Making big steps in trajectories

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a similar computation time

Anisotropic electrical resistivity of LaFeAsO: evidence for electronic nematicity

Single crystals of LaFeAsO were successfully grown out of KI flux. Temperature dependent electrical resistivity was measured with current flow along the basal plane, \rho_perpend(T), as well as with current flow along the crystallographic c-axis, \rho_parallel(T), the latter one utilizing electron beam lithography and argon ion beam milling. The anisotropy ratio was found to lie between \rho_parallel/\rho_perpend = 20 - 200. The measurement of \rho_perpend(T) was performed with current flow along the tetragonal [1 0 0] direction and along the [1 1 0] direction and revealed a clear in-plane anisotropy already at T \leq 175 K. This is significantly above the orthorhombic distortion at T_0 = 147 K and indicates the formation of an electron nematic phase. Magnetic susceptibility and electrical resistivity give evidence for a change of the magnetic structure of the iron atoms from antiferromagnetic to ferromagnetic arrangement along the c-axis at T^\ast = 11 K.Comment: 10 pages, 6 figures, minor change

Neutrino oscillation signatures of oxygen-neon-magnesium supernovae

We discuss the flavor conversion of neutrinos from core collapse supernovae that have oxygen-neon-magnesium (ONeMg) cores. Using the numerically calculated evolution of the star up to 650 ms post bounce, we find that, for the normal mass hierarchy, the electron neutrino flux in a detector shows signatures of two typical features of an ONeMg-core supernova: a sharp step in the density profile at the base of the He shell and a faster shock wave propagation compared to iron core supernovae. Before the shock hits the density step (t ~ 150 ms), the survival probability of electron neutrinos is about 0.68, in contrast to values of 0.32 or less for an iron core supernova. The passage of the shock through the step and its subsequent propagation cause a decrease of the survival probability and a decrease of the amplitude of oscillations in the Earth, reflecting the transition to a more adiabatic propagation inside the star. These changes affect the lower energy neutrinos first; they are faster and more sizable for larger theta_13. They are unique of ONeMg-core supernovae, and give the possibility to test the speed of the shock wave. The time modulation of the Earth effect and its negative sign at the neutronization peak are the most robust signatures in a detector.Comment: 14 pages, 10 figures (16 figure files). Text and graphics added for illustration and clarification; Results unchanged. Version accepted for publication in Physical Review

Nucleosynthesis and Clump Formation in a Core Collapse Supernova

High-resolution two-dimensional simulations were performed for the first five minutes of the evolution of a core collapse supernova explosion in a 15 solar mass blue supergiant progenitor. The computations start shortly after bounce and include neutrino-matter interactions by using a light-bulb approximation for the neutrinos, and a treatment of the nucleosynthesis due to explosive silicon and oxygen burning. We find that newly formed iron-group elements are distributed throughout the inner half of the helium core by Rayleigh-Taylor instabilities at the Ni+Si/O and C+O/He interfaces, seeded by convective overturn during the early stages of the explosion. Fast moving nickel mushrooms with velocities up to about 4000 km/s are observed. This offers a natural explanation for the mixing required in light curve and spectral synthesis studies of Type Ib explosions. A continuation of the calculations to later times, however, indicates that the iron velocities observed in SN 1987 A cannot be reproduced because of a strong deceleration of the clumps in the dense shell left behind by the shock at the He/H interface.Comment: 8 pages, LaTeX, 2 postscript figures, 2 gif figures, shortened and slightly revised text and references, accepted by ApJ Letter

Exact single spin flip for the Hubbard model in d=∞d=\infty

It is shown that the dynamics of a single $\downarrow$-electron interacting with a band of $\uparrow$-electrons can be calculated exactly in the limit of infinite dimension. The corresponding Green function is determined as a continued fraction. It is used to investigate the stability of saturated ferromagnetism and the nature of the ground state for two generic non-bipartite infinite dimensional lattices. Non Fermi liquid behavior is found. For certain dopings the $\downarrow$-electron is bound to the $\uparrow$-holes.Comment: 4 pages, 3 figures included with psfig, Revtex; Phys. Rev. Lett. in press; some amendments made to clarify the calculation of the self-energy, the extrapolation of the continued fraction, and the statements on Fermi-liquid theor

Optimized Herschel/PACS photometer observing and data reduction strategies for moving solar system targets

