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A technique for fitting a straight line to a collection of data points is given. The relationships between the slopes and correlation coefficients, and between the corresponding standard deviations and correlation coefficient are given.
The complicated ways in which electrons interact in many-body systems such as molecules and materials have long been viewed through the lens of local electron correlation and associated correlation functions. However, quantum information science has demonstrated that more global diagnostics of quantum states like the entanglement entropy can provide a complementary and clarifying lens on electronic behavior. One particularly useful measure that can be used to distinguish between quantum and classical sources of entanglement is the accessible entanglement, the entanglement available as a quantum resource for systems subject to conservation laws, such as fixed particle number, due to superselection rules. In this work, we introduce an algorithm and demonstrate how to compute accessible and symmetry-resolved entanglements for interacting fermion systems. This is accomplished by combining an incremental version of the swap algorithm with a recursive auxiliary field quantum Monte Carlo algorithm recently developed by the authors. We apply these tools to study the pairing and charge density waves exhibited in the paradigmatic attractive Hubbard model via entanglement. We find that the particle and spin symmetry-resolved entanglements and their related full probability distribution functions show very clear—and unique—signatures of the underlying electronic behavior even when those features are less pronounced in conventional correlation functions. Altogether, this work provides a systematic means of characterizing the entanglement within quantum systems that can grant a deeper understanding of the complicated electronic behavior that underlies quantum phase transitions and crossovers in many-body systems.
Raman spectroscopy is a widely utilized method for determining information about the solvate species present in electrolyte solutions. Difficulties arise, however, when interpreting the Raman data in terms of correlating the spectroscopic vibrational bands with specific solvate species. Examples are provided to demonstrate how erroneous conclusions may be drawn with regard to the identity and population (distribution) of the solvent-separated ion pair (SSIP), contact ion pair (CIP) and aggregate (AGG) solvate species frequently mentioned in the scientific literature.
In order to study the relation between zone and the atmospheric circulation on a global scale the global correlation has been computed between TOMS total ozone measurements from NIMBUS-7 satellite and collocated geopotential heights analysis at all mandatory pressure levels between 1000-50 mb. The heights are obtained from the 4 deg x 5 deg GLAS analysis that uses both conventional (rawinsonde) and the operational TIROS-N satellite soundings but no ozone data. Zonal averages have been substracted to eliminate the correlation due merely to latitudinal dependence, and emphasize the correlation associated with synoptic features. Tables are presented with correlation coefficients for the four synoptic times covering the Pacific Ocean, Asia, Europe and the Atlantic Ocean, and United States regions. These coverages are approximate since NIMBUS-7 does not observe exactly the same region each day.
Results of an autocorrelation analysis of the Mariner 2 data concerning solar-wind speed obtained in late 1962. A statistically significant correlation associated with the solar rotation has been found near a lag of 27 days; however, the amplitude of the correlation is only about 0.4, in essential agreement with measurements of Vela 2 and 3 during the period from July 1964 to July 1967. The relatively modest correlation is interpreted to mean that a number of speed structures observed by Mariner 2 did not endure for more than one solar rotation; those structures that did endure evolved significantly in shape, amplitude, and solar longitude from one solar rotation to the next. The analysis also shows that typical solar-wind structures occupied about 30 to 45 deg in solar longitude near 1 AU.
Understanding multiple lengthscale correlations in the pair distribution functions (PDFs) of aq. electrolytes is a persistent challenge. Here, the coordination chemistry of polyoxoanions supports an ion-network of cation-coordination polyhedra in NaNO 3(aq) and NaNO 2(aq) that induce long-range solution structure. Further, oxygen correlations associated with Na + -coordination polyhedra have two characteristics lengthscales; 3.5–5.5 Å and 5.5–7.5 Å, the latter solely associated oligomers. The PDF contraction between 5.5–7.5 Å observed in many electrolytes is attributed to the distinct O···O correlation found in dimers and dimer subunits within oligomers.
