Search NASA⌕ Search

SEARCH · Search NASA

Results for “solve”

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 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems

The dynamics of Markovian open quantum systems are described by Lindblad master equations. For fermionic and bosonic systems that are quasi-free, i.e. with Hamiltonians that are quadratic in the ladder operators and Lindblad operators that are linear in the ladder operators, we derive the equation of motion for the covariance matrix. This determines the evolution of Gaussian initial states and the steady states, which are also Gaussian. Using ladder super-operators (a.k.a. third quantization), here we show how the Liouvillian can be transformed to a many-body Jordan normal form which also reveals the full many-body spectrum. Extending previous work by Prosen and Seligman, we treat fermionic and bosonic systems on equal footing with Majorana operators, shorten and complete some derivations, also address the odd-parity sector for fermions, give a criterion for the existence of bosonic steady states, cover non-diagonalizable Liouvillians also for bosons, and include quadratic systems. In extension of the quasi-free open systems, quadratic open systems comprise additional Hermitian Lindblad operators that are quadratic in the ladder operators. While Gaussian states may then evolve into non-Gaussian states, the Liouvillian can still be transformed to a useful block-triangular form, and the equations of motion for k-point Green’s functions form a closed hierarchy. Based on this formalism, results on criticality and dissipative phase transitions in such models are discussed in a companion paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A random-sampling method as an efficient alternative to variational Monte Carlo for solving Gutzwiller wavefunctions

Abstract We present a random-sampling (RS) method for evaluating expectation values of physical quantities using the variational approach. We demonstrate that the RS method is computationally more efficient than the variational Monte Carlo method using the Gutzwiller wavefunctions applied on single-band Hubbard models as an example. Non-local constraints can also been easily implemented in the current scheme that capture the essential physics in the limit of strong on-site repulsion. In addition, we extend the RS method to study the antiferromagnetic states with multiple variational parameters for 1D and 2D Hubbard models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Phoebe: a high-performance framework for solving phonon and electron Boltzmann transport equations

Understanding the electrical and thermal transport properties of materials is critical to the design of electronics, sensors, and energy conversion devices. Computational modeling can accurately predict material properties but, in order to be reliable, requires accurate descriptions of electron and phonon states and their interactions. While first-principles methods are capable of describing the energy spectrum of each carrier, using them to compute transport properties is still a formidable task, both computationally demanding and memory intensive, requiring integration of fine microscopic scattering details for estimation of macroscopic transport properties. To address this challenge, we present Phoebe—a newly developed software package that includes the effects of electron–phonon, phonon–phonon, boundary, and isotope scattering in computations of electrical and thermal transport properties of materials with a variety of available methods and approximations. This open source C++ code combines MPI-OpenMP hybrid parallelization with GPU acceleration and distributed memory structures to manage computational cost, allowing Phoebe to effectively take advantage of contemporary computing infrastructures. We demonstrate that Phoebe accurately and efficiently predicts a wide range of transport properties, opening avenues for accelerated computational analysis of complex crystals.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A puzzle solved after two decades: SN 2002gh among the brightest of superluminous supernovae

ABSTRACT We present optical photometry and spectroscopy of the superluminous SN 2002gh from maximum light to +204 d, obtained as part of the Carnegie Type II Supernova (CATS) project. SN 2002gh is among the most luminous discovered supernovae ever, yet it remained unnoticed for nearly two decades. Using Dark Energy Camera archival images we identify the potential supernova (SN) host galaxy as a faint dwarf galaxy, presumably having low metallicity, and in an apparent merging process with other nearby dwarf galaxies. We show that SN 2002gh is among the brightest hydrogen-poor SLSNe with MV = −22.40 ± 0.02, with an estimated peak bolometric luminosity of 2.6 ± 0.1 × 1044 erg s−1. We discount the decay of radioactive nickel as the main SN power mechanism, and assuming that the SN is powered by the spin-down of a magnetar we obtain two alternative solutions. The first case, is characterized by significant magnetar power leakage, and Mej between 0.6 and 3.2 M⊙, Pspin = 3.2 ms, and B = 5 × 1013 G. The second case does not require power leakage, resulting in a huge ejecta mass of about 30 M⊙, a fast spin period of Pspin ∼ 1 ms, and B ∼ 1.6 × 1014 G. We estimate a zero-age main-sequence mass between 14 and 25 M⊙ for the first case and of about 135 M⊙ for the second case. The latter case would place the SN progenitor among the most massive stars observed to explode as an SN.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

