Search NASA⌕ Search

SEARCH · Search NASA

Results for “ADIABATIC APPROXIMATION”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

Adiabatic Gravitational Waveform Model for Compact Objects Undergoing Quasi-Circular Inspirals Into Rotating Massive Black Holes

We present bhpwave: a new python-based, open-source tool for generating the gravitational waveforms of stellar-mass compact objects undergoing quasicircular inspirals into rotating massive black holes. These binaries, known as extreme-mass-ratio inspirals (EMRIs), are exciting mHz gravitational wave sources for future space-based detectors such as the Laser Interferometer Space Antenna (LISA). Relativistic models of EMRI gravitational wave signals are necessary to unlock the full scientific potential of mHz detectors, yet few open-source EMRI waveform models exist. Thus we built bhpwave, which uses the adiabatic approximation from black hole perturbation theory to rapidly construct gravitational waveforms based on the leading-order inspiral dynamics of the binary. In this work, we present the theoretical and numerical foundations underpinning bhpwave. We also demonstrate how bhpwave can be used to assess the impact of EMRI modeling errors on LISA gravitational wave data analysis. In particular, we find that for retrograde orbits and slowly spinning black holes we can mismodel the gravitational wave phasing by as much as ∼10 radians without significantly biasing EMRI parameter estimation.

Zachary Nasipak↗
DOE OSTI2016

Examining the effect of nonlocality in ( d , n ) transfer reactions

In the last year we have been exploring the effect of the explicit inclusion of nonlocality in (d,p) reactions. The goal of this work is to extend previous studies to (d,n) reactions, which, although similar to (d,p), have specific properties that merit inspection. We apply our methods (both the distorted wave Born approximation and the adiabatic wave approximation) to (d; n) reactions on 16 O, 40 Ca, 48 Ca, 126 Sn, 132 Sn, and 208 Pb at 20 and 50 MeV. As a result, we look separately at the modifications introduced by nonlocality in the final bound and scattering states, as well as the consequences reflected on the differential angular distributions. The cross sections obtained when using nonlocality explicitly are significantly different than those using the local approximation, just as in (d,p). Due to the particular role of Coulomb in the bound state, often we found the effects of nonlocality to be larger in (d,n) than in (d,p). In conclusion, our results con rm the importance of including nonlocality explicitly in deuteron-induced reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2010

Optical Tapers as White-Light WGM Resonators

A theoretical analysis has revealed that tapered optical waveguides could be useful as white-light whispering-gallery-mode (WGM) optical resonators. The compactness and the fixed-narrow-frequency-band nature of the resonances of prior microdisk and microsphere WGM resonators are advantageous in low-power, fixed-narrow-frequency-band applications. However for optical-processing applications in which there are requirements for power levels higher and/or spectral responses broader than those of prior microdisk and microsphere WGM resonators, white-light WGM resonators in the form of optical tapers would be preferable. The theoretical analysis was performed for a multimode, axisymmetric, circular-cross-section waveguide having a taper sufficiently smooth and gradual to justify the approximation of adiabaticity. In this approximation, the equation for the dependence of the electromagnetic field upon the axial (longitudinal) waveguide coordinate can be separated from the equation for the dependence upon the radius and the azimuthal angle.

Strekalov, Dmitry V.↗
NASA NTRS1979

Relativistic blast waves in two dimensions. I - The adiabatic case

Approximate solutions are presented for the dynamical evolution of strong adiabatic relativistic blast waves which result from a point explosion in an ambient gas in which the density varies both with distance from the explosion center and with polar angle in axisymmetry. Solutions are analytical or quasi-analytical for the extreme relativistic case and numerical for the arbitrarily relativistic case. Some general properties of nonplanar relativistic shocks are also discussed, including the incoherence of spherical ultrarelativistic blast-wave fronts on angular scales greater than the reciprocal of the shock Lorentz factor, as well as the conditions for producing blast-wave acceleration.

