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At least 1,063 records · Page 59

Multitiered computational methodology for extracting three-dimensional rotational diffusion coefficients from x-ray photon correlation spectroscopy data without structural information

X-ray photon correlation spectroscopy (XPCS) is a powerful technique for analyzing particle systems by investigating their dynamics in suspensions across a broad range of temporal and spatial scales. This is done by illuminating samples with coherent x-ray beams and calculating the correlation function of the obtained x-ray scattering images. XPCS is uniquely suited for studying Brownian dynamics, consisting of translational and rotational diffusion. While traditional XPCS image analysis techniques can extract translational diffusion components, they are unable to estimate rotational diffusion coefficients. Here, we introduce a methodology that combines the angular-temporal cross-correlation analysis and a algorithmic framework called Multi-Tiered Estimation for Correlation Spectroscopy in 3D for estimating three-dimensional rotational diffusion coefficients from XPCS images of three-dimensional particle systems. We demonstrate our methodology for extracting rotational diffusion coefficients from XPCS data by applying it to simulated noisy x-ray images of systems of crossing nanotubes and proteins that evolve under translational and rotational Brownian motion for different diffusion rates. Furthermore, our results show that our approach determines rotational diffusion coefficients within a few percent error.

97 MATHEMATICS AND COMPUTING↗

Data-driven subtraction of anisotropic flows in jet-like correlation studies in heavy-ion collisions

Measurements of two-particle azimuthal angle correlations are a useful tool to study the distribution of jet energy loss; however, they are complicated because of the significant anisotropic flow background. We devise a data-driven method for subtracting anisotropic flow background in jet-like correlation analysis. We first require a large recoil momentum (P x ) within a given pseudorapidity (η) range from a high-transverse momentum particle to enhance in-acceptance population of away-side jet-like correlations. Then we take the difference of two-particle correlations in the close region and far region with respect to the η region of P x to subtract the anisotropic flow background. Here, we use a toy model which contains only anisotropic flow and pythia8 which has jets, to demonstrate the validity of our data-driven method. The results indicate that the data-driven method can subtract anisotropic flow effectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

Here, we report a systematic measurement of cumulants, C n , for net-proton, proton, and antiproton multiplicity distributions, and correlation functions, κ n , for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The C n and κ n are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, y, and transverse momentum, p T . The data were taken during the first phase of the Beam Energy Scan (BES) program (2010–2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity (|y| < 0.5) and transverse momentum 0.4 < p T < 2.0 GeV/c, using the STAR detector at RHIC. We observe a nonmonotonic energy dependence ($\sqrt{s_{NN}}$ = 7.7–62.4 GeV) of the net-proton C 4 /C 2 with the significance of 3.1σ for the 0–5% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with $\sqrt{s_{NN}}$. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, κ 2 , of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, κ 4 , of protons plays a role in determining the energy dependence of proton C 4 /C 1 below 19.6 GeV, which cannot be understood by the effect of baryon number conservation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Correlations between flow and transverse momentum in Xe + Xe and Pb + Pb collisions at the LHC with the ATLAS detector: A probe of the heavy-ion initial state and nuclear deformation

The correlations between flow harmonics v n for n = 2, 3, and 4 and mean transverse momentum [p T ] in 129 Xe + 129 Xe and 208 Pb + 208 Pb collisions at $\sqrt{s}$ = 5.44 and 5.02 TeV, respectively, are measured using charged particles with the ATLAS detector. The correlations are potentially sensitive to the shape and size of the initial geometry, nuclear deformation, and initial momentum anisotropy. The effects from nonflow and centrality fluctuations are minimized, respectively, via a subevent cumulant method and an event-activity selection based on particle production at very forward rapidity. The v n -[p T ] correlations show strong dependencies on centrality, harmonic number n, p T , and pseudorapidity range. Current models qualitatively describe the overall centralityand system-dependent trends but fail to quantitatively reproduce all features of the data. In central collisions, where models generally show good agreement, the v 2 -[p T ] correlations are sensitive to the triaxiality of the quadruple deformation. Comparison of the model with the Pb + Pb and Xe + Xe data confirms that the 129 Xe nucleus is a highly deformed triaxial ellipsoid that has neither a prolate nor oblate shape. This provides strong evidence for a triaxial deformation of the 129 Xe nucleus from high-energy heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Search for the jet-induced diffusion wake in the quark-gluon plasma via measurements of jet-track correlations in photon-jet events in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV with the ATLAS detector

