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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Cheaper and more noise-resilient quantum state preparation using eigenvector continuation

Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Furthermore, our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

The Eigenvector-Eigenvalue Identity and other pragmatic topics in linear algebra for physicists

Diagonalization of an Hermitian matrix is a common task in physics. All of us have diagonalized 2x2 matrices but few have diagonalized a 3x3 matrix algebraically except in special simplifying cases. In this colloquium, I will discuss the mathematics and methods for diagonalizing small, but larger than 2x2 marices, and discuss the recently rediscovered Eigenvector-Eigenvalue identity. As an explicit, pragmatic example I will use the propagation of neutrino's propagating through matter which is inherently a 3x3 problem.

Parke, Stephen [Fermilab] (ORCID:0000000320286782)↗
DOE OSTI2025

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Toward shell model interactions with credible uncertainties

Background: The nuclear shell model is a powerful framework for predicting nuclear structure observables, but relies on interaction matrix elements fit to experimental data as its inputs. Extending the shell model's applicability, particularly toward dripline nuclei, requires efficient fitting methods and credible uncertainty quantification. Traditional approaches face computational challenges and may underestimate uncertainties. Purpose: We develop and test a framework combining eigenvector continuation and Markov chain Monte Carlo to efficiently fit shell model interaction matrix elements and quantify their uncertainties. Methods: Eigenvector continuation is used to emulate shell model calculations, reducing computational costs. The emulator enables Markov chain Monte Carlo sampling to optimize interaction matrix elements and rigorously assess parametric uncertainties. Here, the framework is benchmarked using the USDB interaction in the 𝑠⁢𝑑 shell. Results: The emulator reproduces the USDB interaction with negligible error, validating its use in shell model fitting applications. However, we find that to obtain credible predictive intervals, the model defect of the shell model itself, rather than experimental or emulator error, must be taken into account in order to obtain credible uncertainties. Conclusions: The proposed framework provides an efficient and rigorous approach for fitting shell model interactions and quantifying uncertainties. Further, the normality assumption used in the past appears sufficient to describe the distribution of interaction matrix elements. However, it is crucial to account for model correlations to avoid underestimating uncertainties.

Nuclear forces↗
DOE OSTI2026

Optimal Transfer Operators in Algebraic Two-Level Methods for Nonsymmetric and Indefinite Problems

Consider an algebraic two-level method applied to the 𝑛-dimensional linear system 𝐴⁢𝒙 = 𝒃 using fine-space preconditioner (i.e., “relaxation” or “smoother”) 𝑀, with 𝑀 ≈ 𝐴, restriction and interpolation 𝑅 and 𝑃, and algebraic coarse-space operator 𝐴 𝑐 : = 𝑅 ∗ ⁢𝐴⁢𝑃. Then, what are the best possible transfer operators 𝑅 and 𝑃 of a given dimension 𝑛 𝑐 < 𝑛? Brannick et al. [12] showed that when 𝐴 and 𝑀 are Hermitian positive definite (HPD), the optimal interpolation is such that its range contains the 𝑛 𝑐 smallest generalized eigenvectors of the matrix pencil (𝐴, 𝑀). Recently, in Ali et al. [5] we generalized this framework to the non-HPD setting, by considering both right (interpolation) and left (restriction) generalized eigenvectors of (𝐴, 𝑀) and defining corresponding nonsymmetric transfer operators {𝑅#, 𝑃#}. Tight convergence bounds for {𝑅#, 𝑃#} are derived in spectral radius, as well as a proof of pseudo-optimality. Note, {𝑅#, 𝑃#} are typically complex valued, which is not practical for real-valued problems. Here, in this work, we build on [5], first characterizing all inner products in which the coarse-space correction defined by {𝑅#, 𝑃#} is orthogonal. We then develop tight two-level convergence bounds in these norms, and prove that the underlying transfer operators {𝑅#, 𝑃#} are genuinely optimal. As a special case, our theory both recovers and extends the HPD results from [12]. Finally, we show how to construct optimal, real-valued transfer operators in the case of that 𝐴 and 𝑀 are real valued, but are not HPD. Numerical examples arising from a discretized advection-reaction equation, wave-equation, and Stokes equations are used to verify and illustrate the theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗
DOE OSTI2025

Understanding the Hydronium Cation in the Solid State: A Study in Synthetic Hydronium Uranyl Phosphate and Arsenate Mineral Systems and Their Irradiation Stability

