On the classical equivalence of monodromy matrices in squashed sigma model

We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models and, according to them, there are two descriptions to describe the classical dynamics 1) the trigonometric description and 2) the rational description, respectively. For every description, a Lax pair is constructed and the associated monodromy matrix is also constructed. In this paper we show the gauge-equivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators.Comment: 32pages, 3figures, references added, introduction and discussion sections revise

The classical origin of quantum affine algebra in squashed sigma models

We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassical limit of quantum affine algebra at quantum level.Comment: 25 pages, 2 figure

Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence

We consider \gamma-deformations of the AdS_5xS^5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real \gamma-deformations of the AdS_5xS^5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.Comment: 18 pages, no figure, LaTeX, v2:references and further clarifications adde

A variability study of the Seyfert 2 galaxy NGC 6300 with XMM-Newton

We present the results of timing analysis of the XMM-Newton observation of the Seyfert 2 galaxy NGC 6300. The hard X-ray spectrum above 2 keV consists of a Compton-thin-absorbed power law, as is often seen in Seyfert 2 galaxies. We clearly detected rapid time variability on a time scale of about 1000 s from the light curve above 2 keV. The excess variance of the time variability (sigma2_RMS) is calculated to be ~0.12, and the periodogram of the light curve is well represented by a power law function with a slope of 1.75. In contrast with previous results from Seyfert 2 nuclei, these variability characteristics are consistent with those of Seyfert 1 galaxies. This consistency suggests that NGC 6300 has a similar black hole mass and accretion properties as Seyfert 1 galaxies. Using the relation between time variability and central black hole mass by Hayashida et al. (1998), the black hole mass of NGC 6300 is estimated to be ~2.8x10^5 Mo. Taking uncertainty of this method into account, the black hole mass is less than 10^7 Mo. Taking the bolometric luminosity of 3.3x10^43 erg/s into consideration, this yields an accretion rate of > 0.03 of the Eddington value, and comparable with estimates from Seyfert 1 galaxies using this method. The time variability analysis suggests that NGC 6300 actually has a Seyfert 1 nucleus obscured by a thick matter, and more generally provides a new pillar of support for the unified model of Seyfert galaxies based on obscuration.Comment: 11 pages, 6 figures, accepted for publication in Ap

Lagrange-Fedosov Nonholonomic Manifolds

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio

FEASIBILITY STUDY ON THE FUSION OF PHITS SIMULATIONS AND THE DLNN ALGORITHM

We have recently have developed an in-situ multiple-channel depth distribution spectrometer (DDS) that can easily acquire on-site measurements of the depth distribution of specific radioactivities of Cs-134 and Cs-137 underground. Despite considerable improvements in the hardware developed for this device, the quantitative method for determining of radioactivities with this DDS device cannot yet achieve satisfactory performance for practical use. For example, this method cannot discriminate each γ-ray spectra of Cs-134 and Cs-137 acquired by the 20 thallium-doped caesium iodine CsI(Tl) scintillation crystal detectors of the DDS device from corresponding depth levels of underground soil. Therefore, we have applied deep learning neural network (DLNN) as a novel radiation measurement technique to discriminate the spectra and to determine the specific radioactivities of Cs-134 and Cs-137. We have developed model soil layers on a virtual space in Monte-Carlo based PHITS simulations and transported γ-ray radiation generated from a particular single soil layer or multiple layers as radiation sources; next, we performed PHITS calculations of those specific radioactivity measurements for each soil layer using DDS device based on machine learning via the DLNN algorithm. In this study, we obtained informative results regarding the feasibility of the proposal innovative radiation measurement method for further practical use in on-site applications

Finsler and Lagrange Geometries in Einstein and String Gravity

We review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kahler geometry and geometric mechanics how they could perform their results in order to be accepted by the community of ''orthodox'' physicists. Although the bulk of former models of Finsler-Lagrange spaces where elaborated on tangent bundles, the surprising result advocated in our works is that such locally anisotropic structures can be modelled equivalently on Riemann-Cartan spaces, even as exact solutions in Einstein and/or string gravity, if nonholonomic distributions and moving frames of references are introduced into consideration. We also propose a canonical scheme when geometrical objects on a (pseudo) Riemannian space are nonholonomically deformed into generalized Lagrange, or Finsler, configurations on the same manifold. Such canonical transforms are defined by the coefficients of a prime metric and generate target spaces as Lagrange structures, their models of almost Hermitian/ Kahler, or nonholonomic Riemann spaces. Finally, we consider some classes of exact solutions in string and Einstein gravity modelling Lagrange-Finsler structures with solitonic pp-waves and speculate on their physical meaning.Comment: latex 2e, 11pt, 44 pages; accepted to IJGMMP (2008) as a short variant of arXiv:0707.1524v3, on 86 page

Thermal Equilibria of Magnetically Supported, Black Hole Accretion Disks

We present new thermal equilibrium solutions for optically thin and thick disks incorporating magnetic fields. The purpose of this paper is to explain the bright hard state and the bright/slow transition observed in the rising phases of outbursts in BHCs. On the basis of the results of 3D MHD simulations, we assume that magnetic fields inside the disk are turbulent and dominated by the azimuthal component and that the azimuthally averaged Maxwell stress is proportional to the total pressure. We prescribe the magnetic flux advection rate to determine the azimuthal magnetic flux at a given radius. We find magnetically supported, thermally stable solutions for both optically thin and thick disks, in which the heating enhanced by the strong magnetic field balances the radiative cooling. The temperature in a low-$\beta$ disk is lower than that in an ADAF/RIAF but higher than that in a standard disk. We also study the radial dependence of the thermal equilibrium solutions. The optically thin, low-$\beta$ branch extends to $\dot M \gtrsim 0.1 {\dot M}_{\rm Edd}$, in which the temperature anti-correlates with the mass accretion rate. Thus optically thin low-$\beta$ disks can explain the bright hard state. Optically thick, low-$\beta$ disks have the radial dependence of the effective temperature $T_{\rm eff} \propto \varpi^{-3/4}$. Such disks will be observed as staying in a high/soft state. Furthermore, limit cycle oscillations between an optically thick low-$\beta$ disk and a slim disk will occur because the optically thick low-$\beta$ branch intersects with the radiation pressure dominated standard disk branch. These limit cycle oscillations will show a smaller luminosity variation than that between a standard disk and a slim disk.Comment: 23 pages, 9 figures, accepted for publication in Ap

Hole Dynamics in the Orthogonal-Dimer Spin System

The dynamics of a doped hole in the orthogonal-dimer spin system is investigated systematically in one, two and three dimensions. By combining the bond-operator method with the self-consistent Born approximation, we argue that a dispersive quasi-particle state in the dimer phase is well defined even for quasi-two-dimensional systems. On the other hand, a doped hole in the plaquette-singlet phase hardly itinerates, forming an almost localized mode. We further clarify that although the quasi-particle weight in the dimer phase is decreased in the presence of the interchain coupling, it is not suppressed but even enhanced upon the introduction of the interlayer coupling.Comment: 8 pages, 10 figure