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Results for “Variational approach”

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At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Renormalization of excitonic properties by polar phonons

Here we employ quasiparticle path integral molecular dynamics to study how the excitonic properties of model semiconductors are altered by electron–phonon coupling. We describe ways within a path integral representation of the system to evaluate the renormalized mass, binding energy, and radiative recombination rate of excitons in the presence of a fluctuating lattice. To illustrate this approach, we consider Fröhlich-type electron–phonon interactions and employ an imaginary time influence functional to incorporate phonon-induced effects nonperturbatively. The effective mass and binding energies are compared with perturbative and variational approaches, which provide qualitatively consistent trends. We evaluate electron-hole recombination rates as mediated through both trap-assisted and bimolecular processes, developing a consistent statistical mechanical approach valid in the reaction limited regime. These calculations demonstrate how phonons screen electron–hole interactions, generically reducing exciton binding energies and increasing their radiative lifetimes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Nonlinear saturation of ballooning modes in stellarators

Ballooning mode saturation is investigated in realistic stellarator configurations using the flux tube approach of Ham et al (2018 Plasma Phys. Control. Fusion 60 075017), Ham et al (2016 Phys. Rev. Lett. 116 235001). The method is adapted to account for the lack of exact force balance in stellarator equilibrium solvers that assume existence of nested flux surfaces. A variational approach for calculating flux tube energy is developed to overcome this force error problem in stellarator numerical equilibria. Saturated (equilibrium) flux tube states that cross 10%–20% of the plasma minor radius are shown to exist for linearly ballooning unstable profiles. It is shown that several features of the displaced flux tube structure in a full nonlinear MHD simulation of Wendelstein 7X are reproduced by our model. Saturated states are found in a compact stellarator equilibrium close but below the marginal ballooning linear instability, i.e. the unperturbed equilibrium is metastable. This suggests that edge-localized-mode-like explosive MHD behavior may be possible in stellarators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1997

An MHD variational principle that admits reconnection

The variational approach of Pfirsch and Sudan's averaged magnetohydrodynamics (MHD) to the stability of a line-tied current layer is summarized. The effect of line-tying on current sheets that might arise in line-tied magnetic flux tubes by estimating the growth rates of a resistive instability using a variational method. The results show that this method provides a potentially new technique to gauge the stability of nearly ideal magnetohydrodynamic systems. The primary implication for the stability of solar coronal structures is that tearing modes are probably constant at work removing magnetic shear from the solar corona.

Rilee, M. L.↗

DOE OSTI2025

Classical and quantum simulations of 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory at finite temperature and density

Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.

Chen, I-Chi [Iowa State Univ., Ames, IA (United St↗

DOE OSTI2021

Variational study of the Kitaev-Heisenberg-Gamma model

Here we compute the low-energy excitation spectrum and the dynamical spin structure factor of the Kitaev-Heisenberg-Gamma model through a variational approach based on the exact fractionalized excitations of the pure Kitaev honeycomb model. This novel approach reveals the physical reason for the asymmetric stability of the Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limits. Moreover, we demonstrate that the fractionalized excitations form bound states in specific regions of each Kitaev spin liquid phase and that certain phase transitions induced by Heisenberg and Gamma interactions are driven by the condensation of such a bound state. Remarkably, this bound state appears as a sharp mode in the dynamical spin structure factor, while its condensation patterns at the appropriate phase transitions provide a simple explanation for the magnetically ordered phases surrounding each Kitaev spin liquid phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Larger than uncorrelated vacancy diffusion contributions in chemically disordered crystalline materials

Arising from a variational approach to compute diffusion coefficients, we introduce “superkinetic kinosons”, which are contributions to the diffusion flux of mobile defects and atomic species by single jump mechanisms that can exceed their uncorrelated values. In vacancy-mediated diffusion in crystalline random and high entropy materials, these contributions primarily arise from intermittent jumps of slow moving atoms that remove the vacancy out of correlation traps and enable a quantification of such effects on the diffusion coefficients. They can be significant contributors to diffusion, even when faster moving atoms have infinite percolation networks. Furthermore, their existence and importance provide fundamental insights about underlying aspects of vacancy diffusion such as formation of localized correlation traps and deviation of vacancy diffusion from percolation behavior.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Gauge constrained algorithm of variational discrete action theory at N = 3 for the multiorbital Hubbard model

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d = ∞ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that N = 3 accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at N = 3, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at N = 3 to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using N = 2 and N = 3 for the SU⁡(2⁢N orb ) Hubbard model in d = ∞ with N orb = 2–8, and compare to numerically exact dynamical mean-field theory solutions where available. Finally, the developments in this work will greatly facilitate the application of VDAT at N = 3 to strongly correlated electron materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Theory of the Kitaev model in a [111] magnetic field

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev’s 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number C = ±1 transitions into an Abelian liquid with C = ±4. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Scaling and merging time-resolved pink-beam diffraction with variational inference

