Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Eigenvalue”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation

Here, we adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a single auxiliary qubit. As a proof of concept, we calculate the energies of the ground state and low-lying electronic excitations of a hydrogen molecule in a minimal basis on a cloud quantum computer. The denominative robustness of our approach is then quantified in terms of a high tolerance to coherent errors in the state preparation and measurement. Conceptually, we note that all quantum phase estimation algorithms ultimately evaluate eigenvalue differences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Topological Defect Engineering and $\mathcal{PT}$ Symmetry in Non-Hermitian Electrical Circuits

In this work, we employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $\mathcal{PT}$ and chiral symmetry anti-$\mathcal{PT (APT)}$. The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $\mathcal{PT}$-symmetric gain and loss on localized edge and defect states in a non-Hermitian Su-Schrieffer-Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the $\mathcal{APT}$-symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel $\mathcal{PT}$-symmetric $\mathbb{Z}_2$ invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not $\mathcal{PT}$ symmetric, the topological defect state disappears and only reemerges when $\mathcal{APT}$ symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Rodeo Algorithm for Quantum Computing

We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $\ [E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by a suppression factor δ, the required computational effort scales as $\ O[|\log \delta|/(p \epsilon)]$, where p s the squared overlap of the initial state with the target eigenvector. The method, which we call the rodeo algorithm, uses auxiliary qubits to control the time evolution of the Hamiltonian minus some tunable parameter E . In this manner, we converge to the target eigenvector with exponential accuracy in the number of measurements. In addition to preparing eigenvectors, the method can also compute the full spectrum of the Hamiltonian. We illustrate the performance with several examples. For energy eigenvalue determination with error $\epsilon$, the computational scaling is $\ O[(\log \epsilon)^2/(p \epsilon)]$. For eigenstate preparation, the computational scaling is $\ O(\log \Delta/p)$, where $\Delta$ is the magnitude of the orthogonal component of the residual vector. The speed for eigenstate preparation is exponentially faster than that for phase estimation or adiabatic evolution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Logarithmic Corrections to Kerr Thermodynamics

Recent work has shown that loop corrections from massless particles generate $\frac{3}{2}$ ⁢log⁡𝑇 Hawking corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS 2 ×𝑆 2 , the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This “not-NHEK” geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits $\frac{3}{2}$ ⁢log⁡𝑇 Hawking behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

General relativity↗
DOE OSTI2025

Lattice QCD Study of Pion Electroproduction and Weak Production from a Nucleon

Quantum fluctuations in QCD influence nucleon structure and interactions, with pion production serving as a key probe of chiral dynamics. In this Letter, we present a lattice QCD calculation of multipole amplitudes at threshold, related to both pion electroproduction and weak production from a nucleon, using two gauge ensembles near the physical pion mass. We develop a technique for spin projection and construct multiple operators for analyzing the generalized eigenvalue problem in both the nucleon-pion system in the center-of-mass frame and the nucleon system with nonzero momentum. The numerical lattice results are then compared with those extracted from experimental data and predicted by low-energy theorems incorporating one-loop corrections. Published by the American Physical Society 2025

Gao, Yu-Sheng (ORCID:0009000406829247)↗
DOE OSTI2022

Nonlinear deformation and elasticity of BCC refractory metals and alloys

Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while nonlinear elasticity describes the response to finite deformations. Here, it was previously shown that uniaxial strain along [100] drives refractory metals and alloys towards mechanical instabilities. These include an extensional instability, and a symmetry-breaking orthorhombic distortion caused by a Jahn-Teller-Peierls instability that splays the cubic lattice vectors. Here we analyze these transitions in depth. Eigenvalues and eigenvectors of the Wallace tensor identify and classify linear instabilities in the presence of strain. We show that both instabilities are discontinuous, leading to discrete jumps in the lattice parameters. We provide physical intuition for the instabilities by analyzing the changes in first-principles energy, stress, bond lengths, and angles upon application of strain. Electronic band structure calculations show differential occupation of bonding and antibonding orbitals, driven by the changing bond lengths and leading to the structural transformations. Strain thresholds for these instabilities depend on the valence electron count.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Optimally tuned starting point for single-shot GW calculations of solids