Shapiro, P. R.↗
DOE OSTI2024

Semiclassical theory of bipolaronic superconductivity in a bond-modulated electron-phonon model

We analyze the transition temperature T c of bipolaronic superconductivity in a bond Su-Schrieffer-Heeger (bond-SSH) model—also known as a bond Peierls model—where the electron hoppings are modulated by bond phonons. Using a semiclassical instanton approximation justifiable in the adiabatic limit of slow phonons, we find that the bipolaron mass is only weakly enhanced, in contrast to the typical large mass enhancement found in standard (Holstein) electron-phonon models. Specifically, in the strong coupling limit, the bipolarons can freely slide within a degenerate manifold rather than become self-trapped. A gas of these bipolarons can undergo a superfluid transition at a critical temperature for which we obtain an upper bound. We find that this bound is exponentially larger than that in the Holstein model. In conclusion, our study provides an analytical understanding of the mechanism behind the high-T c bipolaronic superconductivity numerically observed in [Phys. Rev. X 13, 011010 (2023)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Temperature dependence of the electronic structure of semiconductors and insulators

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Adiabatic description of nonspherical quantum dot models

Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size, making use of the complete sets of exact and adiabatic quantum numbers in appropriate analytic approximations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Cumulative effects in inflation with ultra-light entropy modes

In multi-field inflation one or more non-adiabatic modes may become light, potentially inducing large levels of isocurvature perturbations in the cosmic microwave background. If in addition these light modes are coupled to the adiabatic mode, they influence its evolution on super horizon scales. Here we consider the case in which a non-adiabatic mode becomes approximately massless (''ultralight') while still coupled to the adiabatic mode, a typical situation that arises with pseudo-Nambu-Goldstone bosons or moduli. This ultralight mode freezes on super-horizon scales and acts as a constant source for the curvature perturbation, making it grow linearly in time and effectively suppressing the isocurvature component. We identify a Stückelberg-like emergent shift symmetry that underlies this behavior. As inflation lasts for many e -folds, the integrated effect of this source enhances the power spectrum of the adiabatic mode, while keeping the non-adiabatic spectrum approximately untouched. In this case, towards the end of inflation all the fluctuations, adiabatic and non-adiabatic, are dominated by a single degree of freedom.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3

Accurate modeling of optical spectra requires careful treatment of the molecular structures and vibronic, environmental, and thermal contributions. The accuracy of the computational methods used to simulate absorption spectra is limited by their ability to account for all the factors that affect the spectral shapes and energetics. The ensemble-based approaches are widely used to model the absorption spectra of molecules in the condensed-phase, and their performance is system dependent. The Franck–Condon approach is suitable for simulating high resolution spectra of rigid systems, and its accuracy is limited mainly by the harmonic approximation. In this work, the absorption spectrum of the widely used cyanine Cy3 is simulated using the ensemble approach via classical and quantum sampling, as well as, the Franck–Condon approach. The factors limiting the ensemble approaches, including the sampling and force field effects, are tested, while the vertical and adiabatic harmonic approximations of the Franck–Condon approach are also systematically examined. Our results show that all the vertical methods, including the ensemble approach, are not suitable to model the absorption spectrum of Cy3, and recommend the adiabatic methods as suitable approaches for the modeling of spectra with strong vibronic contributions. We find that the thermal effects, the low frequency modes, and the simultaneous vibrational excitations have prominent contributions to the Cy3 spectrum. The inclusion of the solvent stabilizes the energetics significantly, while its negligible effect on the spectral shapes aligns well with the experimental observations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Uncertainty quantification due to optical potentials in models for ( d , p ) reactions

Recent work has studied the uncertainty in predictions for $A(d,p)B$ reactions using the distorted-wave Born approximation (DWBA), coming from the parametrization of the effective $dA$ interactions [Lovell et al. Phys. Rev. C 95, 024611 (2017)]. There are different levels of sophistication in reaction theories for one-nucleon transfer reactions, including the adiabatic wave approximation (ADWA) which takes deuteron breakup into account to all orders. In this paper, we quantify the uncertainties associated with the ADWA method that come from the parametrization of the NA interactions and compare ADWA with DWBA. Similar to Lovell et al., we use nucleon elastic-scattering data on a wide variety of targets at the appropriate incoming and outgoing energies to constrain the optical potential input to the ADWA theory. Pulling from the χ 2 distribution, we obtain 95% confidence bands for the elastic distributions. From the resulting parameters, we predict 95% confidence bands for the ( d , p ) transfer cross sections. Results obtained with the standard uncorrelated χ 2 are compared to those using the correlated χ 2 of Lovell et al. We also repeat the DWBA calculations for the exact same reactions for comparison purposes. We find that NA elastic-scattering data provide a significant constraint to the interactions, and, when the uncertainties are propagated to the transfer reactions using ADWA, predictions are consistent with the transfer data. The angular distributions for ADWA differ from those predicted by DWBA, particularly at small angles. As in Lovell et al., confidence bands obtained using the uncorrelated χ 2 function are unrealistically narrow and become much wider when the correlated χ 2 function is considered. For most cases, the uncertainty bands obtained in ADWA are narrower than DWBA when using elastic data of similar quality and range. However, given the large uncertainties predicted from the correlated χ 2 function, at this point, the transfer data cannot discriminate between these two methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Validity of the Born-Oppenheimer approximation in the indirect-dissociative-recombination process

