An apprach to generate large and small leptonic mixing angles

We take up the point of view that Yukawa couplings can be either 0 or 1, and the mass patterns of fermions are generated purely from the structure of the Yukawa matrices. We utilize such neutrino as well as charged leptonic textures which lead to (maximal) mixing angles of $\pi/4$ in each sector for relevant transitions. The combined leptonic CKM mixing angles are $\pi/4 \pm \pi/4$ which lead to very small $\sin^2 2 \Theta$ relevant to solar neutrino and LSND experiments. We propose that on the other hand the absence of the charged leptonic partner of the sterile neutrino maintains the angle $\pi/4$ from the neutrino sector for the transition $\nu_\mu \leftrightarrow \nu_s$ and hence atmospheric neutrino anomaly is explained through maximal mixing

Cascading on extragalactic background light

High-energy gamma-rays propagating in the intergalactic medium can interact with background infrared photons to produce e+e- pairs, resulting in the absorption of the intrinsic gamma-ray spectrum. TeV observations of the distant blazar 1ES 1101-232 were thus recently used to put an upper limit on the infrared extragalactic background light density. The created pairs can upscatter background photons to high energies, which in turn may pair produce, thereby initiating a cascade. The pairs diffuse on the extragalactic magnetic field (EMF) and cascade emission has been suggested as a means for measuring its intensity. Limits on the IR background and EMF are reconsidered taking into account cascade emissions. The cascade equations are solved numerically. Assuming a power-law intrinsic spectrum, the observed 100 MeV - 100 TeV spectrum is found as a function of the intrinsic spectral index and the intensity of the EMF. Cascades emit mainly at or below 100 GeV. The observed TeV spectrum appears softer than for pure absorption when cascade emission is taken into account. The upper limit on the IR photon background is found to be robust. Inversely, the intrinsic spectra needed to fit the TeV data are uncomfortably hard when cascade emission makes a significant contribution to the observed spectrum. An EMF intensity around 1e-8 nG leads to a characteristic spectral hump in the GLAST band. Higher EMF intensities divert the pairs away from the line-of-sight and the cascade contribution to the spectrum becomes negligible.Comment: 5 pages, to be published as a research note in A&

On the Accuracy of the Semiclassical Trace Formula

The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system increases, the mean level spacing decreases as $\hbar^d$, while the semiclassical approximation is commonly believed to provide an accuracy of order $\hbar^2$, independently of d. If this were true, the semiclassical trace formula would be limited to systems in d <= 2 only. In the present work we set about to define proper measures of the semiclassical spectral accuracy, and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy, measured in units of the mean level spacing, depends only weakly (if at all) on the dimensionality. Detailed and thorough numerical tests were performed for the Sinai billiard in 2 and 3 dimensions, substantiating the theoretical arguments.Comment: LaTeX, 31 pages, 14 figures, final version (minor changes

Hierarchy and Wave Functions in a Simple Quantum Cosmology

Astrophysical observations indicate the expansion of the universe is accelerating. Applying the holographic entropy conjecture to the cosmological horizon in an accelerating universe suggests the universe has only a finite number of degrees of freedom. This is consistent with a closed universe arising from a quantum fluctuation, with zero total quantum numbers. If space-time has eleven dimensions, and the universe began as a closed force-symmetric ten-dimensional space with characteristic dimension L, seven of the space dimensions must have collapsed to generate the three large space dimensions we see. The holographic conjecture then suggests the initial length scale L must be roughly twenty orders of magnitude larger than the Planck length. Accordingly, the nuclear force must be roughly forty orders of magnitude stronger than gravity, possibly resolving the force hierarchy problem. A wavefunction for the radius of curvature of the universe can be obtained from the Schrodinger equation derived by Elbaz and Novello. The product of this wavefunction and its complex conjugate can be interpreted as the probability density for finding a given radius of curvature in one of the infinity of measurements of the radius of curvature possible (in principle) at any location in a homogeneous isotropic universe.Comment: 4 pages, no figures, abstract corrected to insert omitted word

Constraints on mixing angles of Majorana neutrinos

By combining the inputs from the neutrinoless double beta decay and the fits of cosmological models of dark matter with solar and atmospheric neutrino data, we obtain constraints on two of the mixing angles of Majorana neutrinos, which become stronger when coupled with the reactor neutrino data. These constraints are strong enough to rule out Majorana neutrinos if the small angle solution of solar neutrino puzzle is borne out.Comment: Some corrections and clarifications adde

A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on the basis of numerical evidence.Comment: 8 pages; analysis made more rigorous in the revised versio

Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics

We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on whether the chain is disordered or invariant under lattice translations. In the disordered case, the spectrum is dominated by Anderson localization whereas in the periodic case, the spectrum is arranged in bands. We investigate the special features in the spectral statistics for a periodic chain. For finite N, we define spectral form factors involving correlations both for identical and non-identical Bloch numbers. The short-time regime is treated within the semiclassical approximation, where the spectral form factor can be expressed in terms of a coarse-grained classical propagator which obeys a diffusion equation with periodic boundary conditions. In the long-time regime, the form factor decays algebraically towards an asymptotic constant. In the limit $N\to\infty$, we derive a universal scaling function for the form factor. The theory is supported by numerical results for quasi one-dimensional periodic chains of coupled Sinai billiards.Comment: 33 pages, REVTeX, 13 figures (eps

Semiclassical Treatment of Diffraction in Billiard Systems with a Flux Line

In billiard systems with a flux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diffractive orbits that are scattered on the flux line. We derive a semiclassical approximation for diffractive orbits that are scattered once on a flux line. This approximation is uniformly valid for all scattering angles. The diffractive contributions are necessary in order that semiclassical approximations are continuous if the position of the flux line is changed.Comment: LaTeX, 17 pages, 4 figure

Fate of the Universe, Age of the Universe, Dark Matter, and the Decaying Vacuum Energy

It is shown that in the cosmological models based on a vacuum energy decaying as a^{-2}, where a is the scale factor of the universe, the fate of the universe in regard to whether it will collapse in future or expand forever is determined not by the curvature constant k but by an effective curvature constant k_{eff}. It is argued that a closed universe with k=1 may expand forever, in other words simulate the expansion dynamics of a flat or an open universe because of the possibility that k_{eff}=0 or -1, respectively. Two such models, in one of which the vacuum does not interact with matter and in another of which it does, are studied. It is shown that the vacuum equation of state p_{vac}= -\rho_{vac} may be realized in a decaying vacuum cosmology provided the vacuum interacts wuth matter. The optical depths for gravitational lensing as a function of the matter density and other parameters in the models are calculated at a source redshift of 2. The age of the universe is discussed and shown to be compatible with the new Hipparcos lower limit of 11Gyr. The possibility that a time-varying vacuum energy may serve as dark matter is suggested.Comment: AAS LaTex, 29 pages, published in the Astrophysical Journal, 520, 45, 199

Asymmetric neutrino Yukawa matrices and neutrino mixing

We study leptonic CKM mixing matrices when the neutrino Yukawa matrices are antisymmetric which gives rise to mass patterns suitable to explain solar, atmospheric and LSND neutrino oscillation experiments. Taking diagonal leptonic matrices which can give rise to hierarchical lepton masses, we compute the leptonic CKM matrix.Comment: version to appear in Phys. Rev.