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DOE OSTI2023

Aligned fields double copy to Kerr-NUT-(A)dS

We find Abelian gauge fields that double copy to a large class of black hole spacetimes with spherical horizon topology known as the Kerr-NUT-(A)dS family. Using a multi-Kerr-Schild prescription, we extend the previously-known double copy structure for arbitrarily rotating general dimension black holes, to include NUT charges and an arbitrary cosmological constant. In all cases, these single copy gauge fields are ‘aligned fields’, because their nonzero components align with the principal tensor which generates the Killing structure of the spacetime. In five dimensions, we additionally derive the same single-copy field strengths via the Weyl double copy procedure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Tensor network simulations of quasi-GPDs in the massive Schwinger model

Generalized parton distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED 2 ), within the Hamiltonian formulation of lattice field theory. Quasidistributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasiparton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2004

Estimation of Dynamical Parameters in Atmospheric Data Sets

In this study a new technique is used to derive dynamical parameters out of atmospheric data sets. This technique, called the structure tensor technique, can be used to estimate dynamical parameters such as motion, source strengths, diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. The fundamental algorithm will be extended to the analysis of multi- channel (e.g. multi trace gas) image sequences and to provide solutions to the extended aperture problem. In this study sensitivity studies have been performed to determine the usability of this technique for data sets with different resolution in time and space and different dimensions.

Wenig, Mark O.↗

DOE OSTI2024

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs

In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S –1 . This factorization of S –1 , written as ZZT = S –1 , is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix–matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. II. Deuteron and spectator nucleon tagging

We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (previous article), we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. In Part II (this article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. Methods of light-front quantization are employed to separate nuclear and hadronic structure in the high-energy process and achieve a composite description. The light-front wave function of the polarized deuteron is obtained from a rotationally covariant three-dimensional wave function in the center-of-mass frame of the proton-neutron system. The tagged structure functions are computed in the impulse approximation. The momentum and spin distribution of the active nucleon are controlled by the deuteron polarization and the detected spectator momentum (𝐷/𝑆 wave ratio). The cross section and spin asymmetries are evaluated for general deuteron polarization (vector and tensor, longitudinal and transverse) as functions of the spectator momentum. Tensor-polarized spin asymmetries of order unity are achieved for spectator momenta of approximately 300 MeV, which select configurations with a large 𝐷 wave. Sum rules for the tagged spin structure functions are derived. The results can be used for simulations of spectator tagging in future polarized fixed-target experiments (Jefferson Lab) or at the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Chiral-odd generalized parton distributions in the large-𝑁 𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

We study the nonperturbative properties of the nucleon’s chiral-odd generalized parton distributions (transversity GPDs) in the large-𝑁 𝑐 limit of QCD. This includes the parametric ordering of the spin-flavor components, the polynomiality property of the moments, and the sum rules connecting the GPDs with the tensor form factors. A multipole expansion in the transverse momentum transfer is used to enumerate and interpret the structures in the nucleon matrix element of the chiral-odd partonic operator, including monopole, dipole and quadrupole terms. The 1/𝑁 𝑐 expansion of the GPDs is performed using the abstract mean-field picture of baryons in the large-𝑁 𝑐 limit and its symmetries. We derive a large-𝑁 𝑐 relation between the flavor-nonsinglet GPDs 𝐸$^{𝑢−𝑑}_𝑇$ and $\tilde{𝐻}^{𝑢−𝑑}_𝑇$ and test it with recent lattice QCD results. We show that the polynomiality property and sum rules of the GPDs are fulfilled with the restricted realization of translational and rotational invariance in the mean-field picture. The results provide a basis for the phenomenological analysis of chiral-odd GPDs and hard exclusive processes in the large-𝑁 𝑐 limit, and for calculations in specific dynamical models.

generalized parton distributions↗

NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗

DOE OSTI2024

Holographic tensor networks with bulk gauge symmetries

Abstract Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called “fixed-area states” with flat entanglement spectra, limiting their utility in understanding general features of holographic entanglement. Here, we overcome this limitation by constructing a variant of random tensor networks that enjoys bulk gauge symmetries. Our model includes a gauge theory on a general graph, whose gauge-invariant states are fed into a random tensor network. We show that the model satisfies the quantum-corrected Ryu-Takayanagi formula with a nontrivial area operator living in the center of a gauge-invariant algebra. We also demonstrate nontrivial,n-dependent contributions to the Rényi entropy and Rényi mutual information from this area operator, a feature shared by general holographic states.