An alternative method is introduced to solve a simple two-dimensional model describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of freedom. The two-dimensional R matrix can be constructed simultaneously on the electronic and nuclear surfaces using all three forms developed previously for electron-atom and electron-molecule collisions. These are the eigenchannel R-matrix form, inversion technique of Nesbet and Robicheaux, and the Wigner-Eisenbud-type form using expansion over the poles of the symmetrized Hamiltonian. The 2D R-matrix method is employed to solve a simple model tailored to describe the dissociative recombination and the vibrational excitation of H 2 + cation in the singlet ungerade symmetry 1 Σ u . These results then serve as a (near-exact) benchmark for the following calculation in which the R-matrix states are replaced by their Born-Oppenheimer approximations. Furthermore, the accuracy of this approach and its correction with the first-order nonadiabatic couplings are discussed.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Vibrationally resolved cross sections for proton collisions with hydrogen molecules

The semi-classical molecular convergent close-coupling approach has been applied to proton collisions with molecular hydrogen in the ground electronic and vibrational state. Cross sections for electron loss and electron capture agree well with the experimental data in the intermediate energy range where coupling between electronic reaction channels is strong and previously available calculations produce inconsistent results. Results for elastic scattering and total excitation are compared with effective one-electron coupled-channel calculations, showing that accurate target structure makes an important difference to these cross sections at intermediate energies. The excitation cross sections are calculated using both the fixed-nuclei and adiabatic-nuclei approximations for transitions from the $X^1Σ^+_{\textrm{g}}$ state to the $B^1Σ^+_{\textrm{u}}$, $B'$$^1Σ^+_{\textrm{u}}$, $B''$$^1Σ^+_{\textrm{u}}$, $EF$$^1Σ^+_{\textrm{g}}$, $GK$$^1Σ^+_{\textrm{g}}$, $H$$^1Σ^+_{\textrm{g}}$, $C$$^1Π_{\textrm{u}}$, $D$$^1Π_{\textrm{u}}$, $D'$$^1Π_{\textrm{u}}$, $I$$^1Π_{\textrm{u}}$, and $J$$^1Δ_{\textrm{g}}$ states for proton energies from to keV. We find significant differences between the present ab initio calculations and the equivelocity scaled electron-scattering data that is currently used for collisional-radiative modelling. Furthermore, the adiabatic-nuclei calculations enable us to resolve the final vibrational level after excitation, producing a complete set of cross sections for excitation of ground-state molecular hydrogen for all electronic states up to $n = 3$, where $n$ is the united-atoms-limit principle quantum number.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter

Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. In conclusion, we compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1984

Scattering of electrons from neon atoms

Scattering of electrons from neon atoms is investigated by the polarized-orbital method. The perturbed orbitals calculated with use of the Sternheimer approximation lead to the polarizability 2.803 a(0)-cube in fairly good agreement with the experimental value 2.66 a(0)-cube. Phase shifts for various partial waves are calculated in the exchange, exchange-adiabatic, and polarized-orbital approximations. They are compared with the previous results. The calculated elastic differential, total, and momentum-transfer cross sections are compared with the experimental results. The polarized-orbital approximation yields results which show general improvement over the exchange-adiabatic approximation.

Dasgupta, A.↗
DOE OSTI2014

Braiding fluxes in Pauli Hamiltonian

Aharonov and Casher showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under the slow motion of N fluxons with fluxes Φ{sub a}∈R. The positions, r{sub a}∈R{sup 2}, of the fluxons are viewed as controls. We are interested in the holonomies associated with closed paths in the space of controls. The holonomies can sometimes be abelian, but in general are not. They can sometimes be topological, but in general are not. We analyse some of the special cases and some of the general ones. Our most interesting results concern the cases where holonomy turns out to be topological which is the case when all the fluxons are subcritical, Φ{sub a}<1, and the number of zero modes is D=N−1. If N≥3 it is also non-abelian. In the special case that the fluxons carry identical fluxes the resulting anyons satisfy the Burau representations of the braid group.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