The "TNOs are Cool!: A survey of the trans-Neptunian region" is a Herschel Open Time Key Program that aims to characterize planetary bodies at the outskirts of the Solar System using PACS and SPIRE data, mostly taken as scan-maps. In this paper we summarize our PACS data reduction scheme that uses a modified version of the standard pipeline for basic data reduction, optimized for faint, moving targets. Due to the low flux density of our targets the observations are confusion noise limited or at least often affected by bright nearby background sources at 100 and 160\,$\mu$m. To overcome these problems we developed techniques to characterize and eliminate the background at the positions of our targets and a background matching technique to compensate for pointing errors. We derive a variety of maps as science data products that are used depending on the source flux and background levels and the scientific purpose. Our techniques are also applicable to a wealth of other Herschel solar system photometric observations, e.g. comets and near-Earth asteroids. The principles of our observing strategies and reduction techniques for moving targets will also be applicable for similar surveys of future infrared space projects.Comment: Accepted for publication in Experimental Astronom

Step-wise responses in mesoscopic glassy systems: a mean field approach

We study statistical properties of peculiar responses in glassy systems at mesoscopic scales based on a class of mean-field spin-glass models which exhibit 1 step replica symmetry breaking. Under variation of a generic external field, a finite-sized sample of such a system exhibits a series of step wise responses which can be regarded as a finger print of the sample. We study in detail the statistical properties of the step structures based on a low temperature expansion approach and a replica approach. The spacings between the steps vanish in the thermodynamic limit so that arbitrary small but finite variation of the field induce infinitely many level crossings in the thermodynamic limit leading to a static chaos effect which yields a self-averaging, smooth macroscopic response. We also note that there is a strong analogy between the problem of step-wise responses in glassy systems at mesoscopic scales and intermittency in turbulent flows due to shocks.Comment: 50 pages, 18 figures, revised versio

Construction and Performance of a Micro-Pattern Stereo Detector with Two Gas Electron Multipliers

The construction of a micro-pattern gas detector of dimensions 40x10 cm**2 is described. Two gas electron multiplier foils (GEM) provide the internal amplification stages. A two-layer readout structure was used, manufactured in the same technology as the GEM foils. The strips of each layer cross at an effective crossing angle of 6.7 degrees and have a 406 um pitch. The performance of the detector has been evaluated in a muon beam at CERN using a silicon telescope as reference system. The position resolutions of two orthogonal coordinates are measured to be 50 um and 1 mm, respectively. The muon detection efficiency for two-dimensional space points reaches 96%.Comment: 21 pages, 17 figure

Solution of the off-forward leading logarithmic evolution equation based on the Gegenbauer moments inversion

Using the conformal invariance the leading-log evolution of the off-forward structure function is reduced to the forward evolution described by the conventional DGLAP equation. The method relies on the fact that the anomalous dimensions of the Gegenbauer moments of the off-forward distribution are independent on the asymmetry, or skewedness, parameter and equal to the DGLAP ones. The integral kernels relating the forward and off-forward functions with the same Mellin and Gegenbauer moments are presented for arbitrary asymmetry value.Comment: 11 pages, LaTeX, no figures, revised version, references adde

Raman scattering through a metal-insulator transition

The exact solution for nonresonant A1g and B1g Raman scattering is presented for the simplest model that has a correlated metal-insulator transition--the Falicov-Kimball model, by employing dynamical mean field theory. In the general case, the A1g response includes nonresonant, resonant, and mixed contributions, the B1g response includes nonresonant and resonant contributions (we prove the Shastry-Shraiman relation for the nonresonant B1g response) while the B2g response is purely resonant. Three main features are seen in the nonresonant B1g channel: (i) the rapid appearance of low-energy spectral weight at the expense of higher-energy weight; (b) the frequency range for this low-energy spectral weight is much larger than the onset temperature, where the response first appears; and (iii) the occurrence of an isosbestic point, which is a characteristic frequency where the Raman response is independent of temperature for low temperatures. Vertex corrections renormalize away all of these anomalous features in the nonresonant A1g channel. The calculated results compare favorably to the Raman response of a number of correlated systems on the insulating side of the quantum-critical point (ranging from Kondo insulators, to mixed-valence materials, to underdoped high-temperature superconductors). We also show why the nonresonant B1g Raman response is ``universal'' on the insulating side of the metal-insulator transition.Comment: 12 pages, 11 figures, ReVTe