COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.

The finite size effects of the dynamical structure factors in the XXZ-model are studied in the euclidean time $(\tau)$-representation. Away from the critical momentum $p=\pi$ finite size effects turn out to be small except for the large $\tau$ limit. The large finite size effects at the critical momentum $p=\pi$ signal the emergence of infrared singularities in the spectral $(\omega)$-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse

Measuring Dark Matter Profiles Non-Parametrically In Dwarf Spheroidals: An Application To Draco

We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal galaxy (dSph) Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7 m telescope at McDonald Observatory. Our non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 = 20 pc is well fit by a power law with slope alpha = -1.0 +/- 0.2, consistent with predictions from cold dark matter simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.NSF-0908639Astronom

The stellar populations of the central region of M31

We continue the analysis of the dataset of our spectroscopic observation campaign of M31, by deriving simple stellar population properties (age metallicity and alpha-elements overabundance) from the measurement of Lick/IDS absorption line indices. We describe their two-dimensional maps taking into account the dust distribution in M31. 80\% of the values of our age measurements are larger than 10 Gyr. The central 100 arcsec of M31 are dominated by the stars of the classical bulge of M31. They are old (11-13 Gyr), metal-rich (as high as [Z/H]~0.35 dex) at the center with a negative gradient outwards and enhanced in alpha-elements ([alpha/Fe]~ 0.28+- 0.01 dex). The bar stands out in the metallicity map, where an almost solar value of [Z/H] (~0.02+-0.01 dex) with no gradient is observed along the bar position angle (55.7 deg) out to 600 arcsec from the center. In contrast, no signature of the bar is seen in the age and [alpha/Fe] maps, that are approximately axisymmetric, delivering a mean age and overabundance for the bar and the boxy-peanut bulge of 10-13 Gyr and 0.25-0.27 dex, respectively. The boxy/peanut-bulge has almost solar metallicity (-0.04+- 0.01 dex). The mass-to-light ratio of the three components is approximately constant at M/LV ~ 4.4-4.7 Msol/Lsol. The disk component at larger distances is made of a mixture of stars, as young as 3-4 Gyr, with solar metallicity and smaller M/LV (~3+-0.1 Msol/Lsol). We propose a two-phase formation scenario for the inner region of M31, where most of the stars of the classical bulge come into place together with a proto-disk, where a bar develops and quickly transforms it into a boxy-peanut bulge. Star formation continues in the bulge region, producing stars younger than 10 Gyr, in particular along the bar, enhancing its metallicity. The disk component appears to build up on longer time-scales.Comment: Language-edited version, Accepted for publication in A&

Evidence for non-axisymmetry in M31 from wide-field kinematics of stars and gas

As the nearest large spiral galaxy, M31 provides a unique opportunity to learn about the structure and evolutionary history of this galaxy type in great detail. Among the many observing programs aimed at M31 are microlensing studies, which require good three-dimensional models of the stellar mass distribution. Possible non-axisymmetric structures like a bar need to be taken into account. Due to M31's high inclination, the bar is difficult to detect in photometry alone. Therefore, detailed kinematic measurements are needed to constrain the possible existence and position of a bar in M31. We obtained $\approx$ 220 separate fields with the optical IFU spectrograph VIRUS-W, covering the whole bulge region of M31 and parts of the disk. We derive stellar line-of-sight velocity distributions from the stellar absorption lines, as well as velocity distributions and line fluxes of the emission lines H$\beta$, [OIII] and [NI]. Our data supersede any previous study in terms of spacial coverage and spectral resolution. We find several features that are indicative of a bar in the kinematics of the stars, we see intermediate plateaus in the velocity and the velocity dispersion, and correlation between the higher moment $h3$ and the velocity. The gas kinematics is highly irregular, but is consistent with non-triaxial streaming motions caused by a bar. The morphology of the gas shows a spiral pattern, with seemingly lower inclination than the stellar disk. We also look at the ionization mechanisms of the gas, which happens mostly through shocks and not through starbursts.Comment: 23 pages, 39 figures; accepted for publication in A&

Temperature dependent spatial oscillations in the correlations of the XXZ spin chain

We study the correlation $$ for the XXZ chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.Comment: 4 pages, REVTEX, 6 table

Single Top Quark Production and Decay at Next-to-leading Order in Hadron Collision

We present a calculation of the next-to-leading order QCD corrections, with one-scale phase space slicing method, to single top quark production and decay process $p\bar{p},pp\to t\bar{b}+X\to b\ell\nu\bar{b}+X$ at hadron colliders. Using the helicity amplitude method, the angular correlation of the final state partons and the spin correlation of the top quark are preserved. The effect of the top quark width is also examined.Comment: 47 pages, 9 figure

The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable $N$-state chiral Potts model. We show that the whole set of functional equations is valid for the $Q$-operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the $Q$-operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations added for clearer presentation, References updated-Journal version with modified labelling of sections and formula