Discrete derivatives and symmetries of difference equations

We show on the example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable to find the symmetries of discrete equations. In this way we obtain a symmetry Lie algebra, defined in terms of shift operators, isomorphic to that of the continuous heat equation.Comment: submitted to J.Phys. A 10 Latex page

Mirror effect induced by the dilaton field on the Hawking radiation

We discuss the string creation in the near-extremal NS1 black string solution. The string creation is described by an effective field equation derived from a fundamental string action coupled to the dilaton field in a conformally invariant manner. In the non-critical string model the dilaton field causes a timelike mirror surface outside the horizon when the size of the black string is comparable to the Planck scale. Since the fundamental strings are reflected by the mirror surface, the negative energy flux does not propagate across the surface. This means that the evaporation stops just before the naked singularity of the extremal black string appears even though the surface gravity is non-zero in the extremal limit.Comment: 15 page

Absence of non-linear Meissner effect in YBa2Cu3O6.95

We present measurements the field and temperature dependence of the penetration depth (lambda) in high purity, untwinned single crystals of YBa2Cu3O6.95 in all three crystallographic directions. The temperature dependence of lambda is linear down to low temperatures, showing that our crystals are extremely clean. Both the magnitude and temperature dependence of the field dependent correction to lambda however, are considerably different from that predicted from the theory of the non-linear Meissner effect for a d-wave superconductor (Yip-Sauls theory). Our results suggest that the Yip-Sauls effect is either absent or is unobservably small in the Meissner state of YBa2Cu3O6.95.Comment: 4 pages, 4 figures (Latex file + Postscipt figures

Nebular Spectra of SN 1998bw Revisited: Detailed Study by One and Two Dimensional Models

Refined one- and two-dimensional models for the nebular spectra of the hyper-energetic Type Ic supernova (SN) 1998bw, associated with the gamma-ray burst GRB980425, from 125 to 376 days after B-band maximum are presented. One dimensional, spherically symmetric spectrum synthesis calculations show that reproducing features in the observed spectra, i.e., the sharply peaked [OI] 6300\AA doublet and MgI] 4570\AA emission, and the broad [FeII] blend around 5200\AA, requires the existence of a high-density O-rich core expanding at low velocities (\lsim 8,000 km s$^{-1}$) and of Fe-rich material moving faster than the O-rich material. Synthetic spectra at late phases from aspherical (bipolar) explosion models are also computed with a two-dimensional spectrum synthesis code. The above features are naturally explained by the aspherical model if the explosion is viewed from a direction close to the axis of symmetry ($\sim 30^{\rm o}$), since the aspherical model yields a high-density O-rich region confined along the equatorial axis. By examining a large parameter space (in energy and mass), our best model gives following physical quantities: the kinetic energy $E_{51} \equiv E_{\rm K}/10^{51}$ ergs \gsim 8 - 12 and the main-sequence mass of the progenitor star M_{\rm ms} \gsim 30 - 35 \Msun. The temporal spectral evolution of SN 1998bw also indicates mixing among Fe-, O-, and C-rich regions, and highly clumpy structure.Comment: 38 pages, 22 figures. ApJ, 640 (01 April 2006 issue), in pres

Creation of the universe with a stealth scalar field

The stealth scalar field is a non-trivial configuration without any back-reaction to geometry, which is characteristic for non-minimally coupled scalar fields. Studying the creation probability of the de Sitter universe with a stealth scalar field by the Hartle and Hawking's semi-classical method, we show that the effect of the stealth field can be significant. For the class of scalar fields we consider, creation with a stealth field is possible for a discrete value of the coupling constant and its creation probability is always less than that with a trivial scalar field. However, those creation rates can be almost the same depending on the parameters of the theory.Comment: 7 pages; v2, references added; v3, creation of the open universe adde

Asymptotically Friedmann self-similar scalar field solutions with potential

We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are two distinct one-parameter families of asymptotic solutions,one is asymptotic to the proper Friedmann universe, while the other is asymptotic to the quasi-Friedmann universe, i.e., the Friedmann universe with anomalous solid angle. The asymptotically proper Friedmann solution is possible only if the universe is accelerated or the potential is negative. If the potential is positive, the density perturbation in the asymptotically proper Friedmann solution rapidly falls off at spatial infinity, while the mass perturbation is compensated. In the asymptotically quasi-Friedmann solution, the density perturbation falls off only in proportion to the inverse square of the areal radius and the relative mass perturbation approaches a nonzero constant at spatial infinity. The present result shows that a necessary condition holds in order that a self-gravitating body grows self-similarly due to the constant accretion of quintessence in an accelerating universe.Comment: accepted for publication in Physical Review D, minor correction, typos correcte

