A note on a local ergodic theorem for an infinite tower of coverings

This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and Statistic

Multiwavelength observation from radio through very-high-energy Gamma-ray of OJ 287 during the 12-year cycle flare in 2007

We performed simultaneous multiwavelength observations of OJ 287 with the Nobeyama Millimeter Array for radio, the KANATA telescope and the KVA telescope for optical, the Suzaku satellite for X-ray and the MAGIC telescope for very high energy (VHE) gamma-ray in 2007. The observations were conducted for a quiescent state in April and in a flaring state in November-December. We clearly observed increase of fluxes from radio to X-ray bands during the flaring state while MAGIC could not detect significant VHE gamma-ray emission from the source. We could derive an upper limit (95% confidence level) of 1.7% of the Crab Nebula flux above 150 GeV from about 41.2 hours of the MAGIC observation. A simple SSC model suggests that the observed flaring activity could be caused by evolutions in the distribution of the electron population rather than changes of the magnetic field strength or Doppler beaming factor in the jet.Comment: Contribution to the 31st ICRC, Lodz, Poland, July 200

A Luminous and Fast-Expanding Type Ib Supernova SN 2012au

We present a set of photometric and spectroscopic observations of a bright Type Ib supernova SN 2012au from -6d until ~+150d after maximum. The shape of its early R-band light curve is similar to that of an average Type Ib/c supernova. The peak absolute magnitude is M_R=-18.7+-0.2 mag, which suggests that this supernova belongs to a very luminous group among Type Ib supernovae. The line velocity of He I {\lambda}5876 is about 15,000 km/s around maximum, which is much faster than that in a typical Type Ib supernova. From the quasi-bolometric peak luminosity of (6.7+-1.3)x10^(42) erg/s, we estimate the \Ni mass produced during the explosion as ~0.30 Msun. We also give a rough constraint to the ejecta mass 5-7 Msun and the kinetic energy (7-18)x10^(51) erg. We find a weak correlation between the peak absolute magnitude and He I velocity among Type Ib SNe. The similarities to SN 1998bw in the density structure inferred from the light curve model as well as the large peak bolometric luminosity suggest that SN 2012au had properties similar to energetic Type Ic supernovae.Comment: 15 pages, 5 figures; accepted to ApJ

Decay of Correlations in a Topological Glass

In this paper we continue the study of a topological glassy system. The state space of the model is given by all triangulations of a sphere with $N$ nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7. Energies of nodes with other numbers of neighbors are supposed to be positive. The dynamics is that of flipping the diagonal between two adjacent triangles, with a temperature dependent probability. We consider the system at very low temperatures. We concentrate on several new aspects of this model: Starting from a detailed description of the stationary state, we conclude that pairs of defects (nodes with the "wrong" degree) move with very high mobility along 1-dimensional paths. As they wander around, they encounter single defects, which they then move "sideways" with a geometrically defined probability. This induces a diffusive motion of the single defects. If they meet, they annihilate, lowering the energy of the system. We both estimate the decay of energy to equilibrium, as well as the correlations. In particular, we find a decay like $t^{-0.4}$

Stable Mode Sorting by Two-Dimensional Parity of Photonic Transverse Spatial States

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG_nm input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG modes depending upon whether they have an even or odd value of their orbital angular momentum. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m=1) spatial states, covering the entire Poincare sphere of first-order transverse modes.Comment: 11 pages, 12 figures, 2 appendice

Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete geometric analysis to these problems. Results we obtain are extensions of ones by Kipnis, Olla and Varadhan to crystal lattices.Comment: 41 pages, 7 figure

Infrared/optical - X-ray simultaneous observations of X-ray flares in GRB 071112C and GRB 080506

We investigate the origin of short X-ray flares which are occasionally observed in early stages of afterglows of gamma-ray bursts (GRBs). We observed two events, GRB 071112C and GRB 080506, before the start of X-ray flares in the optical and near-infrared (NIR) bands with the 1.5-m Kanata telescope. In conjunction with published X-ray and optical data, we analyzed densely sampled light curves of the early afterglows and spectral energy distributions (SEDs) in the NIR-X-ray ranges. We found that the SEDs had a break between the optical and X-ray bands in the normal decay phases of both GRBs regardless of the model for the correction of the interstellar extinction in host galaxies of GRBs. In the X-ray flares, X-ray flux increased by 3 and 15 times in the case of GRB 071112C and 080506, respectively, and the X-ray spectra became harder than those in the normal decay phases. No significant variation in the optical-NIR range was detected together with the X-ray flares. These results suggest that the X-ray flares were associated with either late internal shocks or external shocks from two-component jets.Comment: 10 pages, 5 figures, accepted to Astronomy and Astrophysic