This paper presents a measurement of jet-track correlations in photon-jet events, using 1.72 nb −1 of Pb+Pb data at $\sqrt{s_{NN}}$ = 5.02TeV recorded with the ATLAS detector at the LHC. Events with energetic photon-jet pairs are selected, where the photon and jet are approximately back-to-back in azimuth. The angular correlation between jets and charged-particle tracks with transverse momentum (𝑝 T ) in the range 0.5–2.0 GeV in the hemisphere opposite to the jet, |Δ⁢𝜙(jet,track)|>𝜋/2, is measured as a function of their relative pseudorapidity difference, |Δ⁢𝜂(jet,track)|. In central Pb+Pb collisions, these correlations are predicted to be sensitive to the diffusion wake in the quark-gluon plasma resulting from the lost energy of high-𝑝T partons traversing the plasma, with a characteristic modification as a function of |Δ⁢𝜂(jet,track)|. The correlations are examined with different selections on the jet-to-photon 𝑝 T ratio to select events with different degrees of energy loss. No diffusion wake signal is observed within the current sensitivity and upper limits at 95% confidence level on the diffusion wake amplitude are reported.

heavy flavor physics↗

Collision-energy dependence of p t correlations in Au + Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

We present two-particle $p_{\rm t}$ correlations as a function of event centrality for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These results are compared to previous measurements from CERES at the Super Proton Synchrotron and from ALICE at the Large Hadron Collider. The data are compared with UrQMD model calculations and with a model based on a Boltzmann-Langevin approach incorporating effects from thermalization. The relative dynamical correlations for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV show a power law dependence on the number of participant nucleons and agree with the results for Pb+Pb collisions at $\sqrt{s_{\rm NN}} = 2.76~ {\rm TeV}$ from ALICE. As the collision energy is lowered from $\sqrt{s_{\rm NN}}$ = 200 GeV to 7.7 GeV, the centrality dependence of the relative dynamical correlations departs from the power law behavior observed at the higher collision energies. In central collisions, the relative dynamical correlations increase with collision energy up to $\sqrt{s_{\rm NN}}$ = 200 GeV in contrast to previous measurements that showed little dependence on the collision energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Exploring entanglement and spectral split correlations in three-flavor collective neutrino oscillations

In environments with prodigious numbers of neutrinos, such as core-collapse supernovae, neutron star mergers, or the early Universe, neutrino-neutrino interactions are dynamically significant. They can dominate neutrino flavor evolution and force it to be nonlinear, causing collective neutrino oscillations. Such collective oscillations have been studied numerically, for systems with up to millions of neutrinos, using mean-field or one-particle effective approximations. However, such a system of interacting neutrinos is a quantum many-body system, wherein quantum correlations could play a significant role in the flavor evolution—thereby motivating the exploration of many-body treatments that follow the time evolution of these correlations. In many-body flavor evolution calculations with two neutrino flavors, the emergence of spectral splits in the neutrino energy distributions has been found to be correlated with the degree of quantum entanglement across the spectrum. In this work, for the first time, we investigate the emergence of spectral splits in the three-flavor many-body collective neutrino oscillations. We find that the emergence of spectral splits resembles the number and location found in the mean-field approximation but not in the width. Moreover, unlike in the two-flavor many-body calculations, we find that additional degrees of freedom make it more difficult to establish a correlation between the location of the spectral splits and the degree of quantum entanglement across the neutrino energy spectrum. The observation from the two-flavor case, that neutrinos nearest to the spectral split frequency exhibit the highest level of entanglement, is more difficult to ascertain in the three-flavor case because of the presence of multiple spectral splits across different pairwise combinations of flavor and/or mass states. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermal modifications of mesons and energy-energy correlators from real-time simulations of a 𝑈⁡(1) lattice gauge theory

