An edge index for the Quantum Spin-Hall effect

Quantum Spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the Quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take same values as the Spin-Chern number previously introduced in the literature. The result gives an effective tool for the investigation of the edge channels' structure in Quantum Spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge.Comment: 4 pages, 3 figure

Catalogue of 12CO(J=1-0) and 13CO(J=1-0) Molecular Clouds in the Carina Flare Supershell

We present a catalogue of 12CO(J=1-0) and 13CO(J=1-0) molecular clouds in the spatio-velocity range of the Carina Flare supershell, GSH 287+04-17. The data cover a region of ~66 square degrees and were taken with the NANTEN 4m telescope, at spatial and velocity resolutions of 2.6' and 0.1 km/s. Decomposition of the emission results in the identification of 156 12CO clouds and 60 13CO clouds, for which we provide observational and physical parameters. Previous work suggests the majority of the detected mass forms part of a comoving molecular cloud complex that is physically associated with the expanding shell. The cloud internal velocity dispersions, degree of virialization and size-linewidth relations are found to be consistent with those of other Galactic samples. However, the vertical distribution is heavily skewed towards high-altitudes. The robust association of high-z molecular clouds with a known supershell provides some observational backing for the theory that expanding shells contribute to the support of a high-altitude molecular layer.Comment: To be published in PASJ Vol. 60, No. 6. (Issued on December 25th 2008). 35 pages (including 13 pages of tables), 7 figures. Please note that formatting problems with the journal macro result in loss of rightmost data columns in some long tables. These will be fixed in the final published issue. In the meantime, please contact the authors for missing dat

Observations of [C II] 158 micron Line and Far-infrared Continuum Emission toward the High-latitude Molecular Clouds in Ursa Major

We report the results of a rocket-borne observation of [C II] 158\micron line and far-infrared continuum emission at 152.5\micron toward the high latitude molecular clouds in Ursa Major. We also present the results of a follow-up observation of the millimeter ^{12}CO J=1-0 line over a selected region observed by the rocket-borne experiment. We have discovered three small CO cloudlets from the follow-up ^{12}CO observations. We show that these molecular cloudlets, as well as the MBM clouds(MBM 27/28/29/30), are not gravitationally bound. Magnetic pressure and turbulent pressure dominate the dynamic balance of the clouds. After removing the HI-correlated and background contributions, we find that the [C II] emission peak is displaced from the 152.5\micron and CO peaks, while the 152.5\micron continuum emission is spatially correlated with the CO emission. We interpret this behavior by attributing the origin of [C II] emission to the photodissociation regions around the molecular clouds illuminated by the local UV radiation field. We also find that the ratio of the molecular hydrogen column density to velocity-integrated CO intensity is 1.19+-0.29x10^{20} cm^{-2} (K kms^{-1})^{-1} from the FIR continuum and the CO data. The average [C II] /FIR intensity ratio over the MBM clouds is 0.0071, which is close to the all sky average of 0.0082 reported by the FIRAS on the COBE satellite. The average [C II]/CO ratio over the same regions is 420, which is significantly lower than that of molecular clouds in the Galactic plane.Comment: 15 pages, LaTeX (aaspp4.sty) + 2 tables(apjpt4.sty) + 6 postscript figures; accepted for publication in the Astrophysical Journal; Astrophys. J. in press (Vol. 490, December 1, 1997 issue

Star Forming Dense Cloud Cores in the TeV {\gamma}-ray SNR RX J1713.7-3946

RX J1713.7-3946 is one of the TeV {\gamma}-ray supernova remnants (SNRs) emitting synchrotron X rays. The SNR is associated with molecular gas located at ~1 kpc. We made new molecular observations toward the dense cloud cores, peaks A, C and D, in the SNR in the 12CO(J=2-1) and 13CO(J=2-1) transitions at angular resolution of 90". The most intense core in 13CO, peak C, was also mapped in the 12CO(J=4-3) transition at angular resolution of 38". Peak C shows strong signs of active star formation including bipolar outflow and a far-infrared protostellar source and has a steep gradient with a r^{-2.2$\pm$0.4} variation in the average density within radius r. Peak C and the other dense cloud cores are rim-brightened in synchrotron X rays, suggesting that the dense cloud cores are embedded within or on the outer boundary of the SNR shell. This confirms the earlier suggestion that the X rays are physically associated with the molecular gas (Fukui et al. 2003). We present a scenario where the densest molecular core, peak C, survived against the blast wave and is now embedded within the SNR. Numerical simulations of the shock-cloud interaction indicate that a dense clump can indeed survive shock erosion, since shock propagation speed is stalled in the dense clump. Additionally, the shock-cloud interaction induces turbulence and magnetic field amplification around the dense clump that may facilitate particle acceleration in the lower-density inter-clump space leading to the enhanced synchrotron X rays around dense cores.Comment: 22 pages, 7 figures, to accepted in The Astrophysical Journal. A full color version with higher resolution figures is available at http://www.a.phys.nagoya-u.ac.jp/~sano/ApJ10/ms_sano.pd