Here, we present neutron diffraction, electronic structure calculations, and optical vibrational spectroscopic characterization of hydronium uranyl phosphate (HUP), the synthetic analog of chernikovite ((H 3 O)(UO 2 )(PO 4 )·3H 2 O) to gain insight into structural features of the hydronium cation in the solid state. HUP crystallizes in P2 1 /c instead of previously reported P4/ncc 1 at room temperature and Pccn below 302 K. Lower symmetry was required due to hydronium and interstitial water positions within the structure. Crystallographic positions of hydronium cations determined from powder neutron diffraction data are bolstered by Raman and attenuated total reflectance infrared spectroscopic measurements and are further informed by density functional theory with phonon eigenvector analysis for spectral assignments. Finally, HUP and its arsenate analog (trogerite, (H 3 O)(UO 2 )(AsO 4 )·3H 2 O), (HUAs) were studied using He 2+ irradiation as an analog for α radiolysis to investigate the irradiation stability of these phases and the stability of hydronium cations in the solid state. Dose studies were employed wherein each sample was irradiated to 5, 10, 15, 25, and 50 MGy. Structural insight regarding irradiated materials is gained using optical vibrational spectroscopy and powder X-ray diffraction. Surprising irradiation stability of HUAs was found up to 50 MGy of dose, which may have important implications for understanding and modeling the geologic stability of legacy U.

actinides↗
DOE OSTI2024

GPU-Accelerated Solution of the Bethe–Salpeter Equation for Large and Heterogeneous Systems

We present a massively parallel GPU-accelerated implementation of the Bethe–Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting from single-particle eigenvalues and eigenvectors obtained with density functional theory. The algorithms adopted here circumvent the slowly converging sums over empty and occupied states and the inversion of large dielectric matrices through a density matrix perturbation theory approach and a low-rank decomposition of the screened Coulomb interaction, respectively. Further computational savings are achieved by exploiting the nearsightedness of the density matrix of semiconductors and insulators to reduce the number of screened Coulomb integrals. We scale our calculations to thousands of GPUs with a hierarchical loop and data distribution strategy. The efficacy of our method is demonstrated by computing the VEEs of several spin defects in wide-band-gap materials, showing that supercells with up to 1000 atoms are necessary to obtain converged results. We discuss the validity of the common approximation that solves the BSE with truncated sums over empty and occupied states. In conclusion, we then apply our GW-BSE implementation to a diamond lattice with 1727 atoms to study the symmetry breaking of triplet states caused by the interaction of a point defect with an extended line defect.

Absorption spectra↗
DOE OSTI2025

Atomic-scale imaging of frequency-dependent phonon anisotropy

Directly visualizing vibrational anisotropy in individual phonon modes is essential for understanding a wide range of intriguing optical, thermal and elastic phenomena in materials. Although conventional optical and diffraction techniques have been used to estimate vibrational anisotropies, they fall short in achieving the spatial and energy resolution necessary to provide detailed information. Here, we introduce a new form of momentum-selective electron energy-loss spectroscopy, which enables the element-resolved imaging of frequency- and symmetry-dependent vibrational anisotropies with atomic resolution. Vibrational anisotropies manifest in different norms of orthogonal atomic displacements, known as thermal ellipsoids. Using the centrosymmetric strontium titanate as a model system, we observed two distinct types of oxygen vibrations with contrasting anisotropies: oblate thermal ellipsoids below 60 meV and prolate ones above 60 meV. In non-centrosymmetric barium titanate, our approach can detect subtle distortions of the oxygen octahedra by observing the unexpected modulation of q-selective signals between apical and equatorial oxygen sites near 55 meV, which originates from reduced crystal symmetry and may also be linked to ferroelectric polarization. These observations are quantitatively supported by theoretical modelling, which demonstrates the reliability of our approach. The measured frequency-dependent vibrational anisotropies shed new light on the dielectric and thermal behaviours governed by acoustic and optical phonons. Furthermore, the ability to visualize phonon eigenvectors at specific crystallographic sites with unprecedented spatial and energy resolution opens new avenues for exploring dielectric, optical, thermal and superconducting properties.

