventional bounding techniques, sufficient conditions on the average activation time of the attacks are identified via Lyapunov theory, as well as the formulation and solution of a class of bilinear matrix inequalities (BMI). The results are obtained for constant and slowly time-varying loads via input-to-state stability (ISS) tools. Numerical simulations on the IEEE 39-bus test system are also presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Nonrenormalization and Operator Mixing via On-Shell Methods

Using on-shell methods, we present a new perturbative nonrenormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions, we show that longer operators are often restricted from renormalizing shorter operators at the first order where Feynman diagrams exist. The theorem applies quite generally and depends only on the field content of the operators involved. We apply our theorem to operators of dimension five through seven in the standard model effective field theory, including examples of nontrivial zeros in the anomalous-dimension matrix at one through four loops. The zeros at two and higher loops go beyond those previously explained using helicity selection rules. We also include explicit sample calculations at two loops.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Finite N indices and the giant graviton expansion

The superconformal index of N = 4 super-Yang Mills theory with U(N) gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms corresponding to a giant graviton expansion of the index, and provided an explicit formula for the case of a single giant graviton. Here we give similar explicit formulae for an arbitrary number, m ≥ 1, of giant gravitons. We provide 1/2 and 1/16 BPS index examples up to the order where three giant gravitons contribute and demonstrate that the expansion of the matrix integral differs from the giant graviton expansion computed in the supergravity dual. This shows that the giant graviton expansion is not necessarily unique once two or more giant gravitons start appearing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