We investigate thermal properties of a 𝑈⁡(1) lattice gauge theory in 1 + 1 dimensions through real-time simulations. We extract the spectral functions directly coupling to the pseudoscalar and scalar mesons, demonstrating the thermal modifications of these states with increasing temperatures. Introducing the notion of energy-flow operators, we quantify the temporal buildup of correlations in the energy flows across the lattice. We demonstrate that energy-energy correlators fail to factorize to products of energy flows, both in the vacuum and at nonzero temperature, indicating the presence of nontrivial correlations in the quantum states. Our results constitute a first real-time ab initio study of bound-state thermal broadening and finite temperature energy-flow correlations in a gauge theory, providing a benchmark for future studies of hadronic matter under extreme conditions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Factors correlating with significant differences between X-ray structures of myoglobin

Conformational differences between myoglobin structures are studied. Most structural differences in whale myoglobin beyond the uncertainty threshold can be correlated with a few specific structural factors. There are always exceptions and a search for additional factors is needed. The results might have serious implications for biological insights from conformational differences. Validation of general ideas about the origins of conformational differences in proteins is critical in order to arrive at meaningful functional insights. Here, principal component analysis (PCA) and distance difference matrices are used to validate some such ideas about the conformational differences between 291 myoglobin structures from sperm whale, horse and pig. Almost all of the horse and pig structures form compact PCA clusters with only minor coordinate differences and outliers that are easily explained. The 222 whale structures form a few dense clusters with multiple outliers. A few whale outliers with a prominent distortion of the GH loop are very similar to the cluster of horse structures, which all have a similar GH-loop distortion apparently owing to intermolecular crystal lattice hydrogen bonds to the GH loop from residues near the distal histidine His64. The variations of the GH-loop coordinates in the whale structures are likely to be owing to the observed alternative intermolecular crystal lattice bond, with the change to the GH loop distorting bonds correlated with the binding of specific ‘unusual’ ligands. Such an alternative intermolecular bond is not observed in horse myoglobins, obliterating any correlation with the ligands. Intermolecular bonds do not usually cause significant coordinate differences and cannot be validated as their universal cause. Most of the native-like whale myoglobin structure outliers can be correlated with a few specific factors. However, these factors do not always lead to coordinate differences beyond the previously determined uncertainty thresholds. The binding of unusual ligands by myoglobin, leading to crystal-induced distortions, suggests that some of the conformational differences between the apo and holo structures might not be ‘functionally important’ but rather artifacts caused by the binding of ‘unusual’ substrate analogs. The causes of P6 symmetry in myoglobin crystals and the relationship between crystal and solution structures are also discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Robust X-ray angular correlations for the study of meso-structures

As self-assembling nanomaterials become more sophisticated, it is becoming increasingly important to measure the structural order of finite-sized assemblies of nano-objects. These mesoscale clusters represent an acute challenge to conventional structural probes, owing to the range of implicated size scales (10 nm to several micrometres), the weak scattering signal and the dynamic nature of meso-clusters in native solution environments. The high X-ray flux and coherence of modern synchrotrons present an opportunity to extract structural information from these challenging systems, but conventional ensemble X-ray scattering averages out crucial information about local particle configurations. Conversely, a single meso-cluster scatters too weakly to recover the full diffraction pattern. Using X-ray angular cross-correlation analysis, it is possible to combine multiple noisy measurements to obtain robust structural information. This paper explores the key theoretical limits and experimental challenges that constrain the application of these methods to probing structural order in real nanomaterials. A metric is presented to quantify the signal-to-noise ratio of angular correlations, and it is used to identify several experimental artifacts that arise. In particular, it is found that background scattering, data masking and inter-cluster interference profoundly affect the quality of correlation analyses. A robust workflow is demonstrated for mitigating these effects and extracting reliable angular correlations from realistic experimental data.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

