Tsunehiro Obata

Riemann scalar curvature of ideal quantum gases obeying Gentile's statistics

The scalar curvature (R) of ideal quantum gases obeying Gentiles statistics is investigated by the method of information geometrical theory. The R value is specified by the fugacity and the maximum number, p, of particles in a state. The lowest case p = 1, corresponds to Fermi-Dirac statistics and the unbounded case, p, to Bose-Einstein statistics. In contrast to R = 0 for ideal classical gases obeying Boltzmann statistics, we find R = (2)1/2/32 for p2 and R = -(2)1/2/32 for p = 1, in 0 which is the classical limit. This means that a quantum statistical character is left in R, in the classical limit. Also, a correlation between the sign of R and a quantum mechanical exchange effect is recognized for 0 and >>1. Furthermore, we obtain results that support the instability interpretation of R proposed by Janyszek and Mrugala.

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection Γβγα={βγα} + δβα∂γ lnϕ + δγα∂β lnϕ −gβγ∂α ln ψ is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter Ω2. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricgμν and two gauge scalarsϕ andψ. Physically the gravitational potential corresponds togμν in the same way as in general relativity, the gravitational coupling constant toψ−2, and the gravitational mass tou(ϕ, ψ), which is a coscalar of power −1 algebraically made ofϕ andψ. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(ϕ, ψ)=ϕ on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power −4 algebraically made ofψ andu(ϕ, ψ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter Ω2 is experimentally determined by applying the solutions to the solar system.

Gravitational field sensor for prediction of big seismic waves

The authors outline the gravitational field sensor for prediction of large seismic waves. They studied the turbulence of a Newtonian gravitational field due to large seismic waves and the detection of the turbulent field by an interferometric gravitational wave antenna. The cause of the turbulent field is the variation of the mass density in the ground by the waves. The warning system using the antenna is superior to that of a seismograph. When the seismograph and the antenna are set at the same place, for instance, 100 km away from the epicenter of a strong earthquake of M/sub S/ approximately 7, the seismograph does not respond until the arrival of the P-wave, but the antenna will respond to the gravitational field with about a 20-dB sensitivity 7 s before the arrival.<<ETX>>

Variational principle for gravitational equations of the Bianchi identity type

It is shown that a square invariant of the Weyl conformal curvature tensor can lead to a Lagrangian in a variational principle for a gravitational equation in vacuum of the Bianchi identity type which is compatible with the Einstein equation. Moreover we show that such a Lagrangian implicitly includes a conformally invariant theory characterized by two gauge fields and the metric tensor.

A viewpoint of Kaluza–Klein type in elasticity theory

An N‐dimensional anisotropic elastic body without the interior gravity is, under some conditions concerning the Nth dimension, equivalent to an (N−1)‐dimensional isotropic elastic body under the influence of the interior gravity. According to this theorem, our method of solving the equation of free motion of anisotropic elastic bodies includes Bromwich’s method of solving the equation of motion of incompressible isotropic elastic bodies under the influence of the interior gravity.

Hydrodynamics in theO4 gravity

We develop hydrodynamics in a new geometrical gravitational theory, calledO4 gravity, which we recently proposed. According to this formulation, matter is not necessarily conserved. The nonconservation of matter might have been considerable in an early era of cosmological evolution.

Evaluation of the directivity of gravitational wave radiators

A method of evaluation of the directivity of gravitational wave (GW) radiators is given in the form of general equations applicable to most cases such as Webers apparatus and the travelling wave (TW)‐type radiator (the latter proposed by one of the authors). Although it is not generally accepted now, Einsteins weak‐field theory is used for evaluating both near and distant fields. In a numerical example, using our general formula, the TW‐type radiator is considered and it is found that a half‐power angle width of ±5.3° is feasible using a crystal 30 cm in length. Intensity comparison is also made between the resonance vibrator and TW‐type radiators. Under reasonable assumptions, the radiated power of the latter is about 1023 times larger than the former—that means 1040 times higher intensity than the spinning rod first considered by Einstein as a GW source

ON THE SUSCEPTIBILITY IN La2-xSrxCuO4

The magnetic susceptibility χ in La2-xSrxCuO4 shows unusual concentration x- and temperature T-behaviors. The χ at 400 K increases with x in the range 0.04<x<0.25 and decreases in the range 0.25<x<0.33. The maximum at x=0.25 is interpreted in terms of the curvature invension of the O-Fermi surface. At the inflection point the density of states is extremely high, which causes χ to have a temperature behavior: χ=A0+B0/T. The Cooper pair (pairon) has no net spin, and hence its spin contribution to χ is zero. But its motion with the linear dispersion relation: ∊=(2/π)vFp, where vF=Fermi speed, can generate a T-dependent contribution -B1/T. These two contributions generate a χ-maximum at Tm in the range 0.15<x<0.25.

A potential representation of the differential equations of C∞ anisotropic elastic bodies

We give a potential representation to the differential equations of elastic waves propagating along the symmetric direction of C∞ anisotropic elastic bodies. The potential representation is a generalization of Lamb’s potential representation of the differential equations of isotropic elastic bodies. The generalized Lamb’s potential representation reduces the equations of motion to some two‐dimensional Helmholtz equations and constraint equations. Moreover, using the potential representation, we briefly prove the completeness of Mirsky’s solutions of C∞ anisotropic solid and hollow circular cylinders.

Interaction of a three-mass system with gravitational waves

The interaction of a harmonically bound three-mass system with gravitational waves is analyzed in detail. The system resonantly responds to two polarization states of gravitational waves at a given frequency and transforms the two polarization states into two kinds of vibrations which can be clearly distinguished. The averaged cross section and maximum cross section also are given. As compared with a two-mass system under the same conditions, the three-mass system is at the maximum 1.2 times as large as the averaged cross section of the two-mass system, and its maximum cross section is at the maximum 1.5 times as large as that of the two-mass system.