Kinematics of Red Variables in the Solar Neighborhood I. Basic Data Obtained by an SiO Maser Survey

In order to study the streaming motions of miras in the Solar neighborhood, we newly surveyed 379 red variables in the SiO maser lines at 42.821 and 43.122 GHz with the Nobeyama 45m radio telescope. Accurate radial velocities were obtained for 229 (220 new) detected stars. The sample is selected from optical variables found by new automated surveys: the Northern Sky Variability Survey and the All Sky Automated Survey. The new sample consists of the "bluer" objects compared with those observed in the previous SiO surveys. The distances to the objects are estimated using the period-luminosity relation, and they are mostly less than 3 kpc from the Sun. The longitude-velocity diagram reveals three prominent groups of stars deviant from the circular Galactic rotation with a flat rotation curve. In addition to the Hercules group of stars which was studied before, we found two new deviant groups: one toward the Perseus arm and the other toward the Sagittarius arm. These two groups both exhibit anomalous motions toward the Galactic center, which seem to be consistent with the noncircular motions of these spiral arms found in the recent VLBI proper-motion measurements for maser gas clumps.Comment: PASJ 64 no.1 (2012 Feb. 25 issue) in press. A full version including Fig. 8a-m, and Fig. 9 are available at http://www.nro.nao.ac.jp/~lib_pub/report/data/no680.pd

JVN observations of H2O masers around the evolved star IRAS 22480+6002

We report on the H2O maser distributions around IRAS 22480+6002 (=IRC+60370) observed with the Japanese VLBI Network (JVN) at three epochs spanning 2 months. This object was identified as a K-type supergiant in 1970s, which was unusual as a stellar maser source. The spectrum of H2O masers consists of 5 peaks separated roughly equally by a few km/s each. The H2O masers were spatially resolved into more than 15 features, which spread about 50 mas along the east--west direction. However, no correlation was found between the proper motion vectors and their spatial distributions; the velocity field of the envelope seems random. A statistical parallax method applied to the observed proper-motion data set gives a distance of 1.0+-0.4 kpc for this object, that is considerably smaller than previously thought. The distance indicates that this is an evolved star with L~5800 Lsun. This star shows radio, infrared, and optical characteristics quite similar to those of the population II post-AGB stars such as RV Tau variables.Comment: 7 pages, 5 figures, PASJ 60, No. 1 (2008 Feb. 25 issue) in press. High res. figures available at ftp://ftp.nro.nao.ac.jp/nroreport/no657.pdf.g

XXZ Bethe states as highest weight vectors of the sl2sl_2 loop algebra at roots of unity

We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio

Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs

We present formulas for the Clebsch-Gordan coefficients and the Racah coefficients for the root of unity representations ($N$-dimensional representations with $q^{2N}=1$) of $U_q(sl(2))$. We discuss colored vertex models and colored IRF (Interaction Round a Face) models from the color representations of $U_q(sl(2))$. We construct invariants of trivalent colored oriented framed graphs from color representations of $U_q(sl(2))$.Comment: 39 pages, January 199

Level statistics of XXZ spin chains with a random magnetic field

The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude of the random magnetic field h. In the energy spectrum, quantum integrability competes with nonintegrability derived from the randomness, where the XXZ interaction is modified by the parameter $\Delta$. When $\Delta \ne 0$, the level-spacing distribution mostly shows Wigner-like behavior, while when $\Delta$=0, Poisson-like behavior appears although the system is nonintegrable due to randomness. Poisson-like behavior also appears for $\Delta \ne 0$ in the large h limit. Furthermore, the level-spacing distribution depends on the lattice size L, particularly when the random field is weak.Comment: 4 pages, 3 figures, to be published in Phys. Rev.

Gyration radius of a circular polymer under a topological constraint with excluded volume

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely-jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure

Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled XXZ spin chains

The level-spacing distributions of XXZ spin chains with next-nearest-neighbor couplings are studied under periodic boundary conditions. We confirm that integrable XXZ spin chains mostly have the Poisson distribution as expected. On the contrary, the level-spacing distributions of next-nearest-neighbor coupled XXZ chains are given by non-Wigner distributions. It is against the expectations, since the models are nonintegrable.Comment: 4 pages, 4 figures, to be published in Physical Review

On the Dominance of Trivial Knots among SAPs on a Cubic Lattice

The knotting probability is defined by the probability with which an $N$-step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of $N$. In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be $2.5 \times 10^5$ on the cubic lattice.Comment: LaTeX2e, 21 pages, 8 figur

A Measurement of Proper Motions of SiO Maser Sources in the Galactic Center with the VLBA

We report on the high-precision astrometric observations of maser sources around the Galactic Center in the SiO J=1--0 v=1 and 2 lines with the VLBA during 2001 -- 2004. With phase-referencing interferometry referred to the radio continuum source Sgr A*, accurate positions of masers were obtained for three detected objects: IRS 10 EE (7 epochs), IRS 15NE (2 epochs), and SiO 6 (only 1 epoch). Because circumstellar masers of these objects were resolved into several components, proper motions for the maser sources were derived with several different methods. Combining our VLBA results with those of the previous VLA observations, we obtained the IRS 10EE proper motion of 76+-3 km s^{-1} (at 8 kpc) to the south relative to Sgr A*. Almost null proper motion of this star in the east--west direction results in a net transverse motion of the infrared reference frame of about 30+-9 km s^{-1} to the west relative to Sgr A*. The proper-motion data also suggests that IRS 10EE is an astrometric binary with an unseen massive companion.Comment: High-res. figures are available at ftp://ftp.nro.nao.ac.jp/nroreport/no656.pdf.gz . PASJ 60, No. 1 (2008) in pres