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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Hamiltonian simulation in the low-energy subspace

Abstract We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H . This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H . We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dimensional interpolation for metallic hydrogen

In this work, we employ a simple and mostly accurate dimensional interpolation formula using dimensional limits D = 1 and D = ∞ to obtain D = 3 ground-state energy of metallic hydrogen. We also present results describing the phase transitions for different symmetries of three-dimensional structure lattices. The interpolation formula not only predicts fairly accurate energies but also predicts a correct functional form of the energy as a function of the lattice parameters. That allows us to calculate different physical quantities such as the bulk modulus, Debye temperature, and critical transition temperature, from the gradient and the curvature of the energy curve as a function of the lattice parameters. These theoretical calculations suggest that metallic hydrogen is a likely candidate for high temperature superconductivity. The dimensional interpolation formula is robust and might be useful to obtain the energies of complex many-body systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Intrinsic and extinction colour components in SNe Ia and the determination of R V

Context.The colour fluctuations of type Ia supernovae (SNe Ia) include intrinsic and extrinsic components, which both contribute to the observed variability. Previous works proposed a statistical separation of these two contributions, but the individual intrinsic colour contributions of each SN Ia were not extracted. In addition, a large uncertainty remains on the value of the parameterR V , which characterises the dust extinction formula. Aims.Leveraging the known parameterisation of the extinction formula for dust in our Galaxy, and applying it to the host galaxy of SNe Ia, we propose a new method of separation –valid for each SN– using the correlations between colour fluctuations. This also allows us to derive a well-constrained value of the extinction parameterR V with different, possibly smaller systematic errors. We also define a three-dimensional space of intrinsic colour fluctuations. Methods.The key ingredients in this attempt at separating the intrinsic and extinction colour components for each SN –and subsequently measuringR V – are the assumption of a linearized dependence of magnitude on the extinction component of colour, a one-dimensional extra-intrinsic colour space (in addition to CaII H&Kλ3945 and Si IIλ4131 contributions) over four independent colours, and the absence of correlation between the intrinsic and extrinsic variabilities. Results.We show that a consistent solution is found under the previous assumptions, but the observed systematic trends point to a (small) inadequacy of the extinction formula. Once corrected, all systematic extinction effects can be cancelled by choosing a single scaling of the extinction colour component as well as an appropriate value ofR V = 2.181 ± 0.117. The observed colours are described within an accuracy of 0.025 mag. The resulting magnitude variability is 0.13 over allUBVRIbandpasses, and this fluctuation is shown to be independent of the bandpass to within 0.02 mag.

Astronomy & Astrophysics↗
DOE OSTI2021

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Semiclassical transition state theory through the lens of the restricted partition function

The wide adoption of transition state theory in resolving the rates of molecular processes relies on the simplification from reducing the formal and numerical expense of dynamics by a geometric constraint. Such a reduction is at odds with the uncertainty in localization that the uncertainty principle requires. While many forms of semiclassical transition state theory (SCTST) have been aimed at addressing this challenge, a popular approach has relied on resolving the underlying phase space structure of the exact rate formula to leverage Bohr–Sommerfeld quantization. Here, the Hernandez–Miller SCTST reframed the thermal rate formula into an integral of the so-called restricted partition function (RPF) over the action associated with the reaction. The density-of-state SCTST has reframed the rate formula in terms of the instanton’s density of states (DoS). Here, we show the relationship between the RPF-SCTST and the DoS-SCTST and derive the latter from the former. In this way, we help unify these branches of SCTST and provide a clearer formalism for future advances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Gravitational wave background from mergers of large primordial black holes

The Peters formula, which tells how the coalescence time of a binary system emitting gravitational radiation is determined by the initial size and shape of the elliptic orbit, is often used in estimating the merger rate of primordial black holes and the gravitational wave background from the mergers. Valid as it is in some interesting scenarios, such as the analysis of the LIGO-Virgo events, the Peters formula fails to describe the coalescence time if the orbital period of the binary exceeds the value given by the formula. This could underestimate the event rate of mergers that occur before the cosmic time t ~ 10 13 s. As a result, the energy density spectrum of the gravitational wave background could develop a peak, which is from mergers occurring at either t ~ 10 13 s (for black holes with mass M ≳ 10 8 M ⊙ ) or t ~ 10 26 (M/M ⊙ ) -5/3 s (for 10 5 M ⊙ ≲ M ≲ 10 8 M ⊙ ). This can be used to constrain the fraction of dark matter in primordial black holes (denoted by f) if potential probes (such as SKA and U-DECIGO) do not discover such a background, with the result f ≲ 10 -6 –10 -4 for the mass range 10– 10 9 M ⊙ . Finally, we then consider the effect of mass accretion onto primordial black holes at redshift z ~ 10, and find that the merger rate could drop significantly at low redshifts. The spectrum of the gravitational wave background thus gets suppressed at the high-frequency end. This feature might be captured by future detectors such as ET and CE for initial mass M = Script $\mathcal{O}$(10–100) M ⊙ with f ≳ 10 -4 .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The role of supernova convection for the lower mass gap in the isolated binary formation of gravitational wave sources