The dependence of ab initio many-body perturbation theory within the $\textit{GW}$ approximation on the eigensystem used in calculating quasiparticle corrections limits this method's predictive power. Here, we investigate the accuracy of the recently developed Wannier-localized optimally tuned screened range-separated hybrid (WOT-SRSH) functional as a generalized Kohn-Sham starting point for single-shot $\textit{GW}$ ($G_0W_0$) calculations for a range of semiconductors and insulators. Comparison to calculations based on well-established functionals, namely, PBE, PBE0, and HSE, as well as to self-consistent GW schemes and to experiment, shows that band gaps computed via $G_0W_0$@WOT-SRSH have a level of precision and accuracy that is comparable to that of more advanced methods such as quasiparticle self-consistent $\textit{GW}$ and eigenvalue self-consistent $\textit{GW}$. In this work, we also find that $G_0W_0$@WOT-SRSH improves the description of states deeper in the valence band manifold. Finally, we show that $G_0W_0$@WOT-SRSH significantly reduces the sensitivity of computed band gaps to ambiguities in the underlying WOT-SRSH tuning procedure.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Experimental quantum learning of a spectral decomposition

Currently available quantum hardware allows for small-scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits containing a total of 21 variational parameters. Moreover, we variationally diagonalize the unitary to learn its spectral decomposition, i.e., its eigenvalues and eigenvectors. We illustrate how this can be used as a subroutine to compress the depth of dynamical quantum simulations. One can view our implementation as a demonstration of entanglement-enhanced machine learning, as only a single (entangled) training data pair is required to learn a 4 × 4 unitary matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Entanglement Witness for Indistinguishable Electrons Using Solid-State Spectroscopy

Characterizing entanglement in quantum materials is crucial for advancing next-generation quantum technologies. Despite recent strides in witnessing entanglement in magnetic materials with distinguishable spin modes, quantifying entanglement in systems formed by indistinguishable electrons remains a formidable challenge. To solve this problem, we introduce a method to extract various four-fermion correlations by analyzing the nonlinearity in resonant inelastic x-ray scattering spectra. These correlations constitute the primary components of the cumulant two-particle reduced density matrix. We further derive bounds for its eigenvalues and demonstrate the linear scaling with fermionic entanglement depth, providing a reliable witness for entanglement. Using the material-relevant strongly correlated models as examples, we show how this entanglement witness can efficiently quantify multipartite entanglement across different phase regions, highlighting its advantage over quantum Fisher information. Published by the American Physical Society 2025

Liu, Tongtong (ORCID:0000000295324061)↗
DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Colloquium: Eigenvector continuation and projection-based emulators

Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this Colloquium, the development, theory, and applications of eigenvector continuation and projection-based emulators are presented. In conclusion, the basic concepts are introduced, the underlying theory and convergence properties are discussed, and recent applications for quantum systems and future prospects are presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Lindblad many-body scars

Quantum many-body scars have received much recent attention for being both intriguing nonergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with 𝑁 fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify 𝑁/2+1 scars for complex fermions due to the 𝑈⁡(1) symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin chain. We also characterize the physical properties of Lindblad scars. First, the operator size is independent of the disorder realization and has a vanishing variance. By contrast, the operator size for nonscarred states, believed to be quantum chaotic, is well described by a distribution centered around a specific size and a finite variance, which could be relevant for a precise definition of the eigenstate thermalization hypothesis in dissipative quantum chaos. Moreover, the entanglement entropy of these scars has distinct features such as a strong dependence on the partition choice and, in certain cases, a large entanglement.

Eigenstate thermalization↗
DOE OSTI2025

Lanczos algorithm for lattice QCD matrix elements

Recent work [M. L. Wagman, Lanczos, the transfer matrix, and the signal-to-noise problem, .] found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multistate fit results than effective masses—but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of “spurious-state filtering” involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Rotated-Droop Control for Enhanced Stability and Power Decoupling in Microgrids With Complex Line Impedances