The two-year experimental project has been completed to update the Airborne Release and Respirable Fraction (ARF and RF) estimates from the free-fall spills of liquid waste simulants. The objectives of the project at the Savannah River National Laboratory (SRNL) are to: (1) establish a technically defensible bounding approach for a reasonably conservative limit to the fall height used in the Ballinger correlation for the ARF, such that spill heights for near-water density liquid solutions above a critical height result in the same value of the ARF; and (2) provide a revised technical basis and data to support the ARF and RF correlation for free-fall liquid spills of heights from 1 to 10 meters. After peer review, these data and associated correlation will be available for consideration in a revision to DOE-HDBK-3010, Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear Facilities.
We perform ab initio nuclear lattice calculations of the neutron-rich carbon and oxygen isotopes using high-fidelity chiral interactions. We find good agreement with the observed binding energies and compute correlations associated with each two-nucleon interaction channel. For the isospin T = 1 channels, we show that the dependence on T z provides a measure of the correlations among the extra neutrons in the neutron-rich nuclei. For the spin-singlet S-wave channel, we observe that any paired neutron interacts with the nuclear core as well as its neutron pair partner, while any unpaired neutron interacts primarily with only the nuclear core. For the other partial waves, the correlations among the extra neutrons grow more slowly and smoothly with the number of neutrons. These general patterns are observed in both the carbon and oxygen isotopes and may be universal features that appear in many neutron-rich nuclei.
Here, the multiphase transport model is used to investigate the longitudinal broadening of the transverse momentum two-particle correlator C 2 (Δη,Δφ), and its utility to extract the specific shear viscosity, η/s, of the quark-gluon plasma formed in ultrarelativistic heavy ion collisions. The results from these model studies indicate that the longitudinal broadening of C 2 (Δη,Δφ) is sensitive to the value of η/s. However, reliable extraction of the longitudinal broadening of the correlator requires the suppression of possible self-correlations associated with the definition of the collision centrality.
Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.
This study demonstrates how the large concentration fluctuations of polymeric liquids under deformation and flow can be quantitatively studied by applying the spherical harmonic expansion technique to small-angle neutron scattering. Using a series of binary polymer blends, it is shown that the emergence of the so-called butterfly patterns is caused by the change of sign in the leading anisotropic component of the small-angle spectrum, when the scattering is dominated by intermolecular correlation associated with flow-induced demixing. The increasing spatial fluctuations of concentration are evidenced by the enhancement of the isotropic component of the scattering spectrum in the zero-angle limit and peak shift of the leading anisotropic coefficients toward low Q. Additionally, the spherical harmonic expansion framework permits real-space analysis of anisotropic scattering length density correlation in a convenient form. The methodology described in this work provides a concrete venue for quantitative studies of phase behavior of fluids under deformation and flow via small-angle scattering techniques, where mainly qualitative approaches were previously employed.
Methods from Quantum Information Theory are used to scrutinize quantum correlations encoded in the two-quark density matrix over light-cone momentum fractions x 1 and x 2 . A nonperturbative three quark model light-cone wavefunction predicts significant nonclassical correlations associated with the “entanglement negativity” measure for asymmetric and small quark momentum fractions. We perform one step of QCD scale evolution of the entire density matrix, not just its diagonal (dPDF), by computing collinearly divergent corrections due to the emission of a gluon. Finally, we present first qualitative numerical results for single-step scale evolution of quantum entanglement correlations in double quark PDFs. At a higher Q 2 scale, the nonclassical correlations manifest in the dPDF for nearly symmetric momentum fractions.
Electronic correlations associated with incipient magnetism have long been recognized as an important factor in stabilizing the largest atomic volume δ phase of plutonium, although their strength compared to those in the rare earths and neighboring actinides in the periodic table has largely remained a mystery. We show here using calorimetry measurements, together with prior detailed measurements of the phonon dispersion, that the 5f electrons of the δ phase reside in a pseudogapped state, accompanied by reductions in various physical properties below a characteristic temperature T* ≈ 100 K. The small characteristic energy scale of the pseudogapped state implies that the 5f electrons in plutonium are much closer to the threshold for localization and magnetic order than has been suggested by state-of-the-art electronic structure theory, revealing plutonium to be arguably the most strongly correlated of the elements.