ABSTRACT Understanding the astrophysical phenomena involving compact objects requires an insight about the engine behind the core-collapse supernovae (SNe) and the fate of the stellar collapse of massive stars. In particular, this insight is crucial in developing an understanding of the origin and formation channels of the growing populations of the detected black hole–black hole, black hole–neutron star, and neutron star–neutron star mergers. The time-scale of convection growth may have a large effect on the strength of SN explosion and therefore also on the mass distribution of stellar remnants. We adopt new formulas for the relation between the pre-SN star properties and their remnants and check how they impact the population of double compact object (DCO) mergers formed via the isolated binary evolution. The new formulas give one the ability to test a wide spectrum of assumptions on the convection growth time. In particular, the different variants allow for a smooth transition between having a deep mass gap and a remnant mass distribution filled by massive neutron stars and low-mass black holes. We present the distribution of masses, mass ratios, and the local merger rate densities of DCO for the different variants of new formulas and test them together with different approaches to other highly uncertain processes. We find that the mass distribution of DCO mergers is sensitive to the adopted assumption on the SN convection growth time-scale up to $m_1+m_2 \lesssim 35 \, \mathrm{M}_{\odot }$. Between the two extreme tested variants the probability of compact object formation within the mass gap may differ by up to approximately two orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Quantum Langevin theory for two coupled phase-conjugated electromagnetic waves

We provide a general macroscopic phenomenological formula of quantum Langevin equations for two coupled phase-conjugated electromagnetic fields with linear loss (gain) and complex nonlinear coupling coefficient. The macroscopic phenomenological formula is obtained from the coupling matrix to preserve the field commutation relations and correlations, which does not require knowing the microscopic details of light-matter interaction and internal atomic structures. To validate this phenomenological formula, we take spontaneous four-wave mixing in a double-Λ four-level atomic system as an example to numerically confirm that our macroscopic phenomenological result is consistent with that obtained from the microscopic Heisenberg-Langevin theory. We find that a complex-valued nonlinear coupling coefficient can lead to noises even without linear gain or loss. Lastly, we apply the quantum Langevin equations to study the effects of linear gain and loss, complex phase mismatching, as well as complex nonlinear coupling coefficient in entangled photon pair (biphoton) generation, particularly to their temporal quantum correlations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Strategies for simulating the time evolution of Hamiltonian lattice field theories

Simulating the time evolution of quantum field theories given some Hamiltonian H requires developing algorithms for implementing the unitary operator e -iHt . A variety of techniques exist that accomplish this task, with the most common technique used so far being Trotterization, which is a special case of the application of a product formula. However, other techniques exist that promise better asymptotic scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding. In this work we study the performance of such algorithms in simulating lattice field theories. We derive and compare the asymptotic gate complexities of several commonly used simulation techniques in application to Hamiltonian lattice field theories. Using the scalar $\hat{φ}$ 4 theory as a test, we also perform numerical studies and compare the gate costs required by product formulas and signal-processing-based techniques to simulate time evolution. For the latter, we use the linear combination of unitaries (LCU) construction augmented with the quantum Fourier transform circuit to switch between the field and momentum eigenbases, which leads to immediate order-of-magnitude improvement in the cost of preparing the block encoding. Further, this paper also includes a pedagogical review of the techniques used, in particular product formulas, LCU, qubitization, quantum signal processing, as well as the technique for simulating geometrically-local Hamiltonians developed by Haah, Hastings, Kothari, and Low.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution, and we show that it can suppress the PDF at large x . Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large x.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

On the Inductance of a Single-Channel Spark-Gap Switch for Pulsed Power Applications

In this paper, we derive an alternative expression for calculating the inductance of a single-channel spark-gap switch. We believe this new inductance expression provides greater clarity compared to other approaches. Interestingly, both the Rosa formula and the coaxial inductance formula, which are commonly used in such calculations, emerge as special cases of our new expression. To validate the proposed formula, we conducted COMSOL simulations that show excellent agreement with our theoretical predictions.