Ferroelectrics and multiferroics↗
DOE OSTI2026

Mapping Critical Vulnerabilities in Natural Gas Pipeline Systems through Network Centrality and GIS Analytics

Natural gas plays a central role in the US energy landscape, providing 43% of electricity generation in 2023. Its exclusive recovery ability on pipelines for transmission underscores the importance of understanding the disruption recovery ability of this infrastructure. This study employs a network-based analytical framework integrating geographic information systems (GIS) with multiple centrality measures—betweenness, closeness, degree, and eigenvector—to pinpoint key segments and evaluate the structural robustness of the national pipeline network. Pipelines are grouped by System ID and Operator ID to capture variations across organizational and physical structures. The analysis reveals uneven patterns of network influence, where certain pipelines function as critical connectors or dominant hubs. Spatial mapping highlights geographic dependencies and potential chokepoints, offering a clear view of where targeted risk prevention measures would be most effective. The findings provide practical guidance for prioritizing maintenance, enhancing system robustness, and mitigating risks to ensure a stable and secure energy supply. Future research will expand the framework to incorporate dynamic operational data and real-time network behavior.

Peterson, Steven [ORNL] (ORCID:0000000287672998)↗
DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗
DOE OSTI2024

Superconductor to exciton condensate transition in a model copper-oxide material

Abstract Superconductivity and exciton condensation are fundamental phenomena in condensed matter physics, associated with the condensation of electron–electron and electron–hole pairs, respectively, into coherent quantum states. In this study, we present evidence of a superconductor to exciton condensate transition within the context of the three-band Hubbard model of copper-oxide-like materials. As the electron–electron repulsion increases, the superconducting phase is superseded by exciton condensation. In support of theoretical predictions—not yet realized experimentally—we observe the coexistence of the two condensates in the vicinity of the transition where the quantum states become a superposition of electron–electron and electron–hole condensates. Coexistence is rigorously computed from large eigenvalues and their eigenvectors in both the two-electron reduced density matrix (2-RDM) and the particle-hole RDM, which we obtain from a direct variational ground-state energy minimization with respect to the 2-RDM by semidefinite programming. We further discern that adjacent d orbitals and intervening p orbitals facilitate electron–electron pairing between copper orbitals, thereby supporting the superexchange mechanism for superconductivity. These observations suggest the feasibility of witnessing a superconductor to exciton condensate transition in copper-oxide analogs, bearing significant implications for identifying materials conducive to efficient transport processes.

Schouten, Anna O. (ORCID:0000000264255219)↗
DOE OSTI2025

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Wave topology in Hall magnetohydrodynamics

Hall magnetohydrodynamics (HMHD) extends ideal MHD by incorporating the Hall effect via the induction equation, making it more accurate for describing plasma behavior at length scales below the ion skin depth. Despite its importance, a comprehensive description of the eigenmodes in HMHD has been lacking. In this work, we derive the complete spectrum and eigenvectors of HMHD waves and identify their underlying topological structure. We prove that the HMHD wave spectrum is homotopic to that of ideal MHD, consisting of three distinct branches: the slow magnetosonic-Hall waves, the shear Alfvén-Hall waves, and the fast magnetosonic-Hall waves, which continuously reduce to their ideal MHD counterparts in the limit of vanishing Hall parameter. Contrary to a recent claim [Mahajan, Sharma, and Lingam, Phys. Plasmas 31, 090701 (2024)], we find that HMHD does not admit any additional wave branches beyond those in ideal MHD. In conclusion, the key qualitative difference lies in the topological nature of the HMHD wave structure: it exhibits nontrivial topology characterized by a Weyl point—an isolated eigenmode degeneracy point—and associated nonzero Chern numbers of the eigenmode bundles over a 2-sphere in 𝐤-space surrounding the Weyl point.

Alfvén waves↗
DOE OSTI2025

Phonon spectrum in the spin-Peierls phase of CuGeO 3

CuGeO 3 has long been studied as a prototypical example of the spin-Peierls transition in a 𝑆 = 1/2 Heisenberg chain. Despite intensive investigation of this quasi-one-dimensional material, systematic measurements and calculations of the phonon excitations in the dimerized phase have not to date been possible, leaving certain aspects of the spin-Peierls phenomenon unresolved. We perform state-of-the-art density functional theory (DFT) calculations to compute the electronic structure and phonon dynamics in the low-temperature dimerized phase. We also perform high-resolution neutron spectroscopy to measure the full phonon spectrum over multiple Brillouin zones. We find excellent agreement between our numerical and experimental results that extend to all measurement temperatures. Notable features of our phonon spectra include a number of steeply dispersive modes, nonmonotonic dispersion features, and specific phonon anticrossings, which we relate to the mode eigenvectors. By calculating the magnetic interactions within DFT and studying the effects of different phonon modes on the superexchange paths, we discuss the possibility of observing spin-phonon hybridization effects in experiments performed both in and out of equilibrium.