The Supershell-Molecular Cloud Connection in the Milky Way and Beyond

The role of large-scale stellar feedback in the formation of molecular clouds has been investigated observationally by examining the relationship between HI and 12CO(J=1-0) in supershells. Detailed parsec-resolution case studies of two Milky Way supershells demonstrate an enhanced level of molecularisation over both objects, and hence provide the first quantitative observational evidence of increased molecular cloud production in volumes of space affected by supershell activity. Recent results on supergiant shells in the LMC suggest that while they do indeed help to organise the ISM into over-dense structures, their global contribution to molecular cloud formation is of the order of only ~10%.Comment: Proceedings of IAUS 292 - Molecular Gas, Dust, and Star Formation in Galaxies, eds. T. Wong & J. Ott. 4 pages, 3 figure

Topological meaning of Z2_2 numbers in time reversal invariant systems

We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant characterizing time reversal systems, we show that the relative phase between the Kramers doublet reduces the topological quantum number Z to Z$_2$.Comment: 4 pages, typos correcte

Upper Bounds for the Critical Car Densities in Traffic Flow Problems

In most models of traffic flow, the car density $p$ is the only free parameter in determining the average car velocity $\langle v \rangle$. The critical car density $p_c$, which is defined to be the car density separating the jamming phase (with $\langle v \rangle = 0$) and the moving phase (with $\langle v \rangle > 0$), is an important physical quantity to investigate. By means of simple statistical argument, we show that $p_c < 1$ for the Biham-Middleton-Levine model of traffic flow in two or higher spatial dimensions. In particular, we show that $p_{c} \leq 11/12$ in 2 dimension and $p_{c} \leq 1 - \left( \frac{D-1}{2D} \right)^D$ in $D$ ($D > 2$) dimensions.Comment: REVTEX 3.0, 5 pages with 1 figure appended at the back, Minor revision, to be published in the Sept issue of J.Phys.Soc.Japa

Supergiant Shells and Molecular Cloud Formation in the LMC

We investigate the influence of large-scale stellar feedback on the formation of molecular clouds in the Large Magellanic Cloud (LMC). Examining the relationship between HI and 12CO(J=1-0) in supergiant shells (SGSs), we find that the molecular fraction in the total volume occupied by SGSs is not enhanced with respect to the rest of the LMC disk. However, the majority of objects (~70% by mass) are more molecular than their local surroundings, implying that the presence of a supergiant shell does on average have a positive effect on the molecular gas fraction. Averaged over the full SGS sample, our results suggest that ~12-25% of the molecular mass in supergiant shell systems was formed as a direct result of the stellar feedback that created the shells. This corresponds to ~4-11% of the total molecular mass of the galaxy. These figures are an approximate lower limit to the total contribution of stellar feedback to molecular cloud formation in the LMC, and constitute one of the first quantitative measurements of feedback-triggered molecular cloud formation in a galactic system.Comment: 14 pages, 6 figures. Accepted for publication in Ap

Adiabatic Ground-State Properties of Spin Chains with Twisted Boundary Conditions

We study the Heisenberg spin chain with twisted boundary conditions, focusing on the adiabatic flow of the energy spectrum as a function of the twist angle. In terms of effective field theory for the nearest-neighbor model, we show that the period 2 (in unit $2\pi$) obtained by Sutherland and Shastry arises from irrelevant perturbations around the massless fixed point, and that this period may be rather general for one-dimensional interacting lattice models at half filling. In contrast, the period for the Haldane-Shastry spin model with $1/r^2$ interaction has a different and unique origin for the period, namely, it reflects fractional statistics in Haldane's sense.Comment: 6 pages, revtex, 3 figures available on request, to appear in J. Phys. Soc. Jp

MOA-2011-BLG-293Lb: First Microlensing Planet possibly in the Habitable Zone

We used Keck adaptive optics observations to identify the first planet discovered by microlensing to lie in or near the habitable zone, i.e., at projected separation $r_\perp=1.1\pm 0.1\,$AU from its $M_{L}=0.86\pm 0.06\,M_\odot$ host, being the highest microlensing mass definitely identified. The planet has a mass $m_p = 4.8\pm 0.3\,M_{\rm Jup}$, and could in principle have habitable moons. This is also the first planet to be identified as being in the Galactic bulge with good confidence: $D_L=7.72\pm 0.44$ kpc. The planet/host masses and distance were previously not known, but only estimated using Bayesian priors based on a Galactic model (Yee et al. 2012). These estimates had suggested that the planet might be a super-Jupiter orbiting an M dwarf, a very rare class of planets. We obtained high-resolution $JHK$ images using Keck adaptive optics to detect the lens and so test this hypothesis. We clearly detect light from a G dwarf at the position of the event, and exclude all interpretations other than that this is the lens with high confidence (95%), using a new astrometric technique. The calibrated magnitude of the planet host star is $H_{L}=19.16\pm 0.13$. We infer the following probabilities for the three possible orbital configurations of the gas giant planet: 53% to be in the habitable zone, 35% to be near the habitable zone, and 12% to be beyond the snow line, depending on the atmospherical conditions and the uncertainties on the semimajor axis.Comment: Accepted by ApJ, 21 pages, 4 figure