Synthetic Light Curves of Shocked Dense Circumstellar Shells

We numerically investigate light curves (LCs) of shocked circumstellar shells which are suggested to reproduce the observed LC of superluminous SN 2006gy analytically. In the previous analytical model, the effects of the recombination and the bolometric correction on LCs are not taken into account. To see the effects, we perform numerical radiation hydrodynamic calculations of shocked shells by using STELLA, which can numerically treat multigroup radiation transfer with realistic opacities. We show that the effects of the recombination and the bolometric correction are significant and the analytical model should be compare to the bolometric LC instead of a single band LC. We find that shocked circumstellar shells have a rapid LC decline initially because of the adiabatic expansion rather than the luminosity increase and the shocked shells fail to explain the LC properties of SN 2006gy. However, our synthetic LCs are qualitatively similar to those of superluminous SN 2003ma and SN 1988Z and they may be related to shocked circumstellar shells.Comment: 7 pages, 7 figures, 1 table, accepted by Monthly Notices of the Royal Astronomical Societ

Stability conditions and Fermi surface topologies in a superconductor

Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either zero, one, or two spheres in momentum space. With no zeroes, we have a conventional BCS superconductor. The other two cases, ``gapless'' superconductors, appear in mean field theory for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria for those candidate phases. Positivity of number susceptibility appears to provide the most powerful constraint, and renders all the two-zero states that we have examined mechanically unstable. Our results should apply directly to ultracold fermionic atom systems.Comment: 18 pages, 7 figures; v2: some clarifications in Sec. IIC; references added; version accepted for publication in Phys. Rev.

Homogeneous singularities inside collapsing wormholes

We analyze analytically and numerically the origin of the singularity in the course of the collapse of a wormhole with the exotic scalar field Psi with negative energy density, and with this field Psi together with the ordered magnetic field H. We do this under the simplifying assumptions of the spherical symmetry and that in the vicinity of the singularity the solution of the Einstein equations depends only on one coordinate (the homogeneous approximation). In the framework of these assumptions we found the principal difference between the case of the collapse of the ordinary scalar field Phi with the positive energy density together with an ordered magnetic field H and the collapse of the exotic scalar field Psi together with the magnetic field H. The later case is important for the possible astrophysical manifestation of the wormholes.Comment: 10 pages, 5 figures each of which has a),b),c),and d) sub-figures. To be published in "Physical review. D, Particles, fields, gravitation, and cosmology

Phase space contraction and quantum operations

We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as ``quantum phase space contraction rate'' and which is related to a fundamental property of quantum channels: non-unitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attaractor-like structures is displayed.Comment: 8 pages, 6 figures. Changes added according to refferee sugestions. (To appear in PRA

Damping of sound waves in superfluid nucleon-hyperon matter of neutron stars

We consider sound waves in superfluid nucleon-hyperon matter of massive neutron-star cores. We calculate and analyze the speeds of sound modes and their damping times due to the shear viscosity and non-equilibrium weak processes of particle transformations. For that, we employ the dissipative relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated recently [M.E. Gusakov and E.M. Kantor, Phys. Rev. D78, 083006 (2008)]. We demonstrate that the damping times of sound modes calculated using this hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other by several orders of magnitude.Comment: 15 pages, 5 figures, Phys. Rev. D accepte

The Relativistic Hopfield network: rigorous results

The relativistic Hopfield model constitutes a generalization of the standard Hopfield model that is derived by the formal analogy between the statistical-mechanic framework embedding neural networks and the Lagrangian mechanics describing a fictitious single-particle motion in the space of the tuneable parameters of the network itself. In this analogy the cost-function of the Hopfield model plays as the standard kinetic-energy term and its related Mattis overlap (naturally bounded by one) plays as the velocity. The Hamiltonian of the relativisitc model, once Taylor-expanded, results in a P-spin series with alternate signs: the attractive contributions enhance the information-storage capabilities of the network, while the repulsive contributions allow for an easier unlearning of spurious states, conferring overall more robustness to the system as a whole. Here we do not deepen the information processing skills of this generalized Hopfield network, rather we focus on its statistical mechanical foundation. In particular, relying on Guerra's interpolation techniques, we prove the existence of the infinite volume limit for the model free-energy and we give its explicit expression in terms of the Mattis overlaps. By extremizing the free energy over the latter we get the generalized self-consistent equations for these overlaps, as well as a picture of criticality that is further corroborated by a fluctuation analysis. These findings are in full agreement with the available previous results.Comment: 11 pages, 1 figur