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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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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

Applied Dynamical Systems↗
DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗
DOE OSTI2021

Nuclei with Up to $$\varvec{A=6}$$ Nucleons with Artificial Neural Network Wave Functions

The ground-breaking works of Weinberg have opened the way to calculations of atomic nuclei that are based on systematically improvable Hamiltonians. Solving the associated many-body Schrödinger equation involves non-trivial difficulties, due to the non-perturbative nature and strong spin-isospin dependence of nuclear interactions. Artificial neural networks have proven to be able to compactly represent the wave functions of nuclei with up to $A=4$ nucleons. In this work, we extend this approach to $^6$Li and $^6$He nuclei, using as input a leading-order pionless effective field theory Hamiltonian. We successfully benchmark their binding energies, point-nucleon densities, and radii with the highly-accurate hyperspherical harmonics method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

{phi} Meson Photoproduction on the Nucleon and 4He Targets

We study the reaction mechanism of phi-meson photoproduction on the nucleon and He-4 targets by using a dynamical model based on a Hamiltonian. In addition to the dominant contribution of the Pomeron exchange, various meson exchanges are considered in the t channel to describe the CLAS data in the low energy region root s =(1.97-2.84) GeV. The direct phi radiations are taken into account in the s- and u-channels. The backward structures at root s approximate to 2.1 and 2.3 GeV are well reproduced by the inclusion of the s-channel N(2000,5/2(+)) and N(2300,1/2(+))resonances, respectively. We also consider the final phi N interactions by the gluon exchange, the direct phi N interactions, and the box diagrams arising from the couplings with the pi N, rho N, K Lambda, and K Sigma channels. The effects of the final state interactions are found to be very weak. Then the resulting Hamiltonian is used to study the coherent gamma He-4 -> phi He-4 reaction within the distorted-weave impulse approximation. The calculated differential cross sections account for the LEPS data quite well.

Kim, Sang-Ho↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Jarzynski Equality for Conditional Stochastic Work

It has been established that the inclusive work for classical, Hamiltonian dynamics is equivalent to the two-time energy measurement paradigm in isolated quantum systems. However, a plethora of other notions of quantum work has emerged, and thus the natural question arises whether any other quantum notion can provide motivation for purely classical considerations. In the present analysis, we propose the conditional stochastic work for classical, Hamiltonian dynamics, which is inspired by the one-time measurement approach. This novel notion is built upon the change of expectation value of the energy conditioned on the initial energy surface. As main results, we obtain a generalized Jarzynski equality and a sharper maximum work theorem, which account for how non-adiabatic the process is. Our findings are illustrated with the parametric harmonic oscillator.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Monte Carlo simulation of order-disorder transition in refractory high entropy alloys: A data-driven approach

High entropy alloys (HEAs) are a series of novel materials that demonstrate many exceptional mechanical properties. To understand the origin of these attractive properties, it is important to investigate the thermodynamics and elucidate the evolution of various chemical phases. In this work, we introduce a machine learning approach to construct the effective Hamiltonian and study the thermodynamics of HEAs through canonical Monte Carlo simulation. The main characteristic of our method is to use pairwise interactions between atoms as the machine learning features and systematically improve the representativeness of the dataset using active learning from the Monte Carlo samples. We find this method produces highly robust and accurate effective Hamiltonians that give less than 0.1 mRy test error for all the three refractory HEAs: MoNbTaW, MoNbTaVW, and MoNbTaTiW. Using replica exchange to speed up the MC simulation, we calculated the specific heats and short-range order parameters in a wide range of temperatures. For all the studied materials, we find there are two major order-disorder transitions occurring respectively at T 1 and T 2 , where T 1 is near room temperature but T 2 is much higher. Further, we demonstrate that the transition at T 1 is caused by W and Nb while the one at T 2 is caused by the other elements. By comparing with experiments, the results demonstrate that the order-disorder transitions have a profound impact on the strength and ductility of HEAs.

36 MATERIALS SCIENCE↗
DOE OSTI2022

TTDFT: A GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations

We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ~8-fold GPU-CPU speedup for these operations on the largest systems studied. In conclusion, the computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ~7,000 atoms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory

Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the first principle description of many-electron dynamics in chemical and materials systems. Practical rt-TDDFT calculations often avoid the direct simulation of the von Neumann equation, and solve instead a set of Schrödinger equations, of which the dynamics is equivalent to that of the von Neumann equation. However, the time step size employed by the Schrödinger dynamics is often much smaller. Here, in order to improve the time step size and the overall efficiency of the simulation, we generalize a recent work of the parallel transport (PT) dynamics for simulating pure states [An, Lin, Multiscale Model. Simul. 18, 612, 2020] to general quantum states. The PT dynamics provides the optimal gauge choice, and can employ a time step size comparable to that of the von Neumann dynamics. Going beyond the linear and near adiabatic regime in previous studies, we find that the error of the PT dynamics can be bounded by certain commutators between Hamiltonians, density matrices, and their derived quantities. Such a commutator structure is not present in the Schrödinger dynamics. We demonstrate that the parallel transport-implicit midpoint (PT-IM) method is a suitable method for simulating the PT dynamics, especially when the spectral radius of the Hamiltonian is large. The commutator structure of the error bound, and numerical results for model rt-TDDFT calculations in both linear and nonlinear regimes, confirm the advantage of the PT dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

In this work, we present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Study on the magnetothermal properties of the D y 1 - x T b x A l 2 series of compounds

