Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2

The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in terms of the periodic orbits and the spin state is simulated by the uniform distribution on a sphere. In this paper, instead of the uniform distribution, we introduce Brownian motion on a sphere to yield the parametric motion of the energy levels. As a result, the small time expansion of the form factor is obtained and found to be in agreement with the prediction of parametric random matrices in the transition within the GSE universality class. Moreover, by starting the Brownian motion from a point distribution on the sphere, we gradually increase the effect of the spin and calculate the form factor describing the transition from the GOE (Gaussian Orthogonal Ensemble) class to the GSE class.Comment: 25 pages, 2 figure

Lymanα\alpha Emitters beyond Redshift 5:The Dawn of Galaxy Formation

The 8m class telescopes in the ground-based optical astronomy together with help from the ultra-sharp eye of the Hubble Space Telescope have enabled us to observe forming galaxies beyond redshift $z=5$. In particular, more than twenty Ly$\alpha$-emitting galaxies have already been found at $z > 5$. These findings provide us with useful hints to investigate how galaxies formed and then evolved in the early universe. Further, detailed analysis of Ly$\alpha$ emission line profiles are useful in exploring the nature of the intergalactic medium because the trailing edge of cosmic reionization could be close to $z \sim 6$ -- 7, at which forming galaxies have been found recently. We also discuss the importance of superwinds from forming galaxies at high redshift, which has an intimate relationship between galaxies and the intergalactic medium. We then give a review of early cosmic star formation history based on recent progress in searching for Ly$\alpha$-emitting young galaxies beyond redshift 5.Comment: 23 pages, 12 figures, jkas35.sty. To appear in the proceedings of the APCTP WoFormation and Interaction of Galaxies, edited by Hyung Mok Leerkshop o

Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem

We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are studied for finite $N\times N$ matrices in the Gaussian ensemble. In the large $N$ limit the density of eigenvalues is given by a semi-circle law. However, near the origin there is a region of size $1\over N$ in which this density rises from zero to the semi-circle, going through an oscillatory behavior. This cross-over is calculated explicitly by various techniques. We then show to first order in the non-Gaussian character of the probability distribution that this oscillatory behavior is universal, i.e. independent of the probability distribution. We conjecture that this universality holds to all orders. We then extend our consideration to the more complicated block matrices which arise from lattices of matrices considered in our previous work. Finally, we study the case of random real symmetric matrices made of blocks. By using a remarkable identity we are able to determine the oscillatory behavior in this case also. The universal oscillations studied here may be applicable to the problem of a particle propagating on a lattice with random magnetic flux.Comment: 47 pages, regular LateX, no figure

Eigenvalue statistics of the real Ginibre ensemble

The real Ginibre ensemble consists of random $N \times N$ matrices formed from i.i.d. standard Gaussian entries. By using the method of skew orthogonal polynomials, the general $n$-point correlations for the real eigenvalues, and for the complex eigenvalues, are given as $n \times n$ Pfaffians with explicit entries. A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented. This is relevant to May's stability analysis of biological webs.Comment: 4 pages, to appear PR

Use of Potassium Nitrate on Mango Flowering

Review of the authors' experiments in Hawaii suggested that potassium nitrate did not induce flowering but probably stimulated growth of terminal buds, and flowering was determined by the condition of those buds or the environmental conditions at the time. Genotypic differences in response to the treatment were noted

Trapped Noble Gases of Antarctic CO3 Chondrites.

第2回極域科学シンポジウム/第34回南極隕石シンポジウム 11月17日（木） 国立国語研究所 2階講