X-ray-induced piezoresponse during X-ray photon correlation spectroscopy of PbMg 1/3 Nb 2/3 O 3

X-ray photon correlation spectroscopy (XPCS) holds strong promise for observing atomic-scale dynamics in materials, both at equilibrium and during non-equilibrium transitions. Here an in situ XPCS study of the relaxor ferroelectric PbMg 1/3 Nb 2/3 O 3 (PMN) is reported. A weak applied AC electric field generates strong response in the speckle of the diffuse scattering from the polar nanodomains, which is captured using the two-time correlation function. Correlated motions of the Bragg peak are also observed, which indicate dynamic tilting of the illuminated volume. This tilting quantitatively accounts for the observed two-time speckle correlations. The magnitude of the tilting would not be expected solely from the modest applied field, since PMN is an electrostrictive material with no linear strain response to the field. A model is developed based on non-uniform static charging of the illuminated surface spot by the incident micrometre-scale X-ray beam and the electrostrictive material response to the combination of static and dynamic fields. The model qualitatively explains the direction and magnitude of the observed tilting, and predicts that X-ray-induced piezoresponse could be an important factor in correctly interpreting results from XPCS and nanodiffraction studies of other insulating materials under applied AC field or varying X-ray illumination.

36 MATERIALS SCIENCE↗

Characterizing crystalline defects in single nanoparticles from angular correlations of single-shot diffracted X-rays

Characterizing and controlling the uniformity of nanoparticles is crucial for their application in science and technology because crystalline defects in the nanoparticles strongly affect their unique properties. Recently, ultra-short and ultra-bright X-ray pulses provided by X-ray free-electron lasers (XFELs) opened up the possibility of structure determination of nanometre-scale matter with Å spatial resolution. However, it is often difficult to reconstruct the 3D structural information from single-shot X-ray diffraction patterns owing to the random orientation of the particles. This report proposes an analysis approach for characterizing defects in nanoparticles using wide-angle X-ray scattering (WAXS) data from free-flying single nanoparticles. The analysis method is based on the concept of correlated X-ray scattering, in which correlations of scattered X-ray are used to recover detailed structural information. WAXS experiments of xenon nanoparticles, or clusters, were conducted at an XFEL facility in Japan by using the SPring-8 Ångstrom compact free-electron laser (SACLA). Bragg spots in the recorded single-shot X-ray diffraction patterns showed clear angular correlations, which offered significant structural information on the nanoparticles. The experimental angular correlations were reproduced by numerical simulation in which kinematical theory of diffraction was combined with geometric calculations. We also explain the diffuse scattering intensity as being due to the stacking faults in the xenon clusters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

An Optimal Pufferfish Privacy Mechanism for Temporally Correlated Trajectories

Temporally correlated trajectories are ubiquitous, and it has been a challenging problem to protect the temporal correlation from being used against users’ privacy. In this work, we propose an optimal Pufferfish privacy mechanism to achieve better data utility while providing guaranteed privacy of temporally correlated daily trajectories. First, a Laplace noise mechanism is realized through geometric sum of noisy Fourier coefficients of temporally correlated daily trajectories. Then, we prove that the proposed noisy Fourier coefficients’ geometric sum satisfies Pufferfish privacy, i.e. , the so-called FGS-Pufferfish privacy mechanism. Furthermore, we achieve better data utility for a given privacy budget by solving a constrained optimization problem of the noisy Fourier coefficients via the Lagrange multiplier method. What is more, a rigorous mathematical formula has been obtained for the Fourier coefficients’ Laplace noise scale parameters. At last, we evaluate our FGS-Pufferfish privacy mechanism on both simulated and real-life data and find that our proposed mechanism achieves better data utility and privacy compared with the other state-of-the-art existing approach.