Here, in this work, we developed a theoretical model Hamiltonian, in the mean field approximation, to describe the magnetic and magnetocaloric behavior of the series of compounds Dy 1-x Tb x Al 2 (x = 0.00, 0.15, 0.25, 0.30, 0.35, 0.40 and 0.75). We adjusted the exchange parameters λ DyDy , λ TbTb , and λ DyTb to obtain the spin reorientation temperatures (T SR ) and the critical temperature (T C ) for each compound in the series. The results obtained by the Hamiltonian model agree satisfactorily with the experimental results. The heat capacity curves with and without an applied magnetic field, adiabatic temperature variation and isothermal entropy variation were modeled and compared with the experimental data. As the experimental results show, our model was also able to reproduce the change in the spin reorientation process: a first order spin reorientation transition appears for concentrations x = 0.15, 0.25, 0.30, 0.35, and no spin reorientation transitions after x = 0.40.

36 MATERIALS SCIENCE↗
DOE OSTI2021

On the canonical formulation of gauge field theories and Poincaré transformations

We address the Hamiltonian formulation of classical gauge field theories while putting forward results some of which are not entirely new, though they do not appear to be well known. We refer in particular to the fact that neither the canonical energy momentum vector ( P μ ) nor the gauge invariant energy momentum vector ( P inv μ ) do generate space-time translations of the gauge field by means of the Poisson brackets: In a general gauge, one has to consider the so-called kinematical energy momentum vector and, in a specific gauge (like the radiation gauge in electrodynamics), one has to consider the Dirac brackets rather than the Poisson brackets. Similar arguments apply to rotations and to Lorentz boosts and are of direct relevance to the “nucleon spin crisis” since the spin of the proton involves a contribution which is due to the angular momentum vector of gluons and thereby requires a proper treatment of the latter. We conclude with some comments on the relationships between the different approaches to quantization (canonical quantization based on the classical Hamiltonian formulation, Gupta-Bleuler, path integrals, BRST, covariant canonical approaches).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Light mesons with one dynamical gluon on the light front

We obtain the light meson mass spectroscopy from the light-front quantum chromodynamics (QCD) Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock components, together with a three-dimensional confinement. The eigenvectors of the light-front effective Hamiltonian provide a good quality description of the pion electromagnetic form factor, decay constant, and the valence quark distribution functions following QCD scale evolution. We also show that the pion's gluon densities can be probed through the pion-nucleus induced $J/ψ$ production data. Our pion parton distribution functions provide excellent agreement with $J/ψ$ production data from widely different experimental conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Double Inozemtsev limits of the quantum DELL system

In this letter we study various Inozemtsev-type limits of the quantum double elliptic (DELL) system when both elliptic parameters are sent to zero at different rates, while the coupling constant is sent to infinity, such that a certain combination of the three parameters is kept fixed. We find a regime in which such double Inozemtsev limit of DELL produces the elliptic Ruijsenaars-Schneider (eRS) Hamiltonians albeit in an unconventional normalization. We discuss other double scaling limits and anisotropic scaling of coordinates and momenta. In addition we provide a formal expression for the eigenvalues of the eRS Hamiltonians solely in terms of their eigenfunctions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Direct ab initio calculation of the 4 He nuclear electric dipole polarizability

The calculation of nuclear electromagnetic sum rules by directly diagonalizing the nuclear Hamiltonian in a large basis is numerically challenging and has not been performed for A>2 nuclei. With the significant progress of high performance computing, we show that calculating sum rules using numerous discretized continuum states obtained by directly diagonalizing the ab initio no-core shell model Hamiltonian is achievable numerically. Specifically, we calculate the 4 He electric dipole (E1) polarizability, that is an inverse energy weighted sum rule, employing the Daejeon16 NN interaction. We demonstrate that the calculations are numerically tractable as the dimension of the basis increases and are convergent. Our results for the 4 He electric dipole polarizability are consistent with the most recent experimental data and are compared with those of other theoretical studies employing different techniques and various interactions.

Astronomy & Astrophysics↗
DOE OSTI2026

Quantum state preparation with resolution refinement

We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then lifted to higher resolution and adiabatically evolved to produce the corresponding eigenstate of a higher-fidelity Hamiltonian. We give examples of resolution refinement applied to both single-particle basis states as well as a spatial lattice grid. For basis refinement, we compute few-body ground states of the Busch model for interacting particles in a harmonic trap in one dimension. For lattice refinement, we compute Hartree-Fock nuclear states for a central Woods-Saxon potential in three dimensions, and we compute bound states and continuum states in a multi-species Hubbard model of fermions in one dimension. In all cases, the method is efficient and requires an adiabatic evolution time that scales with the inverse of the energy gap times the square root of the system size. We show that this very favorable scaling arises from the fact that resolution refinement does not make large changes to the structure or energies of the low-energy eigenstates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

A class of three-dimensional gyroviscous magnetohydrodynamic models

A Hamiltonian and action principle formalism for deriving three-dimensional gyroviscous magnetohydrodynamic models is presented. The uniqueness of the approach in constructing the gyroviscous tensor from first principles and its ability to explain the origin of the gyromap and the gyroviscous terms are highlighted. The procedure allows for the specification of free functions, which can be used to generate a wide range of gyroviscous models. Through the process of reduction, the noncanonical Hamiltonian bracket is obtained and briefly analysed.

Physics↗