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PHYSICS REPORTS OF KUMAMOTO UNIVERSITY Vol. 11, No. 1

## CONTENTS

Satoshi Yajima, Yoji Higasida, Kiyotaka Kawano and Shin-Ichiro Kubota @.....@1
@Gravitational Anomalies with Curl-vanishing Torsion
abstract

Kiyotaka Kawano, Tsuyoshi Kiyan, Takayoshi Maekawa, Atsushi Tangoda, Hideo Taira and Seiko Yokoi @.....@15
@Note on Assignment of Representation to Right-handed Quarks in SU(3)_CxSU(3)_LxU(1)_N Model
abstract

Tetsuya Yoneda, Tatsuo Akamine, Tomonori Oda, Aya Nagasato and Akio Motoyoshi @.....@25
@Probabilistic Verification of GHZ Argument by a Mixture
abstract

Tetsuya Yoneda, Tatsuo Akamine, Tomonori Oda, Aya Nagasato and Akio Motoyoshi @.....@31
@Systematic Structure of Maximally Entangled Bell-, GHZ-States and Teleportation
abstract

Kenzo Arai, Masa-aki Hashimoto and Takayuki Wakita @.....@37
@Primordial Nucleosynthesis with NACRE Nuclear Reaction Rates
abstract

Kazuto Kimura, Masa-aki Hashimoto, Kenzo Arai and Takao Fukui @.....@49
@Thermal Evolution of the Scale Factor with a Variable Cosmological Term
abstract

Shin Fujimoto, Ryuichi Matsuba, Yasushi Ohta, Kenzo Arai, Osamu Koike and Masa-aki Hashimoto @.....@57
@Nucleosynthesis inside an Advection-Dominated Accretion Flow around a Black Hole
abstract

Ryuichi Matsuba, Shin Fujimoto, Yoshinori Obata and Kenzo Arai @.....@65
@Steady Structure of Advection Dominated Accretion Disks with Global Magnetic Fields
abstract

Shunji Ichihara and Masaru Aniya @.....@73
@Defect Interactions and the Superionic Transition Temperature
abstract

Tomohiro Iseki and Masaru Aniya @.....@79
@Composition Dependence of the Sound Velocity in Liquid Silver
abstract

Kikuo Itoh, Fusao Ichikawa, Yushi Ishida and Noriyuki Nagao @.....@85
@Columnar Grain Structure in Cobalt Films Evaporated Obliquely at Low Substrate Temperature
abstract

Fusao Ichikawa, Takeshi Nakashima, Noriyuki Nagao and Kikuo Itoh @.....@93
@Ellipsometric Investigation in Nickel Films and Aluminum Films
abstract

Satoshi Yajima, Yoji Higasida, Kiyotaka Kawano and Shin-Ichiro Kubota
Gravitational Anomalies with Curl-vanishing Torsion

The chiral anomaly is derived by using the plane wave expansion in the path integral formulation for the system where the fermion of spin 1/2 couples with the gravitational and gauge fields and the totally antisymmetric torsion tensor of which the curl derivative vanishes. The gravitational anomalies with this torsion tensor are derived in the differential geometrical method, and are expressed as those replaced the connection of the anomalies in Riemannian space by the connection containing the torsion tensor which is three times as much as the ordinary one. The terms containing the torsion tensor in the consistent gravitational anomalies can be eliminated by counterterms.

Kiyotaka Kawano, Tsuyoshi Kiyan, Takayoshi Maekawa, Atsushi Tangoda, Hideo Taira and Seiko Yokoi
@Note on Assignment of Representation to Right-handed Quarks in SU(3)_CxSU(3)_LxU(1)_N Model

It is pointed out that in the 331 model there are two possibilities for assignment of the $SU(3)_L$ singlet representation to the right-handed fermions in the families. One of them is to assign the singlet under the {\bf 3} and $\bar {\bf 3}$ representations, and the other is to distinguish the representation of the singlet according to whether the singlet accompanies with the {\bf 3} or ${\bar {\bf 3}}$ representation of the left-handed fermions. Then, two sorts of the Yukawa interactions with the scalar particles are given by considering that (A) the right-handed fermions are the singlet under the {\bf 3} and $\bar {\bf 3}$ representations, and (B) the right-handed fermion accompanying with the left-handed $SU(3)_L$ triplet is the singlet only with respect to a transformation of the {\bf 3} representation and that with the left-handed $SU(3)_L$ antitriplet is the singlet only with respect to a transformation of the $\bar {\bf 3}$ representation. It is shown that the case (B) leads to the natural results for the mass and the interaction terms for the fermions in the families through spontaneous symmetry breaking.

Tetsuya Yoneda, Tatsuo Akamine, Tomonori Oda, Aya Nagasato and Akio Motoyoshi
Probabilistic Verification of GHZ Argument by a Mixture

It is pointed out that a mixture consisting of maximally entangled states of the polarization of three photons can provide a probabilistic verification of the argument given by Greenberger-Horne-Zeilinger. Removal of the EPR paradox in the entanglements of three or more two-state systems is reconfirmed.