Classical droop control in microgrids predominantly assumes inductive line impedance, which simplifies implementation but causes power coupling and steady-state errors in systems with resistive and inductive lines. This paper proposes a rotated-droop control strategy for grid-forming inverters that reformulates the power equations by incorporating the magnitude and angle of the line impedance within a rotated reference frame. This method enhances the decoupling of active and reactive power dynamics without increasing complexity or requiring communication links. A small-signal state-space model was created to capture the dynamic behavior of the system under varying impedance parameters, preserving the original droop gains by rotating the power control structure. This allows eigenvalue-based stability analysis and enhances damping and transient performance. Simulation and experimental results validated the improved power-sharing performance, faster response, and robustness of the proposed method under different impedance conditions. This approach maintains the decentralized structure of the conventional droop control while enabling greater adaptability and scalability, making it suitable for modern inverter-based microgrids with dynamic topologies.

Campo-Ossa, Daniel Dario [Univ. of Puerto Rico, Ag↗
DOE OSTI2024

Grid-Forming Storage Networks: Analytical Characterization of Damping and Design Insights

Grid-forming storage resources are critical to the operation of power grids with high renewable penetration. Over the years, there has been considerable emphasis on understanding the benefits these inverter-based storage resources bring towards managing volatility and enhancing grid reliability but little is studied about the supplementary advantages latent in their operation. This paper investigates one such application in which we explore the impact of grid-forming distributed storage in damping low-frequency inter-area oscillations. We present a detailed analysis characterizing the impact of inverter-droop and storage size on the slower eigenvalues, highlighting potential design considerations for enhancing system stability.

Chatterjee, Kaustav [BATTELLE (PACIFIC NW LAB)] (O↗
DOE OSTI2021

A New Impedance-Based Modeling and Stability Analysis Approach for Power Oscillations Between Grid-Forming Inverters

This paper presents a new modeling and analysis approach to address the small-signal stability issues among interconnected grid-forming (GFM) inverters. A novel phasor domain “power impedance” model is developed to capture the terminal characteristics of GFM inverters. Based on the developed models, a sum-type impedance stability criterion is proposed to analyze the power oscillations between GFM Inverters. The developed models are validated with EMT simulations and the stability analysis results using the proposed stability criterion can match both EMT simulations and eigenvalue analysis. In addition, the application of the developed model can be extended to the stability analysis of large-scale power system with high penetration of GFM inverters.

Liu, Hanchao↗
DOE OSTI2022

On Stability of PQ-Controlled Grid-Following and Droop-Control Grid-Forming Inverters

In this paper, the nonlinearity impacts of PQ-control schemes and LCL filter parameter variations on the stability of grid-interactive inverters are studied under weak grid conditions. This work demonstrates that the control nonlinearity and parameter variations can cause unexpected instability at low power levels. This instability issue in the nominal operating range may occur under specific control parameters due to the shift of the low-frequency eigenvalues of PQ-controlled inverters. A full-order small-signal model for PQ-controlled inverters is applied to analyze this instability issue. Furthermore, the impacts of the droop coefficients on the stability of the droop-controlled grid-forming inverter are also investigated using the closed-loop inverter model. The findings are experimentally verified using a small-scale two-level 208 V, 5 kVA inverter feeding a 12 kW NHR 9410 power grid emulator and a hardware setup of a microgrid fed by two 5 kVA 208V inverters.

Hossen, Tareq↗
DOE OSTI2021

Parametric Comparative Analysis between Virtual Synchronous Generator and Droop-based Inertia for Inverter-Based Microgrids

This paper presents a parametric comparative analysis between the virtual synchronous generator (VSG) method and the droop control method to emulate inertia in the voltage-source inverter (VSI). Droop controllers are commonly used to regulate sharing power in microgrids and distribute power generation proportionally among VSI’s depending on their rated power. Additionally, VSG has been used to regulate the Rate-of-Change-of-Frequency (RoCoF) of the microgrid using virtual inertia. Although both methods can be used to regulate the frequency variation, the influence of each method on the closed loop eigenvalues is not the same. In this work, the transient response of the frequency is analyzed for each method to determine their advantages and disadvantages regarding frequency regulation in microgrid applications. The results were verified by conducting experimental trials using VSI’s. These experiments demonstrated that VSG is more suitable for regulating RoCoF and frequency nadir than droop controllers since it provides inertial support and improves frequency response.

Campo-Ossa, Daniel D.↗