Some properties of the resonant state in quantum mechanics and its computation

The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles would decay exponentially in a fixed volume of integration. Moreover, we introduce new numerical methods of treating the resonant state with the use of the effective potential. We first give a numerical method of finding a resonance pole in the complex energy plane. The method seeks an energy eigenvalue iteratively. We found that our method leads to a super-convergence, the convergence exponential with respect to the iteration step. The present method is completely independent of commonly used complex scaling. We also give a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Since the wave function of the resonant state is diverging away from the scattering potential, it has been previously difficult to follow its time evolution numerically in a finite area.Comment: 20 pages, 12 figures embedde

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

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

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

A peculiar multi-wavelength flare in the Blazar 3C 454.3

The blazar 3C454.3 exhibited a strong flare seen in gamma-rays, X-rays, and optical/NIR bands during 3--12 December 2009. Emission in the V and J bands rose more gradually than did the gamma-rays and soft X-rays, though all peaked at nearly the same time. Optical polarization measurements showed dramatic changes during the flare, with a strong anti-correlation between optical flux and degree of polarization (which rose from ~ 3% to ~ 20%) during the declining phase of the flare. The flare was accompanied by large rapid swings in polarization angle of ~ 170 degree. This combination of behaviors appear to be unique. We have cm-band radio data during the same period but they show no correlation with variations at higher frequencies. Such peculiar behavior may be explained using jet models incorporating fully relativistic effects with a dominant source region moving along a helical path or by a shock-in-jet model incorporating three-dimensional radiation transfer if there is a dominant helical magnetic field. We find that spectral energy distributions at different times during the flare can be fit using modified one-zone models where only the magnetic field strength and particle break frequencies and normalizations need change. An optical spectrum taken at nearly the same time provides an estimate for the central black hole mass of ~ 2.3 * 10^9 M_sun. We also consider two weaker flares seen during the $\sim 200$ d span over which multi-band data are available. In one of them, the V and J bands appear to lead the $\gamma$-ray and X-ray bands by a few days; in the other, all variations are simultaneous.Comment: 11 pages, 4 figures, 2 tables; MNRAS in pres

Nano-displacement measurements using spatially multimode squeezed light

We demonstrate the possibility of surpassing the quantum noise limit for simultaneous multi-axis spatial displacement measurements that have zero mean values. The requisite resources for these measurements are squeezed light beams with exotic transverse mode profiles. We show that, in principle, lossless combination of these modes can be achieved using the non-degenerate Gouy phase shift of optical resonators. When the combined squeezed beams are measured with quadrant detectors, we experimentally demonstrate a simultaneous reduction in the transverse x- and y- displacement fluctuations of 2.2 dB and 3.1 dB below the quantum noise limit.Comment: 21 pages, 9 figures, submitted to "Special Issue on Fluctuations & Noise in Photonics & Quantum Optics" of J. Opt.

Early phase observations of extremely luminous Type Ia Supernova 2009dc

We present early phase observations in optical and near-infrared wavelengths for the extremely luminous Type Ia supernova (SN Ia) 2009dc. The decline rate of the light curve is $\Delta m_{15}(B)=0.65\pm 0.03$, which is one of the slowest among SNe Ia. The peak $V$-band absolute magnitude is $M_{V}=-19.90\pm 0.15$ mag even if the host extinction is $A_{V}=0$ mag. It reaches $M_{V}=-20.19\pm 0.19$ mag for the host extinction of $A_{V}=0.29$ mag as inferred from the observed Na {\sc i} D line absorption in the host. Our $JHK_{s}$-band photometry shows that the SN is one of the most luminous SNe Ia also in near-infrared wavelengths. These results indicate that SN 2009dc belongs to the most luminous class of SNe Ia, like SN 2003fg and SN 2006gz. We estimate the ejected $^{56}$Ni mass of $1.2\pm 0.3$ \Msun for no host extinction case (or 1.6$\pm$ 0.4 M$_{\odot}$ for the host extinction of $A_{V}=0.29$ mag). The C {\sc ii} $\lambda$6580 absorption line keeps visible until a week after maximum, which diminished in SN 2006gz before its maximum brightness. The line velocity of Si {\sc ii} $\lambda$6355 is about 8000 km s$^{-1}$ around the maximum, being considerably slower than that of SN 2006gz, while comparable to that of SN 2003fg. The velocity of the C {\sc ii} line is almost comparable to that of the Si {\sc ii}. The presence of the carbon line suggests that thick unburned C+O layers remain after the explosion. SN 2009dc is a plausible candidate of the super-Chandrasekhar mass SNe Ia