Eigenvalue correlations on Hyperelliptic Riemann surfaces

In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context of random matrix theory this object gives the eigenvalue fluctuations of Hermitian random matrix ensembles where the eigenvalue density is supported on J.Comment: latex 2e, seven pages, one figure. To appear in Journal of Physics

Seeking for toroidal event horizons from initially stationary BH configurations

We construct and evolve non-rotating vacuum initial data with a ring singularity, based on a simple extension of the standard Brill-Lindquist multiple black-hole initial data, and search for event horizons with spatial slices that are toroidal when the ring radius is sufficiently large. While evolutions of the ring singularity are not numerically feasible for large radii, we find some evidence, based on configurations of multiple BHs arranged in a ring, that this configuration leads to singular limit where the horizon width has zero size, possibly indicating the presence of a naked singularity, when the radius of the ring is sufficiently large. This is in agreement with previous studies that have found that there is no apparent horizon surrounding the ring singularity when the ring's radius is larger than about twice its mass.Comment: 24 pages, 14 figure

Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model

We study the hole propagator of the Calogero-Sutherland model with SU(2) internal symmetry. We obtain the exact expression for arbitrary non-negative integer coupling parameter $\beta$ and prove the conjecture proposed by one of the authors. Our method is based on the theory of the Jack polynomials with a prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur

NUGA: the IRAM survey of AGN spiral hosts

The NUclei of GAlaxies (NUGA) project is a combined effort to carry out a high-resolution (<1'') interferometer CO survey of a sample of 12 nearby AGN spiral hosts, using the IRAM array. We map the distribution and dynamics of molecular gas in the inner 1 kpc of the nuclei with resolutions of 10-50 pc, and study the mechanisms for gas fueling of the different low-luminosity AGN. First results show evidence for the occurrence of strong m=1 gas instabilities in Seyferts. NUGA maps allow us to address the origin/nature of m=1 modes and their link with m=2 modes and acoustic instabilities, present in other targets.Comment: 1 gzipped tar file containing 1 Latex file + 3 eps figures. Proceedings of ''Active Galactic Nuclei: from Central Engine to Host Galaxy'', meeting held in Meudon, France, July 23-27, 2002, Eds.: S. Collin, F. Combes and I. Shlosman. To be published in ASP Conference Serie

ALMA reveals the feeding of the Seyfert 1 nucleus in NGC 1566

We report ALMA observations of CO(3-2) emission in the Seyfert 1 galaxy NGC 1566, at a spatial resolution of 25 pc. Our aim is to investigate the morphology and dynamics of the gas inside the central kpc, and to probe nuclear fueling and feedback phenomena. NGC 1566 has a nuclear bar of 1.7 kpc radius and a conspicuous grand design spiral starting from this radius. The ALMA field of view, of diameter 0.9 kpc, lies well inside the nuclear bar and reveals a molecular trailing spiral structure from 50 to 300~pc in size, which is contributing to fuel the nucleus, according to its negative gravity torques. The spiral starts with a large pitch angle from the center and then winds up in a pseudo-ring at the inner Lindblad resonance (ILR) of the nuclear bar. This is the first time that a trailing spiral structure is clearly seen driving the gas inwards inside the ILR ring of the nuclear bar. This phenomenon shows that the massive central black hole has a significant dynamical influence on the gas, triggering its fueling. The gaseous spiral is well correlated with the dusty spiral seen through extinction in HST images, and also with a spiral feature emitting 0.87mm continuum. This continuum emission must come essentially from cold dust heated by the interstellar radiation field. The HCN(4-3) and HCO+(4-3) lines were simultaneously mapped and detected in the nuclear spiral. The HCO+(4-3) line is 3 times stronger than the HCN(4-3), as expected when star formation excitation dominates over active galactic nucleus (AGN) heating. The CO(3-2)/HCO+(4-3) integrated intensity ratio is \sim 100. The molecular gas is in remarkably regular rotation, with only slight non-circular motions at the periphery of the nuclear spiral arms. These perturbations are quite small, and no outflow nor AGN feedback is detected.Comment: 11 pages, 16 figures, accepted in Astronomy and Astrophysic

Common Algebraic Structure for the Calogero-Sutherland Models

We investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis for the rational case.Comment: 7 pages, LaTeX, no figures, some text and references added, minor misprints correcte

ALMA observations of feeding and feedback in nearby Seyfert galaxies: an AGN-driven outflow in NGC 1433

We report ALMA observations of CO(3-2) emission in the Seyfert 2 double-barred galaxy NGC1433, at the unprecedented spatial resolution of 0.5"=24 pc. Our aim is to probe AGN feeding and feedback phenomena through the morphology and dynamics of the gas inside the central kpc. The CO map, which covers the whole nuclear region (nuclear bar and ring), reveals a nuclear gaseous spiral structure, inside the nuclear ring encircling the nuclear stellar bar. This gaseous spiral is well correlated with the dusty spiral seen in Hubble Space Telescope images. The nuclear spiral winds up in a pseudo-ring at 200 pc radius, which might correspond to the inner ILR. Continuum emission is detected at 0.87 mm only at the very centre, and its origin is more likely thermal dust emission than non-thermal emission from the AGN. It might correspond to the molecular torus expected to exist in this Seyfert 2 galaxy. The HCN(4-3) and HCO+(4-3) lines were observed simultaneously, but only upper limits are derived, with a ratio to the CO(3-2) line lower than 1/60 at 3sigma, indicating a relatively low abundance of very dense gas. The kinematics of the gas over the nuclear disk reveal rather regular rotation only slightly perturbed by streaming motions due to the spiral; the primary and secondary bars are too closely aligned with the galaxy major or minor axis to leave a signature in the projected velocities. Near the nucleus, there is an intense high-velocity CO emission feature redshifted to 200 km/s (if located in the plane), with a blue-shifted counterpart, at 2" (100 pc) from the centre. While the CO spectra are quite narrow in the centre, this wide component is interpreted as an outflow involving a molecular mass of 3.6 10^6 Mo and a flow rate 7 Mo/yr. The flow could be in part driven by the central star formation, but is mainly boosted by the AGN through its wind or radio jets.Comment: 11 pages, 9 figures, Accepted in Astronomy and Astrophysic

Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions

Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact that about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F. Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator ${\bold{D}}$, identities of Pfaffians, symmetric functions, hyperelliptic $\sigma$-function and $\wp$-functions; $\wp_{\mu \nu} = -\partial_\mu \partial_\nu \log \sigma$ $= - ({\bold{D}}_\mu {\bold{D}}_\nu \sigma \sigma)/2\sigma^2$. The connection between his theory and the modern soliton theory was also discussed.Comment: AMS-Tex, 12 page

Wannier functions for quasi-periodic finite-gap potentials

In this paper we consider Wannier functions of quasi-periodic g-gap ($g\geq 1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging underlying the definition of Wannier functions for both periodic and quasi-periodic potentials and express Bloch functions and quasi-momenta in terms of hyperelliptic $\sigma$ functions. Using this approach we derive a power series expansion of the Wannier function for quasi-periodic potentials valid at $|x|\simeq 0$ and an asymptotic expansion valid at large distance. These functions are important for a number of applied problems

Bose-Einstein-condensed systems in random potentials

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state. But the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.Comment: Latex file, final published varian