General Approach to Solving Spin Moiré Superstructures

Recently, a host of exciting magnetic textures such as topologically protected skyrmion lattices has been discovered in several bulk metallic lanthanide compounds. In addition to hosting skyrmion phases, a hallmark of this class of materials is the appearance of numerous spin textures characterized by superposition of multiple magnetic modulations: spin moiré superlattices. In order to understand the multitude of complex phases often present in these materials, we require a general-purpose experimental and theoretical framework. Here, we demonstrate such an approach in EuAg4⁢Sb2 by comprehensively characterizing and modeling its three complex zero-field magnetic textures. Systematic symmetry-breaking experiments using uniaxial strain determine that the ground-state incommensurate magnetic phase (ICM1) is single 𝑞, meaning the magnetic moments modulate along one magnetic propagation vector. In contrast, ICM2 and ICM3 are both double 𝑞, meaning they are formed from the superposition of two sinusoidal spin modulations, i.e., spin moiré superlattices. Further, through application of polarized small-angle neutron scattering and spherical neutron polarimetry, we demonstrate that ICM1 is a single-𝑞 cycloid and ICM2 and ICM3 are double-𝑞 vortex lattices. Despite the quasi-two-dimensional nature of EuAg4⁢Sb2, the modulations propagate out of the ab plane, leading to a shift of the spin texture between triangular lattice planes. Further, the ICM3 to ICM2 transition includes an unusual 45° rotation of the magnetic vortex lattice. Motivated by the coexistence of such drastically different phases in this compound, we conclude by developing a phenomenological model that sheds light on the energetic origins of these varied phases. Our experimental probes and theoretical modeling definitively characterize three different and tunable phases in one material and provide insight for the design of topological spin-texture materials.

Neves, Paul [Massachusetts Institute of Technology↗
DOE OSTI2026

Axionlike particles and sterile neutrinos solve the 𝐵 → 𝐾⁢$𝜈⁢\bar{𝜈}$ and 𝐵 → 𝜋⁢𝐾 puzzles

The recent measurement of the branching ratio of 𝐵 + → 𝐾 + +inv (where “inv” denotes invisible states) by the Belle II Collaboration is enhanced relative to the standard model expectation by 2.7⁢𝜎. An older puzzle persists in measurements of the branching ratios and 𝐶⁢𝑃 asymmetries of 𝐵 → 𝜋⁢𝐾 decays. We address these two anomalies in flavor-changing neutral current 𝐵 decays, with a short-lived axionlike particle (ALP) with mass close to that of the 𝜋 0 . In the model with the minimum number of new couplings, the ALP has couplings to the photon, top quark and a heavy sterile neutrino. The ALP contributes to the 𝐵 → 𝜋 0 ⁢𝐾 decays by mixing with the 𝜋 0 . It contributes to 𝐵 + → 𝐾 + + inv by its off-shell coupling to sterile neutrino pairs. The model can explain the excess in the total rate, but not the observed distribution of signal events. We make predictions for all 𝐵 → 𝐾 (*) + inv modes and for the rare kaon decays, 𝐾 + → 𝜋 + + inv and 𝐾 𝐿 → 𝜋 0 + inv. We find an appreciable contribution to the magnetic moment of the muon, and negligible contributions to the magnetic moment of the electron and 𝑏 → 𝑠⁢𝑒 + ⁢𝑒 − .

axion-like particles↗
DOE OSTI2021

Strategies for solving the excited-state self-consistent-field problem for highly excited and multiply ionized states

The dynamics of molecules exposed to intense x-ray radiation involve a large number of multiply ionized and highly excited electronic configurations. To model these dynamics a reliable and efficient electronic structure model is imperative. Employing the Hartree-Fock-Slater electronic structure model in combination with the maximum overlap method, we quantify the associated convergence failures when calculating electronic states of carbon monoxide with multiple vacancies in the core and valence levels. Here, we characterize these cases and describe strategies to overcome the convergence problems. The described techniques not only eliminate all convergence issues for CO but also result in a significant reduction of convergence failures for simulations of the x-ray-induced multiple ionization dynamics of the phenol molecule.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Solving the Bethe-Salpeter equation on a subspace: Approximations and consequences for low-dimensional materials

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation. The repulsive exchange interaction responsible for the singlet-triplet splitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called S approximation [L. X. Benedict, Phys. Rev. B 66, 193105 (2002)PRBMDO0163-182910.1103/PhysRevB.66.193105]. Here, we systematically explore the accuracy of the S approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the S approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energies with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.

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 OSTI2020

𝐹 𝐾 ⁡/𝐹 𝜋 from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles

We report the results of a lattice quantum chromodynamics calculation of 𝐹 𝐾 ⁡/𝐹 𝜋 using Möbius domain-wall fermions computed on gradient-flowed 𝑁 𝑓 =2 +1 +1 highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from 130 ≲ 𝑚 𝜋 ≲ 400 MeV , four lattice spacings of 𝑎 ∼ 0.15, 0.12, 0.09 and 0.06 fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the 𝑎 ∼ 0.06 fm ensemble is helpful, but not necessary to achieve a subpercent determination of 𝐹 𝐾 ⁡/𝐹 𝜋 . We also include an estimate of the strong isospin breaking corrections and arrive at a final result of 𝐹 $\hat{K}$ + ⁡ /𝐹 $\hat{𝜋}$ + = 1.1942⁢(45) with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of |𝑉 𝑢⁢𝑠 |/|𝑉 𝑢⁢𝑑 | = 0.2311⁢(10).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