97 MATHEMATICS AND COMPUTING↗

A Generalized Copula-Polynomial Chaos Expansion for Probabilistic Power Flow Considering Nonlinear Correlations of PV Injections

This paper develops a generalized Copula-polynomial chaos expansion (PCE) framework for power system probabilistic power flow that can handle both linear and nonlinear correlations of uncertain power injections, such as wind and PVs. A data-driven Copula statistical model is used to capture the correlations of uncertain power injections. This allows us to resort to the Rosenblatt transformation to transform correlated variables into independent ones while preserving the dependence structure. This paves the way of leveraging the PCE for surrogate modeling and uncertainty quantification of power flow results, i.e., achieving the probabilistic distributions of power flows. Simulations carried out on the IEEE 57-bus system show that the proposed framework can get much more accurate results than other alternatives with different linear and nonlinear power injection correlations.

copula↗

Effects of Correlated and Uncorrelated Gamma Rays on Neutron Multiplicity Counting

Neutron multiplicity counting relies on time correlation between neutron events to assay the fissile mass, (α,n) to spontaneous fission neutron ratio, and neutron self-multiplication of samples. Gamma-ray sensitive neutron multiplicity counters may misidentify gamma rays as neutrons and therefore miscalculate sample characteristics. Time correlated and uncorrelated gamma-ray-like signals were added into gamma-ray free neutron multiplicity counter data to examine the effects of gamma ray signals being misidentified as neutron signals on assaying sample characteristics. Multiplicity counter measurements with and without gamma-ray-like signals were compared to determine the assay error associated with gamma-ray-like signals at various gamma-ray and neutron rates. Correlated and uncorrelated gamma-ray signals each produced consistent but different measurement errors. Correlated gamma-ray signals most strongly led to fissile mass overestimates, whereas uncorrelated gamma-ray signals most strongly lead to (α,n) neutron overestimates. Gamma-ray sensitive neutron multiplicity counters may be able to account for the effects of gamma-rays on measurements to mitigate measurement uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SU-D-204-04: Correlations Between Dosimetric Indices and Follow-Up Data for Salivary Glands Six Months After Radiation Therapy for Head and Neck Cancer

Purpose: To investigate the correlation between different dosimetric indices of salivary glands (as separate or combined structures) to patient-reported dry mouth 6 months post radiotherapy using the novel patient reported outcome version of the CTCAE (PRO-CTCAE). Methods: Forty-three patients with oropharyngeal squamous cell carcinoma were treated on a prospective multi-institutional study. All patients received de-intensified 60 Gy intensity modulated radiotherapy. Dosimetric constraints were used for the salivary glands (e.g. mean dose to the contralateral-parotid < 26 Gy). We investigated correlations of individual patient dosimetric data of the parotid and submandibular glands (as separate or combined structures) to their self-reported 6 month post-treatment dry mouth responses. Moderate dry mouth responses were most prevalent and were used as the clinical endpoint indicating response. The correlation of Dmean, Dmax and a range of dosevolume (VD) points were assessed through the area under the Receiver Operating Characteristic curve (ROC) and Odds Ratios (OR). Results: Patients reporting non/mild dry mouth response (N=22) had average Dmean = 19.6 ± 6.2Gy to the contralateral-parotid compared to an average Dmean = 28.0 ± 8.3Gy and an AUC = 0.758 for the patients reporting moderate/severe/very severe dry mouth (N=21). Analysis of the range of VD’s for patients who had reported dry mouth showed that for the contralateral-parotid the indices V18 through V22 had the highest area under the curves (AUC) (0.762 – 0.772) compared to a more traditional dosimetric index V30, which had an AUC = 0.732. The highest AUC was observed for the combination of contralateral parotid and contralateral submandibular glands, for which V16 through V28 had AUC = 0.801 – 0.834. Conclusion: Patients who report moderate/severe/very severe dry mouth 6 months post radiotherapy had on average higher Dmean. The V16-V28 of the combination of the contralateral glands showed the highest correlation with the clinical endpoint.