Collision of Domain Walls and Reheating of the Brane Universe

We study a particle production at the collision of two domain walls in 5-dimensional Minkowski spacetime. This may provide the reheating mechanism of an ekpyrotic (or cyclic) brane universe, in which two BPS branes collide and evolve into a hot big bang universe. We evaluate a production rate of particles confined to the domain wall. The energy density of created particles is given as $\rho \approx 20 \bar{g}^4 N_b ~m_\eta^4$ where $\bar{g}$ is a coupling constant of particles to a domain-wall scalar field, $N_b$ is the number of bounces at the collision and $m_\eta$ is a fundamental mass scale of the domain wall. It does not depend on the width $d$ of the domain wall, although the typical energy scale of created particles is given by $\omega\sim 1/d$. The reheating temperature is evaluated as $T_{\rm R}\approx 0.88 ~ \bar{g} ~ N_b^{1/4}$. In order to have the baryogenesis at the electro-weak energy scale, the fundamental mass scale is constrained as m_\eta \gsim 1.1\times 10^7 GeV for $\bar{g}\sim 10^{-5}$.Comment: 10 pages, 12 figure

Principles of Discrete Time Mechanics: IV. The Dirac Equation, Particles and Oscillons

We apply the principles of discrete time mechanics discussed in earlier papers to the first and second quantised Dirac equation. We use the Schwinger action principle to find the anticommutation relations of the Dirac field and of the particle creation operators in the theory. We find new solutions to the discrete time Dirac equation, referred to as oscillons on account of their extraordinary behaviour. Their principal characteristic is that they oscillate with a period twice that of the fundamental time interval T of our theory. Although these solutions can be associated with definite charge, linear momentum and spin, such objects should not be observable as particles in the continuous time limit. We find that for non-zero T they correspond to states with negative squared norm in Hilbert space. However they are an integral part of the discrete time Dirac field and should play a role in particle interactions analogous to the role of longitudinal photons in conventional quantum electrodynamics.Comment: 27 pages LateX; published versio

On the Light Curve and Spectrum of SN 2003dh Separated from the Optical Afterglow of GRB 030329

The net optical light curves and spectra of the supernova (SN) 2003dh are obtained from the published spectra of GRB 030329, covering about 6 days before SN maximum to about 60 days after. The bulk of the U-band flux is subtracted from the observed spectra using early-time afterglow templates, because strong line blanketing greatly depresses the UV and U-band SN flux in a metal-rich, fast-moving SN atmosphere. The blue-end spectra of the gamma-ray burst (GRB)connected hypernova SN 1998bw is used to determine the amount of subtraction. The subtraction of a host galaxy template affects the late-time results. The derived SN 2003dh light curves are narrower than those of SN 1998bw, rising as fast before maximum, reaching a possibly fainter maximum, and then declining ~ 1.2-1.4 times faster. We then build UVOIR bolometric SN light curve. Allowing for uncertainties, it can be reproduced with a spherical ejecta model of Mej ~ 7+/-3 Msun, KE ~ (3.5+/-1.5)E52 ergs, with KE/Mej ~ 5 following previous spectrum modelling, and M(Ni56) ~ (0.4 +0.15/-0.1) Msun. This suggests a progenitor main-sequence mass of about 25-40 Msun, lower than SN 1998bw but significantly higher than normal Type Ic SNe and the GRB-unrelated hypernova SN 2002ap.Comment: 18 pages, 7 figures, published by Ap

On two pieces of folklore in the AdS/CFT duality

In the AdS/CFT duality, it is often said that a local symmetry in a bulk theory corresponds to a global symmetry in the corresponding boundary theory, but the global symmetry can become local when one couples with an external source. As a result, the GKP-Witten relation gives a response function instead of a Green function. We explore this point in details using the example of holographic superconductors. We point out that these points play a crucial role to interpret the holographic London equation properly.Comment: 11 pages, ReVTeX4.1; v2: added discussio