An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

The infinite-$U$ single impurity Anderson model for rare earth alloys is examined with a new set of self-consistent coupled integral equations, which can be embedded in the large $N$ expansion scheme ($N$ is the local spin degeneracy). The finite temperature impurity density of states (DOS) and the spin-fluctuation spectra are calculated exactly up to the order $O(1/N^2)$. The presented conserving approximation goes well beyond the $1/N$-approximation ({\em NCA}) and maintains local Fermi-liquid properties down to very low temperatures. The position of the low lying Abrikosov-Suhl resonance (ASR) in the impurity DOS is in accordance with Friedel's sum rule. For $N=2$ its shift toward the chemical potential, compared to the {\em NCA}, can be traced back to the influence of the vertex corrections. The width and height of the ASR is governed by the universal low temperature energy scale $T_K$. Temperature and degeneracy $N$-dependence of the static magnetic susceptibility is found in excellent agreement with the Bethe-Ansatz results. Threshold exponents of the local propagators are discussed. Resonant level regime ($N=1$) and intermediate valence regime ($|\epsilon_f| <\Delta$) of the model are thoroughly investigated as a critical test of the quality of the approximation. Some applications to the Anderson lattice model are pointed out.Comment: 19 pages, ReVTeX, no figures. 17 Postscript figures available on the WWW at http://spy.fkp.physik.th-darmstadt.de/~frithjof

A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values, such as occupancy and magnetization, obtained directly from the numerical renormalization group calculations.Comment: 13 pages, 7 figur

Mechanical Design of the MID Split-and-Delay Line at the European XFEL

A new split-and-delay line (SDL) is under development for the Materials Imaging and Dynamics (MID) end station at the European XFEL.* The device utilises Bragg reflection to provide pairs of X-ray pulses with an energy of (5 - 10) keV and a continuously tunable time delay of (-10 - 800) ps - thus allowing zero-crossing of the time delay. The mechanical concept features separate positioning stages for each optical element. Those are based on a serial combination of coarse motion axes and a fine alignment 6 DoF Cartesian parallel kinematics**. That allows to meet the contradictory demands of a fast long-range travel of up to 1000 mm and in the same time a precise alignment with a resolution in the nanometer range. Multiple laser interferometers monitor the position of the optical elements and allow an active control of their alignment. All optical elements and mechanics will be installed inside an UHV chamber, including the interferometer and about 100 stepper motors. With this paper we present the mechanical design for the SDL. It will additionally show the design of a prototype of a positioning stage which allows extensive testing of the implemented concepts and techniques

Neutrino fluence after r-process freeze-out and abundances of Te isotopes in presolar diamonds

Using the data of Richter et al. (1998) on Te isotopes in diamond grains from a meteorite, we derive bounds on the neutrino fluence and the decay timescale of the neutrino flux relevant for the supernova r-process. Our new bound on the neutrino fluence F after freeze-out of the r-process peak at mass number A = 130 is more stringent than the previous bound F < 0.045 (in units of 10**37 erg/cm**2) of Qian et al. (1997) and Haxton et al. (1997) if the neutrino flux decays on a timescale tau > 0.65 s. In particular, it requires that a fluence of F = 0.031 be provided by a neutrino flux with tau < 0.84 s. Such a fluence may be responsible for the production of the solar r-process abundances at A = 124-126 (Qian et al. 1997; Haxton et al. 1997). Our results are based on the assumption that only the stable nuclei implanted into the diamonds are retained while the radioactive ones are lost from the diamonds upon decay after implantation (Ott 1996). We consider that the nanodiamonds are condensed in an environment with C/O > 1 in the expanding supernova debris or from the exterior H envelope. The implantation of nuclei would have occurred 10**4-10**6 s after r-process freeze-out. This time interval may be marginally sufficient to permit adequate cooling upon expansion for the formation of diamond grains. The mechanisms of preferential retention/loss of the implanted nuclei are not well understood.Comment: AASTeX, 11 pages, 3 Postscript figure

Nature-Inspired and Energy Efficient Route Planning

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Galactic Archaeology with CoRoT and APOGEE: Creating mock observations from a chemodynamical model

In a companion paper, we have presented the combined asteroseismic-spectroscopic dataset obtained from CoRoT lightcurves and APOGEE infra-red spectra for 678 solar-like oscillating red giants in two fields of the Galactic disc (CoRoGEE). We have measured chemical abundance patterns, distances, and ages of these field stars which are spread over a large radial range of the Milky Way's disc. Here we show how to simulate this dataset using a chemodynamical Galaxy model. We also demonstrate how the observation procedure influences the accuracy of our estimated ages.Comment: 5 pages, 6 figures. To appear in Astronomische Nachrichten, special issue "Reconstruction the Milky Way's History: Spectroscopic surveys, Asteroseismology and Chemo-dynamical models", Guest Editors C. Chiappini, J. Montalb\'an, and M. Steffe

