An arm length stabilization system for KAGRA and future gravitational-wave detectors

Modern ground-based gravitational wave (GW) detectors require a complex interferometer configuration with multiple coupled optical cavities. Since achieving the resonances of the arm cavities is the most challenging among the lock acquisition processes, the scheme called arm length stabilization (ALS) had been employed for lock acquisition of the arm cavities. We designed a new type of the ALS, which is compatible with the interferometers having long arms like the next generation GW detectors. The features of the new ALS are that the control configuration is simpler than those of previous ones and that it is not necessary to lay optical fibers for the ALS along the kilometer-long arms of the detector. Along with simulations of its noise performance, an experimental test of the new ALS was performed utilizing a single arm cavity of KAGRA. This paper presents the first results of the test where we demonstrated that lock acquisition of the arm cavity was achieved using the new ALS. We also demonstrated that the root mean square of residual noise was measured to be 8.2 Hz in units of frequency, which is smaller than the linewidth of the arm cavity and thus low enough to lock the full interferometer of KAGRA in a repeatable and reliable manner

Statistical Mechanical Calculation of Anisotropic Step Stiffness of a Two-Dimensional Hexagonal Lattice Gas Model with Next-Nearest-Neighbor Interactions: Application to Si(111) Surface

We study a two-dimensional honeycomb lattice gas model with both nearest- and next-nearest-neighbor interactions in a staggered field, which describes the surface of stoichiometrically binary crystal. We calculate anisotropic step tension, step stiffness, and equilibrium island shape, by an extended random walk method. We apply the results to Si(111) 7$\times$7 reconstructed surface and high-temperature Si(111) 1$\times$1 surface. We also calculate inter-step interaction coefficient.Comment: revised on May 29 1999: RevTeX v3.1, 10 pages with 9 figures (one figure added

KAGRA: 2.5 generation interferometric gravitational wave detector

The recent detections of gravitational waves (GWs) reported by the LIGO and Virgo collaborations have made a significant impact on physics and astronomy. A global network of GW detectors will play a key role in uncovering the unknown nature of the sources in coordinated observations with astronomical telescopes and detectors. Here we introduce KAGRA, a new GW detector with two 3 km baseline arms arranged in an ‘L’ shape. KAGRA’s design is similar to the second generations of Advanced LIGO and Advanced Virgo, but it will be operating at cryogenic temperatures with sapphire mirrors. This low-temperature feature is advantageous for improving the sensitivity around 100 Hz and is considered to be an important feature for the third-generation GW detector concept (for example, the Einstein Telescope of Europe or the Cosmic Explorer of the United States). Hence, KAGRA is often called a 2.5-generation GW detector based on laser interferometry. KAGRA’s first observation run is scheduled in late 2019, aiming to join the third observation run of the advanced LIGO–Virgo network. When operating along with the existing GW detectors, KAGRA will be helpful in locating GW sources more accurately and determining the source parameters with higher precision, providing information for follow-up observations of GW trigger candidates

Non-universal equilibrium crystal shape results from sticky steps

The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z=z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) using the Monte Carlo method, where p=(dz/dx, dz/dy)$, and represents the thermal averag |p| dependence of , we derive a |p|-expanded expression for the non-universal surface free energy f_{eff}(p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f_{eff}(p).Comment: 31 pages, 21 figure

An arm length stabilization system for KAGRA and future gravitational-wave detectors

Modern ground-based gravitational wave (GW) detectors require a complex interferometer configuration with multiple coupled optical cavities. Since achieving the resonances of the arm cavities is the most challenging among the lock acquisition processes, the scheme called arm length stabilization (ALS) had been employed for lock acquisition of the arm cavities. We designed a new type of the ALS, which is compatible with the interferometers having long arms like the next generation GW detectors. The features of the new ALS are that the control configuration is simpler than those of previous ones and that it is not necessary to lay optical fibers for the ALS along the kilometer-long arms of the detector. Along with simulations of its noise performance, an experimental test of the new ALS was performed utilizing a single arm cavity of KAGRA. This paper presents the first results of the test where we demonstrated that lock acquisition of the arm cavity was achieved using the new ALS. We also demonstrated that the root mean square of residual noise was measured to be 8.2 Hz in units of frequency, which is smaller than the linewidth of the arm cavity and thus low enough to lock the full interferometer of KAGRA in a repeatable and reliable manner

Vicinal Surface with Langmuir Adsorption: A Decorated Restricted Solid-on-solid Model

We study the vicinal surface of the restricted solid-on-solid model coupled with the Langmuir adsorbates which we regard as two-dimensional lattice gas without lateral interaction. The effect of the vapor pressure of the adsorbates in the environmental phase is taken into consideration through the chemical potential. We calculate the surface free energy $f$, the adsorption coverage $\Theta$, the step tension $\gamma$, and the step stiffness $\tilde{\gamma}$ by the transfer matrix method combined with the density-matrix algorithm. Detailed step-density-dependence of $f$ and $\Theta$ is obtained. We draw the roughening transition curve in the plane of the temperature and the chemical potential of adsorbates. We find the multi-reentrant roughening transition accompanying the inverse roughening phenomena. We also find quasi-reentrant behavior in the step tension.Comment: 7 pages, 12 figures (png format), RevTeX 3.1, submitted to Phys. Rev.

Non semi-simple sl(2) quantum invariants, spin case

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order $2r$ where $r>1$ is odd or congruent to $2$ modulo $4$. In this paper we consider the remaining cases where $r$ is congruent to zero modulo $4$ and produce invariants of $3$-manifolds with colored links, equipped with generalized spin structure. For a given $3$-manifold $M$, the relevant generalized spin structures are (non canonically) parametrized by $H^1(M;\mathbb C/2\mathbb Z)$.Comment: 13 pages, 16 figure

Radical-cation salt with novel BEDT-TTF packing motif containing tris(oxalato)germanate(IV)

The synthesis, crystal structure and resistivity of a new semiconducting BEDT-TTF radical-cation salt containing the tris(oxalato)germanate(IV) anion is reported. BEDT-TTF4[Ge(C2O4)3].0.5dichloromethane crystallizes in the space group P21/c, a = 18.322(7), b = 11.919(4), c = 32.746(11) Å, β = 105.797(5)°, V = 6881(4) Å3, T = 295(1) K, Z = 4. Electrical resistivity measurements show that BEDT-TTF4[Ge(C2O4)3].0.5dichloromethane is a semiconductor with an activation energy of 0.224 eV and room temperature resistivity of 212 Ω cm

Multi-Colour Braid-Monoid Algebras

We define multi-colour generalizations of braid-monoid algebras and present explicit matrix representations which are related to two-dimensional exactly solvable lattice models of statistical mechanics. In particular, we show that the two-colour braid-monoid algebra describes the Yang-Baxter algebra of the critical dilute A-D-E models which were recently introduced by Warnaar, Nienhuis, and Seaton as well as by Roche. These and other solvable models related to dense and dilute loop models are discussed in detail and it is shown that the solvability is a direct consequence of the algebraic structure. It is conjectured that the Yang-Baxterization of general multi-colour braid-monoid algebras will lead to the construction of further solvable lattice models.Comment: 32 page