Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “BORN 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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Improved master equation approach to quantum transport: From Born to self-consistent Born approximation

Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Validity of the Born approximation for beyond Gaussian weak lensing observables

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ 3 ) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ 4 ) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Various facets of magnetic charge correlation: Micromagnetic and distorted-wave Born approximation simulations study

The emergent concept of the magnetic charge quasiparticle provides a new realm to study the evolution of magnetic properties in two-dimensional artificially frustrated magnets. Here we report on the exploration of magnetic phases due to various magnetic charge correlation using the complementary numerical techniques of micromagnetic and distorted-wave Born approximation simulations in artificial permalloy honeycomb lattice. The honeycomb element length varies between 10 nm and 100 nm, while the width and thickness are kept within the single domain limit. In addition to the charge ordered loop state, we observe disordered charge arrangement, characterized by the random distribution of ±Q charges, in single domain size honeycomb lattice. As the length of the honeycomb element increases, low multiplicity magnetic charges tend to form contiguous bands in thinner lattice. Thin honeycomb lattice with 100 nm element length exhibits a perfect spin ice pattern, which remains unaffected by the modest increase in the width of element size. We simulate scattering profiles under the pretext of distorted-wave Born approximation formalism for the micromagnetic phases. The results are expected to provide useful guidance in the experimental investigation of magnetic phases in an artificial honeycomb magnet.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

CMB-lensing beyond the Born approximation

We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles ℓ ∼< 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Onsets of hierarchy truncation and self–consistent Born approximation with quantum mechanics prescriptions invariance

The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self–consistent–Born–approximation improvements, should be transferable to their Heisenberg–picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only about how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

CMB weak-lensing beyond the Born approximation: a numerical approach

We perform a complete study of the gravitational lensing effect beyond the Born approximation on the Cosmic Microwave Background (CMB) anisotropies using a multiple-lens raytracing technique through cosmological N-body simulations of the DEMNUni suite. The impact of second-order effects accounting for the non-linear evolution of large-scale structures is evaluated propagating for the first time the full CMB lensing jacobian together with the light rays trajectories. We carefully investigate the robustness of our approach against several numerical effects in the raytracing procedure and in the N-body simulation itself, and find no evidence of large contaminations. We discuss the impact of beyond-Born corrections on lensed CMB observables, and compare our results with recent analytical predictions that appeared in the literature, finding a good agreement, and extend these results to smaller angular scales. We measure the gravitationally-induced CMB polarization rotation that appears in the geodesic equation at second order, and compare this result with the latest analytical predictions. We then present the detection prospect of beyond-Born effects with the future CMB-S4 experiment. We show that corrections to the temperature power spectrum can be measured only if a good control of the extragalactic foregrounds is achieved. Conversely, the beyond-Born corrections on E and B-modes power spectra will be much more difficult to detect.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ 2 = (2) 2 and (71) 2 Å 2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of q z = 0.05 and 0.10 Å −1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both q z values simultaneously, that is, identical fitting parameters were applied at both values of q z . The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for q z = 0.04, 0.05, and 0.06 Å −1 . Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of q z . Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Three-body Faddeev equations in two-particle Alt-Grassberger-Sandhas form with Distorted-Wave-Born-approximation amplitudes as effective potentials

A(d, p)B reactions on heavier nuclei are peripheral at sub-Coulomb energies and can be peripheral even at energies above the Coulomb barrier due to the presence of the distorted waves in the initial and final channels. Usually, to analyze such reactions the distorted-wave-Born-approximation (DWBA) is used. The DWBA amplitude for peripheral reactions is parametrized in terms of the asymptotic normalization coefficient (ANC) of the bound state B = (n A). However, in the DWBA, the coupling of the different channels is not taken into account explicitly. The three-body Faddeev equations written as the two-particle Alt-Grassberger-Sandhas (AGS) equations are very suitable for the analysis of the A(d, p)B reactions because they take into account explicitly the coupling of the different channels. It is well known that the overall normalization of the DWBA amplitude or even of the more advanced continuum-discretized coupled channels (CDCC) amplitude for peripheral reactions (both sub-Coulomb and above the Coulomb barrier) is determined by the ANC. However, it is not apparent that it is the case for the AGS solution due to the coupling of the (d, p) channel to other channels. In this paper, it is proved that the sub-Coulomb A(d, p)B reaction amplitude, which is a solution of the two-body AGS equations, is peripheral and is parametrized in terms of the ANC of the bound state B = (nA) if the corresponding DWBA amplitude is peripheral. Both nonlocal separable and local nuclear interaction potentials between the constituent particles are considered. To prove the peripheral character of the AGS amplitude for the sub-Coulomb A(d, p)B reactions the effective potentials are expressed in terms of the corresponding sub-Coulomb DWBA amplitudes of the different channels. The analysis of the A(d, p)B reactions above the Coulomb barrier requires the inclusion of the optical potentials. Hence, to analyze such reactions, the AGS equations are generalized by including the optical nuclear potentials in the same manner as it is done in the DWBA. The obtained AGS equations contain the DWBA effective potentials with distorted waves generated by the sum of the nuclear optical and the channel Coulomb potentials. It is shown that if the DWBA amplitude is peripheral than it is also the case for the AGS amplitude, which is also parametrized in terms of the ANC of the bound state B = (nA). Furthermore, the inclusion of the coupling of the different channels in the AGS formalism allows one to improve the treatment of the peripheral sub-Coulomb and above the Coulomb (d, p) reactions compared to the DWBA and CDCC method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

