High pressure growth and electron transport properties of superconducting SmFeAsO1-xHx single crystals

We report the single crystal growth and characterization of the highest Tc iron-based superconductor SmFeAsO1-xHx. Some sub-millimeter-sized crystals were grown using the mixture flux of Na3As + 3NaH + As at 3.0 GPa and 1473 K. The chemical composition analyses confirmed 10% substitution of hydrogen for the oxygen site (x = 0.10), however, the structural analyses suggested that the obtained crystal forms a multi-domain structure. By using the FIB technique we fabricated the single domain SmFeAsO0.9H0.10 crystal with the Tc of 42 K, and revealed the metallic conduction in in-plane (rhoab), while semiconducting in the out-of-plane (rhoc). From the in-plane Hall coefficient measurements, we confirmed that the dominant carrier of SmFeAsO0.9H0.10 crystal is an electron, and the hydride ion occupied at the site of the oxygen ion effectively supplies a carrier electron per iron following the equation: O2- = H- + e-.Comment: 4 figures, 2 table

Pareto law and Pareto index in the income distribution of Japanese companies

In order to study the phenomenon in detail that income distribution follows Pareto law, we analyze the database of high income companies in Japan. We find a quantitative relation between the average capital of the companies and the Pareto index. The larger the average capital becomes, the smaller the Pareto index becomes. From this relation, we can possibly explain that the Pareto index of company income distribution hardly changes, while the Pareto index of personal income distribution changes sharply, from a viewpoint of capital (or means). We also find a quantitative relation between the lower bound of capital and the typical scale at which Pareto law breaks. The larger the lower bound of capital becomes, the larger the typical scale becomes. From this result, the reason there is a (no) typical scale at which Pareto law breaks in the income distribution can be understood through (no) constraint, such as the lower bound of capital or means of companies, in the financial system.Comment: 12 pages, 8 figure

cM<1c_M<1 String Theory as a Constrained Topological Sigma Model

It has been argued by Ishikawa and Kato that by making use of a specific bosonization, $c_M=1$ string theory can be regarded as a constrained topological sigma model. We generalize their construction for any $(p,q)$ minimal model coupled to two dimensional (2d) gravity and show that the energy--momentum tensor and the topological charge of a constrained topological sigma model can be mapped to the energy--momentum tensor and the BRST charge of $c_M<1$ string theory at zero cosmological constant. We systematically study the physical state spectrum of this topological sigma model and recover the spectrum in the absolute cohomology of $c_M<1$ string theory. This procedure provides us a manifestly topological representation of the continuum Liouville formulation of $c_M<1$ string theory.Comment: 12 pages, Latex file, UG-9/9

Relations between a typical scale and averages in the breaking of fractal distribution

We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law in the large scale region and deviate further from the power law in the smaller scale region, we employ 2-dim quantum gravity modified by the $R^2$ term. As examples of distributions in the real world which have similar property to this model, we consider those of personal income in Japan over latest twenty fiscal years. We find relations between the typical scale and several kinds of averages in this model, and observe that these relations are also valid in recent personal income distributions in Japan with sufficient accuracy. We show the existence of the fiscal years so called bubble term in which the gap has arisen in power law, by observing that the data are away from one of these relations. We confirm, therefore, that the distribution of this model has close similarity to those of personal income. In addition, we can estimate the value of Pareto index and whether a big gap exists in power law by using only these relations. As a result, we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions.Comment: 17 pages, latex, 13 eps figure

TOPOLOGICAL MATTER, MIRROR SYMMETRY AND NON-CRITICAL (SUPER)STRINGS

We study the realization of the (super) conformal topological symmetry in two-dimensional field theories. The mirror automorphism of the topological algebra is represented as a reflection in the space of fields. As a consequence, a double BRST structure for topological matter theories is found. It is shown that the implementation of the topological symmetry in non-critical (super)string theories depends on the matter content of the two realizations connected by the mirror transformation.Comment: 45 pages, phyzzx, no figure

Topological Aspects of an Antisymmetric Background Field on Orbifolds

We study string theory on orbifolds in the presence of an antisymmetric constant background field in detail and discuss some of new aspects of the theory. It is pointed out that the term with the antisymmetric background field can be regarded as a topological term like a Chern-Simons term or a Wess-Zumino term. Detailed analysis in the operator formalism shows that orbifold models with topologically nontrivial twists exhibit various anomalous behavior: Zero mode variables obey nontrivial quantization conditions. Coordinate transformations which define orbifolds are modified at quantum level. Wave functions of twisted strings in general acquire nontrivial phases when they move around non-contractible loops on orbifolds. Zero mode eigenvalues are shifted from naively expected values, in favor of modular invariance.Comment: 45 pages, Latex file, NBI-HE-93-01, KOBE-TH-93-0

Symmetries between Untwisted and Twisted Strings on Asymmetric Orbifolds

We study symmetries between untwisted and twisted strings on asymmetric orbifolds. We present a list of asymmetric orbifold models to possess intertwining currents which convert untwisted string states to twisted ones, and vice versa. We also present a list of heterotic strings on asymmetric orbifolds with supersymmetry between untwisted and twisted string states. Some of properties inherent in asymmetric orbifolds, which are not shared by symmetric orbifolds, are pointed out.Comment: Plain Tex, 35 pages, NBI-HE-92-34, KOBE-92-0