Much of the structure of cosmological correlators is controlled by their singularities, which in turn are fixed in terms of flat-space scattering amplitudes. An important challenge is to interpolate between the singular limits to determine the full correlators at arbitrary kinematics. This is particularly relevant because the singularities of correlators are not directly observable, but can only be accessed by analytic continuation. In this paper, we study rational correlators — including those of gauge fields, gravitons, and the inflaton — whose only singularities at tree level are poles and whose behavior away from these poles is strongly constrained by unitarity and locality. We describe how unitarity translates into a set of cutting rules that consistent correlators must satisfy, and explain how this can be used to bootstrap correlators given information about their singularities. We also derive recursion relations that allow the iterative construction of more complicated correlators from simpler building blocks. In flat space, all energy singularities are simple poles, so that the combination of unitarity constraints and recursion relations provides an efficient way to bootstrap the full correlators. In many cases, these flat-space correlators can then be transformed into their more complex de Sitter counterparts. As an example of this procedure, we derive the correlator associated to graviton Compton scattering in de Sitter space, though the methods are much more widely applicable.
EuMnSb 2 is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. In this study we present single-crystal neutron diffraction, magnetization, and heat-capacity data as well as polycrystalline 151 Eu Mössbauer data which show that three AFM phases exist as a function of temperature, and we present a detailed analysis of the magnetic structure in each phase. The Mn magnetic sublattice orders into a C-type AFM structure below T N Mn = 323 (1) K with the ordered Mn magnetic moment μ Mn lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below T N Eu1 = 23 (1) K with the ordered Eu magnetic moment μ Eu canted away from the layer normal and μ Mn retaining its higher temperature order. μ Eu is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $\mathcal{Pn'm'a'}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below T N Eu2 =9 (1) K reveals a third AFM phase where μ Mn remains unchanged but μ Eu develops an additional substantial in-plane canting. This phase has MSG $\mathcal{P11}$ $\frac{2_1}{a′}$. We also find some evidence of short-range magnetic correlations associated with the Eu between 12 K≲ T≲ 30 K . Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg model. We then discuss implications of the various AFM states in EuMnSb 2 and their potential for tuning topological properties.
A new precision half-life measurement of 13 N has been conducted using the TwinSol β-counting station at the University of Notre Dame. Here, the measured value of $t^{new}_{1/2}$ = 597.05(19) s differs from the previous world value by about 2.8σ. An evaluation of the 13N half-life results in a $t^{world}_{1/2}$ = 597.19(22) s. Updated Standard Model predictions for the Fermi to Gamow-Teller mixing ratio ρ and its associated correlation parameters have been calculated using the new 13 N world half life in preparation for a future measurement of the mixing ratio. Finally, an ab initio no-core configuration interaction (NCCI) calculation for the B(GT) of this decay, carried out using the Daejeon16 interaction, has been carried out, revealing the need for higher-order chiral corrections.
Statistical electron parameter correlations associated with high-speed streams are determined with the aim of identifying one or more locally active solar wind heat flux instabilities. Evidence that points toward local regulation of the heat flux at 1 AU is presented, and the results of a search for special signatures expected from the action of the Alfven, magnetosonic, and whistler flux instabilities are discussed. It is shown that under certain conditions, the whistler mode can be active in regulating the heat flux at 1 AU.
Algorithms were developed for the extraction of two components of mean velocity, standard deviation, and the associated correlation coefficient from laser transit anemometry (LTA) data ensembles. The solution method is based on an assumed two-dimensional Gaussian probability density function (PDF) model of the flow field under investigation. The procedure consists of transforming the data ensembles from the data acquisition domain (consisting of time and angle information) to the velocity space domain (consisting of velocity component information). The mean velocity results are obtained from the data ensemble centroid. Through a least squares fitting of the transformed data to an ellipse representing the intersection of a plane with the PDF, the standard deviations and correlation coefficient are obtained. A data set simulation method is presented to test the data reduction process. Results of using the simulation system with a limited test matrix of input values is also given.