Physics↗

DOE OSTI2020

Theoretical and Phenomenological Studies of the Nucleon Structure in High Energy Reactions

The understanding of the internal structure of the proton and other strongly interacting particles is at the forefront of modern nuclear physics research. Generalized Parton Distribution Functions (GPDs) are a powerful tool to advance the understanding of hadron structure. In addition to the information about the one- dimensional collinear momentum distributions of partons (quarks, anti-quarks, and gluons) known from studies of high energy deep-inelastic reactions, GPDs also carry information on the distribution of partons in the transverse plane, and allow us in this way to access the three-dimensional structure of the nucleon. GPDs can be studied in hard-exclusive reactions and contain also information on the energy-momentum tensor form factors which will allow us to gain insights on quantities like pressure or angular momentum distribution inside the nucleon. The goal of this thesis is to deepen our understanding of the three-dimensional structure of the nucleon. We investigate energy-momentum tensor form factors and densities, and all leading-twist GPDs in the bag model. This quark model provides a consistent theoretical framework to investigate many general concepts that have recently attracted interest, and allows one to study insightful limits like the large-Nc limit, heavy-quark limit or the non-relativistic limit. Another important aspect of this thesis is the discussion of the monopole and quadrupole contributions to the angular momentum density. Finally, the description of pseudoscalar meson production in exclusive processes in terms of GPDs is discussed in the Goloskokov-Kroll model and implemented in the PARTONS framework, a software development project which will provide direct support for experiments at the Jefferson National Lab and the future Electron-Ion Collider.

Tezgin, Kemal↗

DOE OSTI2021

TwInflation

The general structure of Hybrid Inflation remains a very well-motivated mechanism for lower-scale cosmic inflation in the face of improving constraints on the tensor-to-scalar ratio. However, as originally modeled, the “waterfall” field in this mechanism gives rise to a hierarchy problem (η–problem) for the inflaton after demanding standard effective field theory (EFT) control. We modify the hybrid mechanism and incorporate a discrete “twin” symmetry, thereby yielding a viable, natural and EFT-controlled model of non-supersymmetric low-scale inflation, “Twinflation”. Analogously to Twin Higgs models, the discrete exchange-symmetry with a “twin” sector reduces quadratic sensitivity in the inflationary potential to ultra-violet physics, at the root of the hierarchy problem. The observed phase of inflation takes place on a hilltop-like potential but without fine-tuning of the initial inflaton position in field-space. We also show that all parameters of the model can take natural values, below any associated EFT-cutoff mass scales and field values, thus ensuring straightforward theoretical control. We discuss the basic phenomenological considerations and constraints, as well as possible future directions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Learning local equivariant representations for large-scale atomistic dynamics

Abstract A simultaneously accurate and computationally efficient parametrization of the potential energy surface of molecules and materials is a long-standing goal in the natural sciences. While atom-centered message passing neural networks (MPNNs) have shown remarkable accuracy, their information propagation has limited the accessible length-scales. Local methods, conversely, scale to large simulations but have suffered from inferior accuracy. This work introduces Allegro, a strictly local equivariant deep neural network interatomic potential architecture that simultaneously exhibits excellent accuracy and scalability. Allegro represents a many-body potential using iterated tensor products of learned equivariant representations without atom-centered message passing. Allegro obtains improvements over state-of-the-art methods on QM9 and revMD17. A single tensor product layer outperforms existing deep MPNNs and transformers on QM9. Furthermore, Allegro displays remarkable generalization to out-of-distribution data. Molecular simulations using Allegro recover structural and kinetic properties of an amorphous electrolyte in excellent agreement with ab-initio simulations. Finally, we demonstrate parallelization with a simulation of 100 million atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor \nu=2/3 ν = 2 / 3 . The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body M M -clustering property within any given number of Landau levels, that is, wave functions with M M th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the M=3 M = 3 case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2012

Simulations of Magnetic Reconnection - Kinetic Mechanisms Underlying the Fluid Description of Ions