60 APPLIED LIFE SCIENCES↗

SU-F-T-133: Uniform Scanning Proton Therapy for Lung Cancer: Toxicity and Its Correlation with Dosimetry

Purpose: To analyze the toxicity of uniform scanning proton therapy for lung cancer patients and its correlation with dose distribution. Methods: In this study, we analyzed the toxicity of 128 lung cancer patients, including 18 small cell lung cancer and 110 non small cell lung cancer patients. Each patient was treated with uniform scanning proton beams at our center using typically 2–4 fields. The prescription was typically 74 Cobalt gray equivalent (CGE) at 2 CGE per fraction. 4D Computerized Tomography (CT) scans were used to evaluate the target motion and contour the internal target volume, and repeated 3 times during the course of treatment to evaluate the need for plan adaptation. Toxicity data for these patients were obtained from the proton collaborative group (PCG) database. For cases of grade 3 toxicities or toxicities of interest such as esophagitis and radiation dermatitis, dose distributions were reviewed and analyzed in attempt to correlate the toxicity with radiation dose. Results: At a median follow up time of about 21 months, none of the patients had experienced Grade 4 or 5 toxicity. The most common adverse effect was dermatitis (81%: 52%-Grade 1, 28%-Grade 2, and 1% Grade 3), followed by fatigue (48%), Cough (46%), and Esophagitis (45%), as shown in Figure 1. Severe toxicities, such as Grade 3 dermatitis or pain of skin, had a clear correlation with high radiation dose. Conclusion: Uniform scanning proton therapy is well tolerated by lung cancer patients. Preliminary analysis indicates there is correlation between severe toxicity and high radiation dose. Understanding of radiation resulted toxicities and careful choice of beam arrangement are critical in minimizing toxicity of skin and other organs.

60 APPLIED LIFE SCIENCES↗

Doping dependence of correlation effects in K{sub 1−x}Fe{sub 2−y}Se{sub 2} superconductors: LDA’ + DMFT investigation

We present a detailed LDA’ + DMFT investigation of the doping dependence of correlation effects in the novel K{sub 1−x}Fe{sub 2−y}Se{sub 2} superconductor. Calculations are performed at four different hole doping levels, starting from a hypothetical stoichiometric composition with the total number of electrons equal to 29 per unit cell through 28 and 27.2 electrons toward the case of 26.52, which corresponds to the chemical composition K{sub 0.76}Fe{sub 1.72}Se{sub 2} studied in recent ARPES experiments. In the general case, the increase in hole doping leads to quasiparticle bands in a wide energy window ±2 eV around the Fermi level becoming more broadened by lifetime effects, while correlation-induced compression of Fe-3d LDA’ bandwidths stays almost the same, of the order of 1.3 for all hole concentrations. However, close to the Fermi level, the situation is more complicated. In the energy interval from −1.0 eV to 0.4 eV, the bare Fe-3d LDA’ bands are compressed by significantly larger renormalization factors up to 5 with increased hole doping, while the value of Coulomb interaction remains the same. This fact manifests the increase in correlation effects with hole doping in the K{sub 1−x}Fe{sub 2−y}Se{sub 2} system. Moreover, in contrast to typical pnictides, K{sub 1−x}Fe{sub 2−y}Se{sub 2} does not have well-defined quasiparticle bands on the Fermi levels, but has a “pseudogap”-like dark region instead. We also find that with the growth of hole doping, Fe-3d orbitals of various symmetries are affected by correlations differently in different parts of the Brillouin zone. To illustrate this, we determine the quasiparticle mass renormalization factors and energy shifts that transform the bare Fe-3d LDA’ bands of various symmetries into LDA’ + DMFT quasiparticle bands. These renormalization factors effectively mimic more complicated energy-dependent self-energy effects and can be used to analyze the available ARPES data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