Wilson surfaces and higher dimensional knot invariants

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.Comment: 31 pages, 9 figure

Quasars and galaxy formation

Quasars are widely believed to be powered by accretion onto supermassive black holes and there is now considerable evidence for a link between mergers, quasars and the formation of spheroids. Cattaneo, Haehnelt & Rees (1999) have demonstrated that a very simple model in which supermassive black holes form and accrete most of their mass in mergers of galaxies of comparable masses can reproduce the observed relation of black hole mass to bulge luminosity. Here we show that this simple model can account for the luminosity function of quasars and for the redshift evolution of the quasar population provided a few additional assumptions are made. We use the extended Press-Schechter formalism to simulate the formation of galaxies in hierarchical models of the formation of structures and we assume that, when two galaxies of comparable masses merge, their central black holes coalesce and a fraction of the gas in the merger remnant is accreted by the supermassive black hole over a time-scale of about 10^7 yr. We find that the decrease in the merging rate with cosmic time and the depletion in the amount of cold gas available due to the formation of stars are not sufficient to explain the strong decline in the space density of bright quasars between z=2 and z=0, since larger and larger structures form, which can potentially host brighter and brighter quasars. To explain the redshift evolution of the space density of bright quasars between z=2 and z=0 we need to assume that there is a dependence on redshift either in the fraction of available gas accreted or in the time-scale for accretion.Comment: 8 pages, 8 figures, submitted to MNRA

Integral Invariants of 3-Manifolds

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo

Black Holes and Cosmological Constant in Bosonic String Theory: Some Remarks

(some corrections in the semiclassical study and one reference added).Comment: 17 pages; PHYZZX; IFUM 450/F

How do galaxies acquire their mass?

We introduce a toy model that describes (in a single equation) the mass in stars as a function of halo mass and redshift. Our model includes the suppression of gas accretion from gravitational shock heating and AGN jets mainly for M_halo > M_shock ~ 10^12 M_Sun and from a too hot IGM onto haloes with v_circ < 40 km/s, as well as stellar feedback that drives gas out of haloes mainly with v_circ < 120 km/s. We run our model on the merger trees of the haloes and subhaloes of a high-resolution dark matter cosmological simulation. The galaxy mass is taken as the maximum between the mass given by the model and the sum of the masses of its progenitors (reduced by tidal stripping). Designed to reproduce the present-day stellar mass function of galaxies, our model matches fairly well the evolution of the cosmic stellar density. It leads to the same z=0 relation between central galaxy stellar and halo mass as the one found by abundance matching and also as that previously measured at high mass on SDSS centrals. Our model also predicts a bimodal distribution (centrals and satellites) of stellar masses for given halo mass, in good agreement with SDSS observations. The relative importance of mergers depends much more on stellar than halo mass. Galaxies with m_stars > 10^11 M_Sun/h acquire most of their mass through mergers (mostly major and gas-poor), as expected from our model's shutdown of gas accretion at high M_halo. However, mergers are rare for m_stars < 10^11 M_Sun/h (greater than our mass resolution), a consequence of the curvature of the stellar vs. halo mass relation. So gas accretion must be the dominant growth mechanism for intermediate and low mass galaxies, e.g. dwarf ellipticals in clusters, except that gas-rich galaxy mergers account for the bulk of the growth of ellipticals with m_stars ~ 10^10.5 M_Sun/h, which we predict must be the typical mass of ULIRGs.Comment: 18 pages, 12 figures, A&A in press (major re-write and updated figures from version 1

Hybrid quantum key distribution using coherent states and photon-number-resolving detectors

We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. In the presence of direct reconciliation, the PNR strategy is still the best one against individual attacks, but for the collective ones the homodyne-based scheme is still to be preferred as the channel transmissivity decreases.Comment: 5 pages, 5 figures. We extended our analysis to reverse reconciliation and to collective attack

Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes

We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity. We choose radiative boundary conditions at the vertical boundaries in which the heat flux is propor- tional to the fourth power of the temperature. We compare the results with the corresponding cases in which fixed temperature boundary conditions are applied. The most notable result is that the formation of a fully convective state in which the density is nearly constant as a function of height and the heat is transported to the upper and lower boundaries by overturning motions is robust and persists even in cases with radiative boundary conditions. Interestingly, in the convective regime, although the diffusive transport is negligible the mean stratification does not relax to an adiabatic state.Comment: 11 pages, 4 figures, accepted for publication in ApJ Letter

Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables

We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows. For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B). In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.Comment: TeX, 39 page

A Counterexample to the Quantizability of Modules

Let a Poisson structure on a manifold M be given. If it vanishes at a point m, the evaluation at m defines a one dimensional representation of the Poisson algebra of functions on M. We show that this representation can, in general, not be quantized. Precisely, we give a counterexample for M=R^n, such that: (i) The evaluation map at 0 can not be quantized to a representation of the algebra of functions with product the Kontsevich product associated to the Poisson structure. (ii) For any formal Poisson structure extending the given one and vanishing at zero up to second order in epsilon, (i) still holds. We do not know whether the second claim remains true if one allows the higher order terms in epsilon to attain nonzero values at zero