Because of its ability to transfer the energy stored in magnetic field together with the breaking of the flux freezing constraint, magnetic reconnection is considered as one of the most important phenomena in plasma physics. When it happens in a collision less environment such as the terrestrial magnetosphere, it should a priori be modelled with in the framework of kinetic physics. The evidence of kinetic features has incidentally for a long time, been shown by researchers with the help of both numerical simulations and satellite observations. However, most of our understanding of the process comes from the more intuitive fluid interpretation with simple closure hypothesis which do not include kinetic effects. To what extent are these two separate descriptions of the same phenomenon related? What is the role of kinetic effects in the averaged/fluid dynamics of reconnection? This thesis addresses these questions for the proton population in the particular case of anti parallel merging with the help of 2D Hybrid simulations. We show that one can not assume, as is usually done, that the acceleration of the proton flow is only due to the Laplace force. Our results show, for symmetric and asymmetric connection, the importance of the pressure force, opposed to the electric one on the separatrices, in the decoupling region. In the symmetric case, we emphasize the kinetic origin of this force by analyzing the proton distribution functions and explain their structure by studying the underlying particle dynamics. Protons, as individual particles, are shown to bounce in the electric potential well created by the Hall effect. The spatial divergence of this well results in a mixing in phase space responsible for the observed structure of the pressure tensor. A detailed energy budget analysis confirms the role of the pressure force for the acceleration; but, contrary to what is sometimes assumed, it also reveals that the major part of the incoming Poynting flux is transferred to the thermal energy flux rather than to the convective kinetic energy flux, although the latter is generally supposed dominant. In the symmetric case, we propose the pressure tensor to be an additional proxy of the ion decoupling region in satellite data and verify this suggestion by studying a reconnection event encountered by the Cluster spacecrafts. Finally, the last part of this thesis is devoted to the study of the kinetic structure of asymmetric tangential current sheets where connection can develop. This theoretical part consists in finding a steady state solution to the Vlasov-Maxwell system for the protons in such a configuration. We present the theory and its first confrontation to numerical tests.

Aunai, icolas↗

NASA NTRS1990

Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Speziale, Charles G.↗

NASA NTRS1991

Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

Speziale, Charles G.↗

DOE OSTI2025

Sign Problem in Tensor-Network Contraction

We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks with only positive entries has lower computational complexity as compared to tensor networks with general real or complex entries. This raises the question of how this transition in computational complexity manifests itself in the hardness of different tensor-network-contraction schemes. We pursue this question by studying random tensor networks with varying bias toward positive entries. First, we consider contraction via Monte Carlo sampling and find that the transition from hard to easy occurs when the tensor entries become predominantly positive; this can be understood as a tensor-network manifestation of the well-known negative-sign problem in quantum Monte Carlo. Second, we analyze the commonly used contraction based on boundary tensor networks. The performance of this scheme is governed by the number of correlations in contiguous parts of the tensor network (which by analogy can be thought of as entanglement). Remarkably, we find that the transition from hard to easy—i.e., from a volume-law to a boundary-law scaling of entanglement—already occurs for a slight bias of the tensor entries toward a positive mean, scaling inversely with the bond dimension D , and thus the problem becomes easy the earlier the larger D occurs. This is in contrast both to expectations and to the behavior found in Monte Carlo contraction, where the hardness at fixed bias increases with the bond dimension. To provide insight into this early breakdown of computational hardness and the accompanying entanglement transition, we construct an effective classical statistical-mechanical model that predicts a transition at a bias of the tensor entries of 1 / D , confirming our observations. We conclude by investigating the computational difficulty of computing expectation values of tensor-network wave functions (projected entangled-pair states, PEPSs) and find that in this setting, the complexity of entanglement-based contraction always remains low. We explain this by providing a local transformation that maps PEPS expectation values to a positive-valued tensor network. This not only provides insight into the origin of the observed boundary-law entanglement scaling but also suggests new approaches toward PEPS contraction based on positive decompositions. Published by the American Physical Society 2025

Chen, Jielun (ORCID:0000000178411545)↗

NASA NTRS1987

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Estabrook, Frank B.↗

NASA NTRS2004

Parameter Estimation in Atmospheric Data Sets

In this study the structure tensor technique is used to estimate dynamical parameters in atmospheric data sets. The structure tensor is a common tool for estimating motion in image sequences. This technique can be extended to estimate other dynamical parameters such as diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. As a test scenario this technique will be applied to modeled dust data. In this case vertically integrated dust concentrations were used to derive wind information. Those results can be compared to the wind vector fields which served as input to the model. Based on this analysis, a method to compute atmospheric data parameter fields will be presented. .

Wenig, Mark↗