Inhomogeneous Quantum Mixmaster: from Classical toward Quantum Mechanics

Starting from the Hamiltonian formulation for the inhomogeneous Mixmaster dynam- ics, we approach its quantum features through the link of the quasi-classical limit. We fix the proper operator-ordering which ensures that the WKB continuity equation overlaps the Liouville theorem as restricted to the configuration space. We describe the full quantum dynamics of the model in some details, providing a characterization of the (discrete) spectrum with analytic expressions for the limit of high occupation number. One of the main achievements of our analysis relies on the description of the ground state morphology, showing how it is characterized by a non-vanishing zero-point energy associated to the Universe anisotropy degrees of freedomComment: 17 pages, 6 figures, to appear on Classical and Quantum Gravity PACS: 04.20.Jb, 98.80.Dr, 83

Classical and Quantum Aspects of the Inhomogeneous Mixmaster Chaoticity

We refine Misner's analysis of the classical and quantum Mixmaster in the fully inhomogeneous picture; we both connect the quantum behavior to the ensemble representation, both describe the precise effect of the boundary conditions on the structure of the quantum states.Comment: 3 pages, 2 figures, proceedings of the XI Marcel Grossmann meeting on Relativistic Astrophysics, July 23-29, 2006, Berli

Covariant Description of the Inhomogeneous Mixmaster Chaos

We outline the covariant nature of the chaos characterizing the generic cosmological solution near the initial singularity. Our analysis is based on a "gauge" independent ADM-reduction of the dynamics to the physical degrees of freedom, and shows that the dynamics is isomorphic point by point in space to a billiard on a Lobachevsky plane. The Jacobi metric associated to the geodesic flow is constructed and a non-zero Lyapunov exponent is explicitly calculated. The chaos covariance emerges from the independence of the form of the lapse function and the shift vector.Comment: 3 pages, 1 figure, proceedings of the XI Marcel Grossmann meeting on Relativistic Astrophysics, July 23-29, 2006, Berli

Signatures of the neutrino thermal history in the spectrum of primordial gravitational waves

In this paper we study the effect of the anisotropic stress generated by neutrinos on the propagation of primordial cosmological gravitational waves. The presence of anisotropic stress, like the one generated by free-streaming neutrinos, partially absorbs the gravitational waves (GWs) propagating across the Universe. We find that in the standard case of three neutrino families, 22% of the intensity of the wave is absorbed, in fair agreement with previous studies. We have also calculated the maximum possible amount of damping, corresponding to the case of a flat Universe completely dominated by ultrarelativistic collisionless particles. In this case 43% of the intensity of the wave is absorbed. Finally, we have taken into account the effect of collisions, using a simple form for the collision term parameterized by the mean time between interactions, that allows to go smoothly from the case of a tigthly-coupled fluid to that of a collisionless gas. The dependence of the absorption on the neutrino energy density and on the effectiveness of the interactions opens the interesting possibility of observing spectral features related to particular events in the thermal history of the Universe, like neutrino decoupling and electron-positron annihilation, both occurring at T~1 MeV. GWs entering the horizon at that time will have today a frequency \nu\sim 10^{-9} \Hz, a region that is going to be probed by Pulsar Timing Arrays.Comment: V1: 14 pages, 2 figures. To appear in Gen. Rel. Grav. V2: References Adde

Vector Field Induced Chaos in Multi-dimensional Homogeneous Cosmologies

We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists for any number of spatial dimensions and for all homogeneous models. We derive the Poincar\'e return map associated to the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a 4-dimensional space time, the oscillatory regime here constructed overlap the usual Belinski-Khalatnikov-Liftshitz one.Comment: 3 pages, proceedings of the XI Marcel Grossmann meeting on Relativistic Astrophysics, July 23-29, 2006, Berli

Linear Two-Dimensional MHD of Accretion Disks: Crystalline structure and Nernst coefficient

We analyse the two-dimensional MHD configurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline structure outlined in Coppi (2005), dealing with a local model too, when a specific accretion rate is taken into account. We limit our attention to the linearised MHD formulation of the electromagnetic back-reaction characterising the equilibrium, by fixing the structure of the radial, vertical and azimuthal profiles. Since we deal with toroidal currents only, the consistency of the model is ensured by the presence of a small collisional effect, phenomenologically described by a non-zero constant Nernst coefficient (thermal power of the plasma). Such an effect provides a proper balance of the electron force equation via non zero temperature gradients, related directly to the radial and vertical velocity components. We show that the obtained profile has the typical oscillating feature of the crystalline structure, reconciled with the presence of viscosity, associated to the differential rotation of the disk, and with a net accretion rate. In fact, we provide a direct relation between the electromagnetic reaction of the disk and the (no longer zero) increasing of its mass per unit time. The radial accretion component of the velocity results to be few orders of magnitude below the equatorial sound velocity. Its oscillating-like character does not allow a real matter in-fall to the central object (an effect to be searched into non-linear MHD corrections), but it accounts for the out-coming of steady fluxes, favourable to the ring-like morphology of the disk.Comment: 15 pages, 1 figure, accepted for publication on Modern Physics Letters

Hierarchical Structuring of Video Previews by Leading-Cluster-Analysis

3noClustering of shots is frequently used for accessing video data and enabling quick grasping of the associated content. In this work we first group video shots by a classic hierarchical algorithm, where shot content is described by a codebook of visual words and different codebooks are compared by a suitable measure of distortion. To deal with the high number of levels in a hierarchical tree, a novel procedure of Leading-Cluster-Analysis is then proposed to extract a reduced set of hierarchically arranged previews. The depth of the obtained structure is driven both from the nature of the visual content information, and by the user needs, who can navigate the obtained video previews at various levels of representation. The effectiveness of the proposed method is demonstrated by extensive tests and comparisons carried out on a large collection of video data. of digital videos has not been accompanied by a parallel increase in its accessibility. In this context, video abstraction techniques may represent a key components of a practical video management system: indeed a condensed video may be effective for a quick browsing or retrieval tasks. A commonly accepted type of abstract for generic videos does not exist yet, and the solutions investigated so far depend usually on the nature and the genre of video data.openopenBenini, Sergio; Migliorati, Pierangelo; Leonardi, RiccardoBenini, Sergio; Migliorati, Pierangelo; Leonardi, Riccard