On the Z_p-ranks of tamely ramified Iwasawa modules

For a prime number p, we denote by K the cyclotomic Z_p-extension of a number field k. For a finite set S of prime numbers, we consider the S-ramified Iwasawa module which is the Galois group of the maximal abelian pro-p-extension of K unramified outside S. This paper treats the case where S does not contain p and k is the rational number field or an imaginary quadratic field. In this case, we prove the explicit formulae for the free ranks of the S-ramified Iwasawa modules as abelian pro-p groups, by using Brumer's p-adic version of Baker's theorem on the linear independence of logarithms of algebraic numbers

Improvement of the hot QCD pressure by the minimal sensitivity criterion

The principles of minimal sensitivity (PMS) criterion is applied to the perturbative free energy density, or pressure, of hot QCD, which include the $\sim g_s^6 \ln g_s$ and part of the $\sim g_s^6$ terms. Applications are made separately to the short- and long-distance parts of the pressure. Comparison with the lattice results, at low temperatures, shows that the resultant `` optimal'' approximants are substantially improved when compared to the $\bar{MS}$ results. In particular, for the realistic case of three quark flavors, the `` optimal'' approximants are comparable with the lattice results.Comment: 14 pages, 9 figures, LaTe

Broken-symmetry-adapted Green function theory of condensed matter systems:towards a vector spin-density-functional theory

The group theory framework developed by Fukutome for a systematic analysis of the various broken symmetry types of Hartree-Fock solutions exhibiting spin structures is here extended to the general many body context using spinor-Green function formalism for describing magnetic systems. Consequences of this theory are discussed for examining the magnetism of itinerant electrons in nanometric systems of current interest as well as bulk systems where a vector spin-density form is required, by specializing our work to spin-density-functional formalism. We also formulate the linear response theory for such a system and compare and contrast them with the recent results obtained for localized electron systems. The various phenomenological treatments of itinerant magnetic systems are here unified in this group-theoretical description.Comment: 17 page

Generally covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.Comment: final version, to appear in Annals Phy

High-precision CTE measurement of hybrid C/SiC composite for cryogenic space telescopes

This paper presents highly precise measurements of thermal expansion of a "hybrid" carbon-fiber reinforced silicon carbide composite, HB-Cesic\textregistered - a trademark of ECM, in the temperature region of \sim310-10K. Whilst C/SiC composites have been considered to be promising for the mirrors and other structures of space-borne cryogenic telescopes, the anisotropic thermal expansion has been a potential disadvantage of this material. HB-Cesic\textregistered is a newly developed composite using a mixture of different types of chopped, short carbon-fiber, in which one of the important aims of the development was to reduce the anisotropy. The measurements indicate that the anisotropy was much reduced down to 4% as a result of hybridization. The thermal expansion data obtained are presented as functions of temperature using eighth-order polynomials separately for the horizontal (XY-) and vertical (Z-) directions of the fabrication process. The average CTEs and their dispersion (1{\sigma}) in the range 293-10K derived from the data for the XY- and Z-directions were 0.805$\pm$0.003\times10$^{-6}$ K$^{-1}$ and 0.837\pm0.001\times10$^{-6}$ K$^{-1}$, respectively. The absolute accuracy and the reproducibility of the present measurements are suggested to be better than 0.01\times10$^{-6}$ K$^{-1}$ and 0.001\times(10)^{-6} K^{-1}, respectively. The residual anisotropy of the thermal expansion was consistent with our previous speculation regarding carbon-fiber, in which the residual anisotropy tended to lie mainly in the horizontal plane.Comment: Accepted by Cryogeincs. 12 pages, 3 figures, 1 tabll

Dispersion of resonant Raman scattering in ∏-conjugated polymers: role of the even parity excitons

Journal ArticleResonant Raman scattering dispersion of the most strongly coupled phonon frequencies with the excitation laser photon energy is measured in terms of a dispersion rate parameter D and quantified in a variety of p conjugated polymer films. D was found to be large in nonluminescent polymers and small in luminescent polymers. We show that D is determined by the dependence of the even parity excitons (Ag) on the polymer conjugation length, and this may serve as a useful spectroscopy for the 2Ag exciton in nonluminescent polymers where it is otherwise optically inactive

New Matsushiro underground cosmic ray station (220 M.W.E. in depth)

A new underground cosmic ray station has been opened at Matsushiro, Japan, and a multidirectional (17 directional channels) muon telescope has been installed at an effective vertical depth of 220 m.w.e. The counting rates are; 8.7 x 10,000/hr for the wide vertical component and 2.0 x 10,000/hr for the vertical component. Continuous observation has been performed since March 22,1984. Some details of the telescope and preliminary analyzed results of the data are presented

Choreographic Three Bodies on the Lemniscate

We show that choreographic three bodies {x(t), x(t+T/3), x(t-T/3)} of period T on the lemniscate, x(t) = (x-hat+y-hat cn(t))sn(t)/(1+cn^2(t)) parameterized by the Jacobi's elliptic functions sn and cn with modulus k^2 = (2+sqrt{3})/4, conserve the center of mass and the angular momentum, where x-hat and y-hat are the orthogonal unit vectors defining the plane of the motion. They also conserve the moment of inertia, the kinetic energy, the sum of square of the curvature, the product of distance and the sum of square of distance between bodies. We find that they satisfy the equation of motion under the potential energy sum_{i<j}(1/2 ln r_{ij} -sqrt{3}/24 r_{ij}^2) or sum_{i<j}1/2 ln r_{ij} -sum_{i}sqrt{3}/8 r_{i}^2, where r_{ij} the distance between the body i and j, and r_{i} the distance from the origin. The first term of the potential energies is the Newton's gravity in two dimensions but the second term is the mutual repulsive force or a repulsive force from the origin, respectively. Then, geometric construction methods for the positions of the choreographic three bodies are given