Structure and diffusion time scales of disordered clusters

The eigenvalue spectra of the transition probability matrix for random walks traversing critically disordered clusters in three different types of percolation problems show that the random walker sees a developing Euclidean signature for short time scales as the local, full-coordination constraint is iteratively applied.Comment: 5 pages, 4 figures, submitted to Physics Letters

Exact Solutions to the Two-dimensional BF and Yang-Mills Theories in the Light-cone Gauge

It is shown that the BRS-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the $\widetilde{B}^2$ term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang-Mills theory is also obtained.Comment: 11 pages, LaTe

Diffusion and spectral dimension on Eden tree

We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension $d_s$ and the walk dimension $d_w$ and test the scaling relation $d_s = 2d_f/d_w$ ($=2d/d_w$ for an Eden tree). Finite-size induced crossovers are observed, whereby the system crosses over from a short-time regime where this relation is violated (particularly in two dimensions) to a long-time regime where the behavior appears to be complicated and dependent on dimension even qualitatively.Comment: 11 pages, Plain TeX with J-Phys.sty style, HLRZ 93/9

The Dog on the Ship: The "Canis Major Dwarf Galaxy" as an Outlying Part of the Argo Star System

Overdensities in the distribution of low latitude, 2MASS giant stars are revealed by systematically peeling away from sky maps the bulk of the giant stars conforming to ``isotropic'' density laws generally accounting for known Milky Way components. This procedure, combined with a higher resolution treatment of the sky density of both giants and dust allows us to probe to lower Galactic latitudes than previous 2MASS giant star studies. While the results show the swath of excess giants previously associated with the Monoceros ring system in the second and third Galactic quadrants at distances of 6-20 kpc, we also find a several times larger overdensity of giants in the same distance range concentrated in the direction of the ancient constellation Argo. Isodensity contours of the large structure suggest that it is highly elongated and inclined by about 3 deg to the disk, although details of the structure -- including the actual location of highest density, overall extent, true shape -- and its origin, remain unknown because only a fraction of it lies outside highly dust-obscured, low latitude regions. Nevertheless, our results suggest that the 2MASS M giant overdensity previously claimed to represent the core of a dwarf galaxy in Canis Major (l ~ 240 deg) is an artifact of a dust extinction window opening to the overall density rise to the more significant Argo structure centered at larger longitude (l ~ 290 +- 10 deg, b ~ -4 +- 2 deg).Comment: 4 pages, 4 figure

The Virgo High-Resolution CO Survey. II. Rotation Curves and Dynamical Mass Distributions

Based on a high-resolution CO survey of Virgo spirals with the Nobeyama Millimeter-wave Array, we determined the dynamical centers using velocity fields, and derived position-velocity diagrams (PVDs) along the major axes of the galaxies across their dynamical centers. We applied a new iteration method to derive rotation curves (RCs), which reproduce the observed PVDs. The obtained high-accuracy RCs generally show steep rise in the central 100 to 200 pc regions, followed by flat rotation in the disk. We applied a deconvolution method to calculate the surface-mass density (SMD) using the RCs based on two extreme assumptions that the mass distribution is either spherical or thin-disk shaped. Both assumptions give nearly identical results, agreeing with each other within a factor of two at any radii. The SMD distributions revealed central massive cores with peak SMD of 10^4 - 10^5 Msun pc^-2 and total mass within 200 pc radius of the order of about 10^9 Msun Correlation analysis among the derived parameters show that the central CO-line intensity is positively correlated with the central SMD, which suggests that the deeper is the gravitational potential, the higher is the molecular gas concentration in the nuclei regardless morphological types.Comment: PASJ 2003 in press, Latex 12 pages, 6 figures (Bigger gif/ps figures available at http://www.ioa.s.u-tokyo.ac.jp/radio/virgo2

Geometry of fully coordinated, two-dimensional percolation

We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same universality class with ordinary percolation statically but not so dynamically. We show that there are large differences in the number and distribution of the interior sites between the two problems which may account for the different dynamic nature.Comment: ReVTeX, 5 pages, 6 figure

There are no abnormal solutions of the Bethe−-Salpeter equation in the static model

The four-point Green's function of static QED, where a fermion and an antifermion are located at fixed space positions, is calculated in covariant gauges. The bound state spectrum does not display any abnormal state corresponding to excitations of the relative time. The equation that was established by Mugibayashi in this model and which has abnormal solutions does not coincide with the Bethe$-$Salpeter equation. Gauge transformation from the Coulomb gauge also confirms the absence of abnormal solutions in the Bethe$-$Salpeter equation.Comment: 11 pages, late