Time-resolved x-ray crystallography (TR-X) at synchrotrons and free electron lasers is a promising technique for recording dynamics of molecules at atomic resolution. While experimental methods for TR-X have proliferated and matured, data analysis is often difficult. Extracting small, time-dependent changes in signal is frequently a bottleneck for practitioners. Recent work demonstrated this challenge can be addressed when merging redundant observations by a statistical technique known as variational inference (VI). However, the variational approach to time-resolved data analysis requires identification of successful hyperparameters in order to optimally extract signal. In this case study, we present a successful application of VI to time-resolved changes in an enzyme, DJ-1, upon mixing with a substrate molecule, methylglyoxal. We present a strategy to extract high signal-to-noise changes in electron density from these data. Furthermore, we conduct an ablation study, in which we systematically remove one hyperparameter at a time to demonstrate the impact of each hyperparameter choice on the success of our model. We expect this case study will serve as a practical example for how others may deploy VI in order to analyze their time-resolved diffraction data.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Revisiting excitation gaps in the fractional quantum Hall effect

Recent systematic measurements of the quantum well width dependence of the excitation gaps of fractional quantum Hall states in high mobility samples open the possibility of a better quantitative understanding of this important issue. Here we present what we believe to be accurate theoretical gaps including the effects of finite width and Landau level (LL) mixing. While theory captures the width dependence, there still remains a deviation between the calculated and the measured gaps, presumably caused by disorder. It is customary to model the experimental gaps of the n/(2n ± 1) states as Δ n/(2n+1) = Ce 2 /[(2n ± 1)ϵl]-Γ, where ϵ is the dielectric constant of the background semiconductor and l is the magnetic length; the first term is interpreted as the cyclotron energy of composite fermions and Γ as a disorder-induced broadening of composite-fermion LLs. Fitting the gaps for various fractional quantum Hall states, we find that Γ can be nonzero even in the absence of disorder.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements

The adaptive variational quantum dynamics simulation (AVQDS) method performs real-time evolution of quantum states using automatically generated parametrized quantum circuits that often contain substantially fewer gates than Trotter circuits. Here we report an improved version of the method, which we call AVQDS(T), by porting the tiling efficient trial circuits with rotations implemented simultaneously technique. The algorithm adaptively adds layers of disjoint unitary gates to the ansatz circuit so as to keep the McLachlan distance, a measure of the accuracy of the variational dynamics, below a fixed threshold. Here we perform benchmark noiseless AVQDS(T) simulations of quench dynamics in local spin models and compare with an alternative adaptive variational approach on quantum resource requirement. Quantum dynamical simulations implementing realistic noise channels are also reported. Finally, we propose a way to substantially alleviate the measurement overhead of AVQDS(T) while maintaining high accuracy by synergistically integrating quantum circuit calculations on quantum processing units with classical calculations using, e.g., tensor networks to evaluate the quantum geometric tensor. We showcase that this approach enables AVQDS(T) to deliver more accurate results than simulations using a fixed ansatz of comparable final depth for a significant time duration with fewer quantum resources.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Solving nuclear structure problems with the adaptive variational quantum algorithm

Here we use the Lipkin-Meshkov-Glick (LMG) model and the valence-space nuclear shell model to examine the likely performance of variational quantum eigensolvers in nuclear-structure theory. The LMG model exhibits both a phase transition and spontaneous symmetry breaking at the mean-field level in one of the phases, features that characterize collective dynamics in medium-mass and heavy nuclei. We show that with appropriate modifications, the ADAPT-VQE algorithm, a particularly flexible and accurate variational approach, is not troubled by these complications. We treat up to 12 particles and show that the number of quantum operations needed to approach the ground-state energy scales linearly with the number of qubits. We find similar scaling when the algorithm is applied to the nuclear shell model with realistic interactions in the sd and pf shells. Although most of these simulations contain no noise, we use a noise model from real IBM hardware to show that for the LMG model with four particles, weak noise has no effect on the efficiency of the algorithm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Advancing the Frontiers of Deep Learning for Low-Dose 3D Cone-Beam CT Reconstruction

X-ray computed tomography (CT) is an important noninvasive medical imaging modality for studying the structural details of internal organs. Image reconstruction in CT is an inverse problem of recovering an object's internal structure from the absorption profile of X-ray beams (sinogram) measured using a detector. The classical variational approach for CT reconstruction minimizes an energy functional using an appropriate iterative algorithm. Motivated by the success of deep learning (DL), researchers have begun to leverage training data and enhanced computing capabilities in recent years to produce high-fidelity reconstructed images. Nonetheless, much of the academic research in DL algorithms for CT has focused primarily on the two-dimensional setting (with simplified forward operators and noise model) for proofs-of-concept, and a comprehensive benchmarking of various classical and data-driven CT reconstruction approaches has not beenundertaken. The key objective of our CT reconstruction grand challenge was to promote methodological advancements for both classical and DL-based approaches for clinical CT with a reasonably accurately simulated 3D CT forward operator and noise model. We have utilized the publicly available LIDC-IDRI dataset and simulated sinograms and FDK images corresponding to two dose levels (clinical- and low-dose, constituting two tracks of the challenge) starting from the normal-dose images as the ground truth. In this paper, we summarize the motivation, context, and results of our challenge, and highlight the future research directions in DL for clinical CT.

