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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Faster spectral density calculation using energy moments

Abstract Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate the recently proposed Gaussian Integral Transform technique in terms of Fourier moments of the system Hamiltonian which can be computed efficiently on a quantum computer. One of the main advantages of this framework is that it allows for an important reduction of the computational cost by exploiting previous knowledge about the energy moments of the spectral density. For a simple model of medium mass nucleus like $$^{40}$$ 40 Ca and target energy resolution of 1 MeV we find an expected speed-up of $$\approx 125$$ ≈ 125 times for the calculation of the giant dipole response and of $$\approx 50$$ ≈ 50 times for the simulation of quasi-elastic electron scattering at typical momentum transfers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1981

On the power spectral density of quadrature modulated signals

The conventional (no-offset) quadriphase modulation technique suffers from the fact that hardlimiting will restore the frequency sidelobes removed by proper filtering. Thus, offset keyed quadriphase modulation techniques are often proposed for satellite communication with bandpass hardlimiting. A unified theory is developed which is capable of describing the power spectral density before and after the hardlimiting process. Using the in-phase and the quadrature phase channel with arbitrary pulse shaping, analytical results are established for generalized quadriphase modulation. In particular MSK, OPSK or the recently introduced overlapped raised cosine keying all fall into this general category. It is shown that for a linear communication channel, the power spectral density of the modulated signal remains unchanged regardless of the offset delay. Furthermore, if the in phase and the quadrature phase channel have identical pulse shapes without offset, the spectrum after bandpass hardlimiting will be identical to that of the conventional QPSK modulation. Numerical examples are given for various modulation techniques. A case of different pulse shapes in the in phase and the quadrature phase channel is also considered.

Yan, T. Y.↗
NASA NTRS2009

Power Spectral Density Specification and Analysis of Large Optical Surfaces

The 2-dimensional Power Spectral Density (PSD) can be used to characterize the mid- and the high-spatial frequency components of the surface height errors of an optical surface. We found it necessary to have a complete, easy-to-use approach for specifying and evaluating the PSD characteristics of large optical surfaces, an approach that allows one to specify the surface quality of a large optical surface based on simulated results using a PSD function and to evaluate the measured surface profile data of the same optic in comparison with those predicted by the simulations during the specification-derivation process. This paper provides a complete mathematical description of PSD error, and proposes a new approach in which a 2-dimentional (2D) PSD is converted into a 1-dimentional (1D) one by azimuthally averaging the 2D-PSD. The 1D-PSD calculated this way has the same unit and the same profile as the original PSD function, thus allows one to compare the two with each other directly.

wavefront↗
DOE OSTI2024

Dirac spectral density in N f = 2 + 1 QCD at T = 230 MeV

We compute the renormalized Dirac spectral density in N f = 2 + 1 QCD at physical quark masses, temperature T = 230 MeV , and system size L s = 3.4 fm . To that end, we perform a pointwise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of the Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a nontrivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical, (ii) improve the upper bound for IR phase transition temperature T IR so that the new window is 200 < T IR < 230 MeV , and (iii) are consistent with the nonrestoration of anomalous U A ( 1 ) symmetry (chiral limit) below T = 230 MeV . Published by the American Physical Society 2024

Alexandru, Andrei (ORCID:0000000345471554)↗
NASA NTRS1982

The power spectral density of digital modulations transmitted over nonlinear channels

This paper examines by analytical methods the power spectral densities of digital modulations (in particular, staggered and unstaggered quadrature modulations) passed through band-limited nonlinear channels. Previously observed (by computer simulation or hardware measurement) behavior of such spectra with regard to the suppression or restoration of its sidelobes after passing through the nonlinearity is verified analytically. Several examples corresponding to specific quadrature modulations and filter-nonlinearity combinations are presented as illustrations of the general results.

Divsalar, D.↗
NASA NTRS1980

Hamiltonian indices and rational spectral densities

Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

Byrnes, C. I.↗