Introduction to Arithmetic Mirror Symmetry

We describe how to find period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds. These families can be seen as varieties over a finite field, in which case we show in an explicit example that the number of points of a generic element can be given in terms of p-adic period integrals. We also discuss several approaches to finding zeta functions of mirror manifolds and their factorizations. These notes are based on lectures given at the Fields Institute during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics

Graded cluster expansion for lattice systems

In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of disordered lattice systems in the Griffiths' phase. We suppose that the system satisfies a mixing condition in a subset of the lattice whose complement is sparse enough namely, large regions are widely separated. We then show how it is possible to construct a convergent multi-scale cluster expansion

Born reciprocity and the 1/r potential

Many structures in nature are invariant under the transformation (p,r)->(br,-p/b), where b is some scale factor. Born's reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale $b = m\Omega$. We find that an $\Omega \sim 1.5\times 10^{-15}$ Hz has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.Comment: 14 pages, with 4 figures, Latex, requires epsf.tex and iop style file

Distribution and density of the partition function zeros for the diamond-decorated Ising model

Exact renormalization map of temperature between two successive decorated lattices is given, and the distribution of the partition function zeros in the complex temperature plane is obtained for any decoration-level. The rule governing the variation of the distribution pattern as the decoration-level changes is given. The densities of the zeros for the first two decoration-levels are calculated explicitly, and the qualitative features about the densities of higher decoration-levels are given by conjecture. The Julia set associated with the renormalization map is contained in the distribution of the zeros in the limit of infinite decoration level, and the formation of the Julia set in the course of increasing the decoration-level is given in terms of the variations of the zero density.Comment: 8 pages,8figure

Unveiling Soft Gamma-Ray Repeaters with INTEGRAL

Thanks to INTEGRAL's long exposures of the Galactic Plane, the two brightest Soft Gamma-Ray Repeaters, SGR 1806-20 and SGR 1900+14, have been monitored and studied in detail for the first time at hard-X/soft gamma rays. This has produced a wealth of new scientific results, which we will review here. Since SGR 1806-20 was particularly active during the last two years, more than 300 short bursts have been observed with INTEGRAL. and their characteristics have been studied with unprecedented sensitivity in the 15-200 keV range. A hardness-intensity anticorrelation within the bursts has been discovered and the overall Number-Intensity distribution of the bursts has been determined. In addition, a particularly active state, during which ~100 bursts were emitted in ~10 minutes, has been observed on October 5 2004, indicating that the source activity was rapidly increasing. This eventually led to the Giant Flare of December 27th 2004, for which a possible soft gamma-ray (>80 keV) early afterglow has been detected. The deep observations allowed us to discover the persistent emission in hard X-rays (20-150 keV) from 1806-20 and 1900+14, the latter being in a quiescent state, and to directly compare the spectral characteristics of all Magnetars (two SGRs and three Anomalous X-ray Pulsars) detected with INTEGRAL.Comment: 8 pages, 7 figures, Presented at the conference "Isolated Neutron Stars: from the Surface to the Interior", London, UK, 24-28 April 200

Exotic clouds in the local interstellar medium

The neutral interstellar medium (ISM) inside the Local Bubble (LB) has been known to have properties typical of the warm neutral medium (WNM). However, several recent neutral hydrogen (HI) absorption experiments show evidence for the existence of at least several cold diffuse clouds inside or at the boundary of the LB, with properties highly unusual relative to the traditional cold neutral medium. These cold clouds have a low HI column density, and AU-scale sizes. As the kinematics of cold and warm gas inside the LB are similar, this suggests a possibility of all these different flavors of the local ISM belonging to the same interstellar flow. The co-existence of warm and cold phases inside the LB is exciting as it can be used to probe the thermal pressure inside the LB. In addition to cold clouds, several discrete screens of ionized scattering material are clearly located inside the LB. The cold exotic clouds inside the LB are most likely long-lived, and we expect many more clouds with similar properties to be discovered in the future with more sensitive radio observations. While physical mechanisms responsible for the production of such clouds are still poorly understood, dynamical triggering of phase conversion and/or interstellar turbulence are likely to play an important role.Comment: 10 pages, refereed, accepted for publication in the proceedings of the "From the Outer Heliosphere to the Local Bubble: Comparisons of New Observations with Theory" conference, Space Science Review

One-dimensional spin-1/2 Heisenberg antiferromagnet in a weak external magnetic field

The one dimensional spin-1/2 Heisenberg antiferromagnet in a weak magnetic field h is studied using the bosonization method. We derive a set of renormalization group equations. The fixed point is reached when the field is scaled to the value at which the system is quarter-filled. As the magnetic field varies, a continuum line of fixed points is formed. We compute the uniform longitudinal susceptibility $\chi_z(h)$. The singular behavior of $\chi_z(h)$ as $h\to 0$ is found to be contained in $1/\ln(h_o/h)$ with $h_o$ a non-universal constant. The spin-spin correlations in the magnetic field are calculated.Comment: 5 pages, 1 figure, published on PR

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02