Isosbestic Points: Theory and Applications

We analyze the sharpness of crossing ("isosbestic") points of a family of curves which are observed in many quantities described by a function f(x,p), where x is a variable (e.g., the frequency) and p a parameter (e.g., the temperature). We show that if a narrow crossing region is observed near x* for a range of parameters p, then f(x,p) can be approximated by a perturbative expression in p for a wide range of x. This allows us, e.g., to extract the temperature dependence of several experimentally obtained quantities, such as the Raman response of HgBa2CuO4+delta, photoemission spectra of thin VO2 films, and the reflectivity of CaCu3Ti4O12, all of which exhibit narrow crossing regions near certain frequencies. We also explain the sharpness of isosbestic points in the optical conductivity of the Falicov-Kimball model and the spectral function of the Hubbard model.Comment: 12 pages, 11 figure

Commissioning and Alignment of the ATLAS Inner Detector using Cosmic Data

The ATLAS experiment is one of the two general purpose detectors at the LHC at CERN. ATLAS is equipped with a charged particle tracking system built on three sub-detectors, which provide high precision measurements made from a high detector granularity. The pixel and microstrip sub-detectors, which use the silicon technology, are complemented with the transition radiation tracker. The ATLAS detector is operational since 2008 and more than ten million cosmic tracks crossing the Inner Detector have been collected in 2008 and 2009. These data are used for the commissioning of the experiment. The alignment of the Inner Detector tracking system was performed using the 2008 cosmic data. The tracking performance obtained using this alignment is approaching the one obtained using Monte Carlo simulated with perfectly aligned geometry. The effect of systematic misalignments on physics measurements is being studied

The moduli space of hypersurfaces whose singular locus has high dimension

Let $k$ be an algebraically closed field and let $b$ and $n$ be integers with $n\geq 3$ and $1\leq b \leq n-1.$ Consider the moduli space $X$ of hypersurfaces in $\mathbb{P}^n_k$ of fixed degree $l$ whose singular locus is at least $b$-dimensional. We prove that for large $l$, $X$ has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear $b$-dimensional subspace of $\mathbb{P}^n$. The proof will involve a probabilistic counting argument over finite fields.Comment: Final version, including the incorporation of all comments by the refere

Non-perturbative approaches to magnetism in strongly correlated electron systems

The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough $U$. Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of $U$ above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view.Comment: 11 pages, Latex, and 6 postscript figures; Z. Phys. B, in pres

Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids

We study varieties with a term-definable poset structure, "po-groupoids". It is known that connected posets have the "strict refinement property" (SRP). In [arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with the SRP have definable factor congruences and if the similarity type is finite, directly indecomposables are axiomatizable by a set of first-order sentences. We obtain such a set for semidegenerate varieties of connected po-groupoids and show its quantifier complexity is bounded in general

Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds

We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part of a certain Fano 3-fold. This result supports Conjecture A below, while Conjecture A (or alternatively the rational connectedness conjecture in [KoMiMo] which is still open when the dimension is at least 4) would imply that every log terminal Fano variety has a finite fundamental group (now a Theorem of S. Takayama).Comment: Journal of Pure and Applied Algebra, to appear; 24 page

Tone-activated, remote, alert communication system

Pocket sized transmitter, frequency modulated by crystal derived tones, with integral loop antenna provides police with easy operating alert signal communicator which uses patrol car radio to relay signal. Communication channels are time shared by several patrol units

Commissioning and Alignment of the ATLAS Inner Detector Using Cosmic Data

The ATLAS experiment is one of the two general purpose detectors at the Large Hadron Collider. ATLAS is equipped with a charged particle tracking system built on three subdetectors, which provide high precision measurements made from a fine detector granularity. The pixel and microstrip subdetectors, which use the silicon technology, are complemented with the transition radiation tracker. The ATLAS detector is operational since 2008 and more than ten million cosmic tracks have been collected in 2008 and 2009. These data are used for the commissioning of the experiment. The current status of the Pixel, SCT and TRT detectors will be reviewed. We will report on the commissioning of the detector, including overviews on services, connectivity and observed problems. Alignment constants are calculated and the detector is calibrated. The required precision for the alignment of the most sensitive coordinates of the silicon sensors is just a few microns. The outline of the alignment algorithm and its implementation of the alignment software, its framework and the data flow will be discussed. The calibration of the silicon subdetectors, like the determination of the lorentz angle, is presented. The overall performance of the charged particle tracking system is studied

Telescopic actions

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold.Comment: +higher dimension

Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.Comment: 14 pages, 9 figures; introduction expanded, references added; published versio