Tetsuya Yoneda, Tatsuo Akamine, Tomonori Oda, Aya Nagasato and Akio Motoyoshi
Systematic Structure of Maximally Entangled Bell-, GHZ-States and Teleportation

Structures of maximally entangled Bell states, GHZ states and the original scheme of teleportation are investigated. Teleportation using each maximally entangled Bell and GHZ state as ancilla is systematically analyzed. It is shown that maximally entangled state can be represented by a vector consisting of complete set of the state vectors for each subsystem inserted spin matrices between them. It is confirmed that teleportation has general structure which can be divided into two unitarilly transformed GHZ states.

Kenzo Arai, Masa-aki Hashimoto and Takayuki Wakita
@Primordial Nucleosynthesis with NACRE Nuclear Reaction Rates

Primordial abundances of light elements are calculated with new reaction rates provided by the European compilation of reaction rates for astrophysics (NACRE) using both standard and non-standard big bang models with inclusion of degenerate neutrinos. The impact of nuclear reaction rate uncertainties on the derived abundances is stressed from detailed comparison of calculated abundances with combinations of the current observational data on $^4$He, D and $^7$Li. New constraints are presented to the nucleon-to-photon ratio and the degeneracy parameters, yielding many separate domains in the parameter space. It is also deduced new prediction of primordial abundances for $^6$Li and $^{11}$B.

Kazuto Kimura, Masa-aki Hashimoto, Kenzo Arai and Takao Fukui
@Thermal Evolution of the Scale Factor with a Variable Cosmological Term

Thermal evolution of the scale factor with a variable cosmological term is investigated. Realistic energy density (radiation plus matter) is adopted to examine nonsingular models advocated by Overduin and Cooperstock. It is shown that the temperature predicted from the nonsingular models does not attain enough high for primordial nucleosynthesis to proceed.

Shin Fujimoto, Ryuichi Matsuba, Yasushi Ohta, Kenzo Arai, Osamu Koike and Masa-aki Hashimoto
@Nucleosynthesis inside an Advection-Dominated Accretion Flow around a Black Hole

We investigate nucleosynthesis inside an ADAF around a black hole of 10 $M_\odot$, using the self-similar solutions and the nuclear network. It is found that in the region $r < 300\, r_g$, where $r_g$ is the Schwarzshild radius, all heavy elements are disintegrated through ($\gamma, \alpha$) processes because of high temperatures. At $r < 200\, r_g$ there remain only protons and neutrons with ${\rm n/p} = 0.603$, and the produced abundance of $^6$Li amounts to $^6$Li/H $\simeq 2 \times 10^{-9}$, while $^7$Li is completely exhausted. The abundance distribution inside ADAFs depends weakly on the viscous parameter, the ratio of specific heats and the mass accretion rate.

Ryuichi Matsuba, Shin Fujimoto, Yoshinori Obata and Kenzo Arai
Steady Structure of Advection Dominated Accretion Disks with Global Magnetic Fields

We investigate steady structure of advection dominated accretion disks penetrated by global magnetic fields. The magnetic diffusivity is treated as a free parameter from a usual viscous parameter. It is found that, as the field intensifies, the angular momentum is removed more efficiently from the disk, the infall velocity increases and the disk is thinning.

Shunji Ichihara and Masaru Aniya
Defect Interactions and the Superionic Transition Temperature

The influence of the defect-defect interaction on the superionic transition temperature is studied theoretically. Analytical expressions of superionic transition temperature are obtained for the linear, square root and cube root model of defect-defect interactions. In the case where the electronic subsystem is ignored, it is shown that the form of the concentration dependence describing the defect interaction plays a minor role in the determination of superionic transition temperature.

Tomohiro Iseki and Masaru Aniya
Composition Dependence of the Sound Velocity in Liquid Silver

A two fluid model of superionic melt is presented. The model is applied to study the composition dependence of the sound velocity in liquid silver chalcogenides. It is shown that the model reproduces reasonably well the behavior observed experimentally.

Kikuo Itoh, Fusao Ichikawa, Yushi Ishida and Noriyuki Nagao
Columnar Grain Structure in Cobalt Films Evaporated Obliquely at Low Substrate Temperature

The columnar grain structure of cobalt films evaporated obliquely at low substrate temperature was investigated. The substrate temperature $T_{\rm S}$ was varied from 113 K to 313 K. The incidence angle was 60$^\circ$ and the pressure during evaporation was $4.0 \times 10^{-3}$ Pa. The results obtained are as follows: (1) In the $T_{\rm S}$ range of 230 K -- 270 K the columnar grains grow high and form the well-defined bundle; (2) Below 220 K of $T_{\rm S}$ the dense columnar grains grow to the beam direction and their bundling diminish. Result (2) suggests the crystallographic contribution to the formation of the columnar grain structure.

Fusao Ichikawa, Takeshi Nakashima, Noriyuki Nagao and Kikuo Itoh
Ellipsometric Investigation in Nickel Films and Aluminum Films

Measurements of the geometrical anisotropy of thin films have been made using a reflection ellipsometory. The background and analyzing method of them are explained. Also a system useful for these measurements is described. Optical constants of obliquely deposited nickel and aluminum films were obtained by using this system. The relation between anisotropies of films and process conditions were discussed.

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Email: arai@aster.sci.kumamoto-u.ac.jp

Last updated: November 1, 2000