On X-ray-singularities in the f-electron spectral function of the Falicov-Kimball model

The f-electron spectral function of the Falicov-Kimball model is calculated within the dynamical mean-field theory using the numerical renormalization group method as the impurity solver. Both the Bethe lattice and the hypercubic lattice are considered at half filling. For small U we obtain a single-peaked f-electron spectral function, which --for zero temperature-- exhibits an algebraic (X-ray) singularity ($|\omega|^{-\alpha}$) for $\omega \to 0$. The characteristic exponent $\alpha$ depends on the Coulomb (Hubbard) correlation U. This X-ray singularity cannot be observed when using alternative (Keldysh-based) many-body approaches. With increasing U, $\alpha$ decreases and vanishes for sufficiently large U when the f-electron spectral function develops a gap and a two-peak structure (metal-insulator transition).Comment: 8 pages, 8 figures, revte

Stellar Populations and Star Cluster Formation in Interacting Galaxies with the Advanced Camera for Surveys

Pixel-by-pixel colour-magnitude and colour-colour diagrams - based on a subset of the Hubble Space Telescope Advanced Camera for Surveys Early Release Observations - provide a powerful technique to explore and deduce the star and star cluster formation histories of the Mice and the Tadpole interacting galaxies. In each interacting system we find some 40 bright young star clusters (20 <= F606W (mag) <= 25, with a characteristic mass of ~3 x 10^6 Msun), which are spatially coincident with blue regions of active star formation in their tidal tails and spiral arms. We estimate that the main events triggering the formation of these clusters occurred ~(1.5-2.0) x 10^8 yr ago. We show that star cluster formation is a major mode of star formation in galaxy interactions, with >= 35% of the active star formation in encounters occurring in star clusters. This is the first time that young star clusters have been detected along the tidal tails in interacting galaxies. The tidal tail of the Tadpole system is dominated by blue star forming regions, which occupy some 60% of the total area covered by the tail and contribute ~70% of the total flux in the F475W filter (decreasing to ~40% in F814W). The remaining pixels in the tail have colours consistent with those of the main disk. The tidally triggered burst of star formation in the Mice is of similar strength in both interacting galaxies, but it has affected only relatively small, spatially coherent areas.Comment: 23 pages in preprint form, 6 (encapsulated) postscript figures; accepted for publication in New Astronomy; ALL figures (even the grey-scale ones) need to be printed on a colour printer style files included; for full-resolution paper, see http://www.ast.cam.ac.uk/STELLARPOPS/ACSpaper

Isotope shifts of the (3s3p)3^3P0,1,2_{0,1,2} - (3s4s)3^3S1_1 Mg I transitions

We report measurements of the isotope shifts of the (3s3p)$^3$P$_{0,1,2}$ - (3s4s)$^3$S$_1$ Mg I transitions for the stable isotopes $^{24}$Mg (I=0), $^{25}$Mg (I=5/2) and $^{26}$Mg (I=0). Furthermore the $^{25}$Mg $^3$S$_1$ hyperfine coefficient A($^3$S$_1$) = (-321.6 $\pm$ 1.5) MHz is extracted and found to be in excellent agreement with state-of-the-art theoretical predictions giving A($^3$S$_1$) = -325 MHz and B($^3$S$_1$) $\simeq 10^{-5}$ MHz. Compared to previous measurements, the data presented in this work is improved up to a factor of ten.Comment: 4 pages, 4 figures submitted to PR

Tau and atrophy: domain-specific relationships with cognition.

BackgroundLate-onset Alzheimer's disease (AD) is characterized by primary memory impairment, which then progresses towards severe deficits across cognitive domains. Here, we report how performance in cognitive domains relates to patterns of tau deposition and cortical thickness.MethodsWe analyzed data from 131 amyloid-β positive participants (55 cognitively normal, 46 mild cognitive impairment, 30 AD) of the Alzheimer's Disease Neuroimaging Initiative who underwent magnetic resonance imaging (MRI), flortaucipir (FTP) positron emission tomography, and neuropsychological testing. Surface-based vertex-wise and region-of-interest analyses were conducted between FTP and cognitive test scores, and between cortical thickness and cognitive test scores.ResultsFTP and thickness were differentially related to cognitive performance in several domains. FTP-cognition associations were more widespread than thickness-cognition associations. Further, FTP-cognition patterns reflected cortical systems that underlie different aspects of cognition.ConclusionsOur findings indicate that AD-related decline in domain-specific cognitive performance reflects underlying progression of tau and atrophy into associated brain circuits. They also suggest that tau-PET may have better sensitivity to this decline than MRI-derived measures of cortical thickness