density functional theory↗
DOE OSTI2025

Toward scalable bound-to-resonance extrapolations for few- and many-body systems

In open quantum many-body systems, the theoretical description of resonant states of many particles strongly coupled to the continuum can be challenging. Such states are commonplace in, for example, exotic nuclei and hadrons, and can reveal important information about the underlying forces at play in these systems. In this work, we demonstrate that the complex-augmented eigenvector continuation (CA-EC) method, originally formulated for the two-body problem with uniform complex scaling, can reliably perform bound-to-resonance extrapolations for genuine three-body resonances having no bound subsystems. Here, we first establish that three-body bound-to-resonance extrapolations are possible by benchmarking different few-body approaches, and we provide arguments to explain how the extrapolation works in the many-body case. We furthermore pave the way towards scalable resonance extrapolations in many-body systems by showing that the CA-EC method also works in the Berggren basis, studying a realistic application using the Gamow shell model.

Ab initio calculations↗
DOE OSTI2024

First-principles investigation of elastic, vibrational, and thermodynamic properties of kagome metals CsM 3 Te 5 (M = Ti, Zr, Hf)

Kagome metals are a unique class of quantum materials characterized by their distinct atomic lattice arrangement, featuring interlocking triangles and expansive hexagonal voids. These lattice structures impart exotic properties, including superconductivity, interaction-driven topological many-body phenomena, and magnetism, among others. The kagome metal CsM 3 ⁢Te 5 (where M = Ti, Zr, or Hf) exhibits both superconductivity and nontrivial topological electronic properties, offering a promising platform for exploring topological superconductivity. This study employs first-principles density functional theory calculations to systematically analyze the elastic, mechanical, vibrational, thermodynamic, and electronic properties of CsM 3 ⁢Te 5 (M = Ti, Zr, Hf). Our calculations reveal that the studied compounds—CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 —are ductile metals with elastic properties akin to the hexagonal Bi and Sb, with average elastic constants, including a bulk modulus of 27 GPa, a shear modulus of 11 GPa, and Young's modulus of 29 GPa. We observe peculiar dispersionless, flat, phonon branches in the vibrational spectra of these metals. Additionally, we thoroughly analyze the symmetries of the zone-center phonon eigenvectors and predict vibrational fingerprints of the Raman- and infrared-active phonon modes. The analysis of thermodynamic properties reveals the Einstein temperature for CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 to be 66, 54, and 53 K, respectively. Our orbital-decomposed electronic structure calculations reveal significant in-plane steric interactions and multiple Dirac band crossings near the Fermi level. We further investigate the role of spin-orbit coupling effect on the studied properties. Furthermore, this theoretical investigation sheds light on the intriguing quantum behavior of kagome metals.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Atomic dynamics in 𝑀⁢Cr⁢𝑋 2 (𝑀=Ag, Cu; 𝑋 = S, Se) across magnetic and superionic transitions

Here, a systematic study of atomic dynamics and thermal properties of the family of layered chalcogenide compounds 𝑀⁢Cr⁢𝑋 2 (𝑀= Ag, Cu; 𝑋 = S, Se) was performed, including neutron and x-ray scattering, thermal characterization, and first-principles simulations. In all compounds, we observe a breakdown of specific phonon modes across the superionic phase transition, for phonons whose eigenvectors exhibit large contributions of mobile ions. In particular, the nondispersive portions of transverse acoustic (TA) branches at short-wavelengths and the low-energy optical phonons with large contributions from Ag + or Cu + become severely damped in the superionic phase. However, well-defined quasiparticles persist in the superionic state for long-wavelength TA phonons. In the case of AgCrS 2 , the coupling of lattice dynamics with its antiferromagnetic transition was also investigated. The magnetic ordering couples with the monoclinic–rhombohedral structural transition, and the Cr 3+ spin arrangement strongly affects the phonon dispersions. We qualitatively reproduce the magnetic and nuclear components of the INS measurement for antiferromagnetic AgCrS 2 by combining models of spin-waves and spin-polarized first-principles phonon simulations. Quasielastic magnetic fluctuations persist in the paramagnetic phase up to high temperature, but are clearly distinguished from the nuclear component through their momentum dependence. Finally, we report measurements of the thermal properties of the selenide compounds and find good agreement with our DFT simulations.

36 MATERIALS SCIENCE↗