COMSOL↗
DOE OSTI2021

Extracting Resilience Metrics From Distribution Utility Data Using Outage and Restore Process Statistics

Resilience curves track the accumulation and restoration of outages during an event on an electric distribution grid. We show that a resilience curve generated from utility data can always be decomposed into an outage process and a restore process and that these processes generally overlap in time. We use many events in real utility data to characterize the statistics of these processes, and derive formulas based on these statistics for resilience metrics such as restore duration, customer hours not served, and outage and restore rates. The formulas express the mean value of these metrics as a function of the number of outages in the event. We also give a formula for the variability of restore duration, which allows us to predict a maximum restore duration with 95% confidence. Overall, we give a simple and general way to decompose resilience curves into outage and restore processes and then show how to use these processes to extract resilience metrics from standard distribution system data.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Fast and Accurate Intersections on a Sphere

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.

Environmental sciences↗
DOE OSTI2021

Exact multi-instanton solutions to self-dual Yang–Mills equation on curved spaces

We find exact multi-instanton solutions to the self-dual Yang–Mills equation on a large class of curved spaces with SO(3) isometry, generalizing the results previously found on R 4 . Here, the solutions are featured with explicit multi-centered expressions and topological properties. As examples, we demonstrate the approach on several different curved spaces, including the Einstein static universe and R × dS$^{E}_{3}$, and show that the exact multi-instanton solutions exist on these curved backgrounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Review of Particle Physics

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,200 new measurements from 903 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 118 reviews are updated, including many that are heavily revised.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Emergence of quantum-field theory in causal diamonds

The experimental successes of quantum-field theory do not justify using it to describe even a finite fraction of the entanglement entropy of a causal diamond with its exterior, in the limit of large diamonds. Susskind and Uglum and Jacobson conjectured that this divergent entropy could be thought of as a renormalization of Newton’s constant in the Bekenstein–Hawking formula, if we applied that formula to arbitrary causal diamonds. Jacobson showed that this leads to a derivation of the null projection of Einstein’s equations as the hydrodynamic equations of the area law for arbitrary diamonds, a derivation which has the added virtue of demonstrating that the cosmological constant is not an energy density. Using a gauge choice adapted to causal diamond boundaries, we revisit arguments of Carlip and Solodukhin that the proper theory of near horizon states is a (cut-off) (1 + 1)-dimensional conformal field theory, with central charge proportional to the transverse area. This leads to a universal formula for fluctuations of the modular Hamiltonian of a diamond, which we argue is compatible with the explanation of the temperature of de Sitter space in terms of an identification between localized energy and the number of constrained q-bits of the holographic degrees of freedom.

Astronomy & Astrophysics↗
DOE OSTI2024

Origin of the arrow of time in quantum mechanics

We point out that time’s arrow is naturally induced by quantum mechanical evolution, whenever the systems have a very large number [Formula: see text] of nondegenerate states and a Hamiltonian bounded from below. When [Formula: see text] is finite, the arrow is imperfect, since evolution can resurrect past states. In the limit [Formula: see text] the arrow is fixed by the “tooth of time”: the decay of excited states induced by spontaneous emission to the ground state, mediated by interactions and a large number of decay products which carry energy and information to infinity. This applies to individual isolated atoms, and does not require a coupling to a separate large heath bath.

Astronomy & Astrophysics↗
DOE OSTI2021

Lower bound for the neutrino magnetic moment from kick velocities induced at the birth of neutron stars

We show that the neutrino chirality flip, which can take place in the core of a neutron star at birth, is an efficient process to allow neutrinos to anisotropically escape, thus providing a to induce the neutron star kick velocities. The process is not subject to the no-go theorem since although the flip from left- to right-handed neutrinos happens at equilibrium, the reverse process does not take place given that right-handed neutrinos do not interact with matter and therefore detailed balance is lost. For simplicity, we model the neutron star core as being made of strange quark matter. We find that the process is efficient when the neutrino magnetic moment is not smaller than [Formula: see text], where [Formula: see text] is the Bohr magneton. When this lower bound is combined with the most stringent upper bound, which uses the luminosity data obtained from the analysis of SN 1987A, our results set a range for the neutrino magnetic moment given by [Formula: see text]. The obtained kick velocities for natal conditions are consistent with the observed ones and span the correct range of radii for typical magnetic field intensities.

Physics↗