FINITE-ELEMENT DISTORED WAVE BORN APPROXIMATION FOR SURFACE SCATTERING

FE-DWBA is a software package that computes the x-ray scattering patterns of objects that locate on a surface or buried next to a surface, such as the nano-circuits and nano-patterns of the mask used in the extreme ultraviolet lithography. It can incorporate the dynamical scattering effect (photons scattered multiple times), which is predominant in surface scattering and yield high-fidelity scattering patterns. The application includes surface imaging using x-rays, and critical dimension determination for semiconductor manufacturing.

HU, MAIOQI↗
DOE OSTI2014

On the mathematical treatment of the Born-Oppenheimer approximation

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Electronic structure and optical properties of quantum crystals from first principles calculations in the Born–Oppenheimer approximation

In this work, we develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born–Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron–ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born–Oppenheimer approximation. Based on the Kubo–Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Magnetoconductivity in Weyl semimetals: Effect of chemical potential and temperature

This work presents detailed analyses of magnetoconductivities in a Weyl semimetal within the Born and self-consistent Born approximations. In the presence of charged impurities, linear magnetoresistance can occur when the charge carriers are mainly from the zeroth (n = 0) Landau level. Interestingly, the linear magnetoresistance is very robust against changes of temperature as long as the charge carriers come mainly from the zeroth Landau level. We denote this parameter regime as the high-field regime. In contrast, the linear magnetoresistance disappears once the charge carriers from the higher Landau levels can provide notable contributions. Our analysis indicates that the deviation from linear magnetoresistance is mainly due to the deviation of the longitudinal conductivity from 1/B behavior. We discovered two important features of the self-energy approximation: (i) A dramatic jump of σ xx , when the n = 1 Landau level begins to contribute charge carriers, which is the beginning point of the middle-field regime, when decreasing the external magnetic field from high field; (ii) in the low-field regime, σ xx exhibits B -5/3 behavior, causing the magnetoresistance ρ xx to exhibit B 1/3 behavior. A detailed and careful numerical calculation indicates that the self-energy approximation (including both the Born and the self-consistent Born approximations) does not explain the recent experimental observation of linear magnetoresistance in Weyl semimetals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Three-dimensional imaging using coherent x rays at grazing incidence geometry

We have developed a three-dimensional coherent diffraction imaging algorithm to retrieve phases of diffraction patterns of samples in grazing incidence small angle x-ray scattering experiments. The algorithm interprets the diffraction patterns using the distorted-wave Born approximation instead of the Born approximation, as in this case, the existence of a reflected beam from the substrate causes the diffraction pattern to deviate significantly from the simple Fourier transform of the object. Detailed computer simulations show that the algorithm works. Verification with real experiments is planned.

Yang, Yi↗
DOE OSTI2016

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Reexamining the high-order harmonic generation of HD molecule in non-Born-Oppenheimer approximation

The high-order harmonic generation of the HD molecule is studied in non-Born-Oppenheimer approximation. It is found that there are only the odd harmonics in the harmonic spectrum of the HD molecule though the generation of even harmonics is possible in principle. Theoretical analysis [T. Kreibich et al., Phys. Rev. Lett. 87, 103901 (2001)] reveals that the nuclear dipole moment can contribute to the generation of the even harmonics, but the acceleration of the nucleus is about three orders of magnitude less than that of the electron. Hence, the even harmonics cannot be observed in the harmonic spectrum of the HD molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations

We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed by Iles-Smith et al. [Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Electron impact excitation of helium in Debye plasma

The probability, differential, and integral scattering cross sections of the 1{sup 1}S→2{sup 1}S and 1{sup 1}S→2{sup 1}P transitions of helium have been calculated in the first Born approximation. The projectile-target interactions depending on the temperature and the density of plasma are described by the Debye-Hückel model. Wave functions of the target before and after collision were modeled by non orthogonal Hartree-Fock orbitals. The wave functions parameters are calculated with the Ritz variational method. We improve our unscreened first Born approximation integral cross sections by using the BE-scaled (B stands for binding energy and E excitation energy) method. The second Born approximation has also been used to calculate the excitation cross sections in Debye plasma. Our calculations are compared to other theoretical and experimental results where applicable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