X-ray tomography↗

DOE OSTI2021

Single-component-at-a-time variation study for glass-ceramic waste forms

Here, a 51-sample composition variation study was performed on glass-ceramic waste forms for a raffinate waste stream from aqueous reprocessing of used nuclear fuel containing high fractions of Mo, alkalis, alkaline earths (AEs), and rare earths (REs). The study was designed with a single-component-at-a-time variation approach off a centroid composition. The components that were varied included Al, B, Ca, Li, Mo, Na, REs, Si, Zr, and Others (containing minor components). Data analysis included crystallization curves, microstructure, and phase compositions. A number of components (i.e., Li 2 O, B 2 O 3 , REO x , MoO 3 , Na 2 O, and ZrO 2 ) significantly impacted the concentration and chemistry of phases, especially the primary phases of oxyapatite [i.e., Ca 2 RE 8 (SiO 4 ) 6 O 2 ] and powellite (i.e., AEMoO 4 ), precipitated in the slow-cool heat-treated waste forms; minor phases included cerianite [i.e., Ce x Zr (1-x) O 2 ], Ba-molybdate [i.e., Ba(Gd 0.67 Mo 0.33 O 3 ], noble metals, pollucite (i.e., CsAlSiO 4 ), and RE-borosilicate (i.e., RE 3 BSi 2 O 10 ).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Deep Sequencing of MHC-Adapted Viral Lines Reveals Complex Recombinational Exchanges With Endogenous Retroviruses Leading to High-Frequency Variants

Experimental evolution (serial passage) of Friend virus complex (FVC) in mice demonstrates phenotypic adaptation to specific host major histocompatibility complex (MHC) genotypes. These evolved viral lines show increased fitness and virulence in their host-genotype-of-passage, but display fitness and virulence tradeoffs when infecting unfamiliar host MHC genotypes. Here, we deep sequence these viral lines in an attempt to discover the genetic basis of FVC adaptation. The principal prediction for genotype-specific adaptation is that unique mutations would rise to high frequency in viral lines adapted to each host MHC genotype. This prediction was not supported by our sequencing data as most observed high-frequency variants were present in each of our independently evolved viral lines. However, using a multi-variate approach to measure divergence between viral populations, we show that populations of replicate evolved viral lines from the same MHC congenic mouse strain were more similar to one another than to lines derived from different MHC congenic mouse strains, suggesting that MHC genotype does predictably act on viral evolution in our model. Sequence analysis also revealed rampant recombination with endogenous murine leukemia virus sequences (EnMuLVs) that are encoded within the BALB/c mouse genome. The highest frequency variants in all six lines contained a 12 bp insertion from a recombinant EnMuLV source, suggesting such recombinants were either being favored by selection or were contained in a recombinational hotspot. Interestingly, they did not reach fixation, as if they are low fitness. The amount of background mutations linked to FVC/EnMuLV variable sites indicated that FVC/EnMuLV recombinants had not reached mutation selection equilibrium and thus, that EnMuLV sequences are likely continuously introgressing into the replicating viral population. These discoveries raise the question: is the expression of EnMuLV sequences in mouse splenocytes that permit recombination with exogenous FVC a pathogen or host adaptation?

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

ZnO-Au Hybrid Metamaterial Thin Films with Tunable Optical Properties

ZnO-Au nanocomposite thin films have been previously reported as hybrid metamaterials with unique optical properties such as plasmonic resonance properties and hyperbolic behaviors. In this study, Au composition in the ZnO-Au nanocomposites has been effectively tuned by target composition variation and thus resulted in microstructure and optical property tuning. Specifically, all the ZnO-Au nanocomposite thin films grown through the pulsed laser deposition (PLD) method show obvious vertically aligned nanocomposite (VAN) structure with the Au nanopillars embedded in the ZnO matrix. Moreover, the average diameter of Au nanopillars increases as Au concentration increases, which also leads to the redshifts in the surface plasmon resonance (SPR) wavelength and changes in the hyperbolic behaviors of the films. As a whole, this work discusses how strain-driven tuning of optical properties and microstructure resulted through a novel Au concentration variation approach which has not been previously attempted in the ZnO-Au thin film system. These highly ordered films present great promise in the areas of sensing, waveguides, and nanophotonics to name a few.

Bhatt, Nirali A.↗