Orbit decomposition of Jordan matrix algebras of order three under the automorphism groups

The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification, explicitly, in terms of the cross product of H. Freudenthal and the characteristic polynomial.Comment: v2, 32 pages, presentation improved, minor errors corrected, and the title changed as appeared in J. Math. Sci. Univ. Toky

The explanation of the deformed Schild string

The author comments on [1]. One of the deformed actions can express the Neveu-Schwarz-Ramond superstring under three gauge conditions. One of these depends on a matrix induced by the string coordinate.Comment: 6 page

Primordial fractal density perturbations and structure formation in the Universe: 1-Dimensional collisionless sheet model

Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze the time evolution of fractal density perturbations in Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will come out. We assume a one-dimensional collisionless sheet model with initial Cantor-type fractal perturbations. The nonlinear structure seems to approach some attractor with a unique fractal dimension, which is independent of the fractal dimensions of initial perturbations. A discrete self-similarity in the phase space is also found when the universal nonlinear fractal structure is reached.Comment: 17 pages, 19 jpeg figures. Accepted for publication in ApJ. Figures are also available from http://www.phys.waseda.ac.jp/gravity/~tatekawa/0003124/figs.tar.g

Spin Configuration in the 1/3 Magnetization Plateau of Azurite Determined by NMR

High magnetic field $^{63,65}$Cu NMR spectra were used to determine the local spin polarization in the 1/3 magnetization plateau of azurite, Cu$_3$(CO$_3$)$_2$(OH)$_2$, which is a model system for the distorted diamond antiferromagnetic spin-1/2 chain. The spin part of the hyperfine field of the Cu2 (dimer) sites is found to be field independent, negative and strongly anisotropic, corresponding to $\approx$10 % of fully polarized spin in a $d$-orbital. This is close to the expected configuration of the "quantum" plateau, where a singlet state is stabilized on the dimer. However, the observed non-zero spin polarization points to some triplet admixture, induced by strong asymmetry of the diamond bonds $J_1$ and $J_3$.Comment: Phys. Rev. Lett. 102, in press (2009

Statistical Mechanics of Self--Gravitating System : Cluster Expansion Method

We study statistical mechanics of the self--gravitating system applying the cluster expansion method developed in solid state physics. By summing infinite series of diagrams, we derive a complex free energy whose imaginary part is related to the relaxation time of the system. Summation of another series yields two--point correlation function whose correlation length is essentially given by the Jeans wavelength of the system.Comment: 4 pages including 2 eps figures, RevTe

Cosmic structures via Bose Einstein condensation and its collapse

We develop our novel model of cosmology based on the Bose-Einstein condensation. This model unifies the Dark Energy and the Dark Matter, and predicts multiple collapse of condensation, followed by the final acceleration regime of cosmic expansion. We first explore the generality of this model, especially the constraints on the boson mass and condensation conditions. We further argue the robustness of this model over the wide range of parameters of mass, self coupling constant and the condensation rate. Then the dynamics of BEC collapse and the preferred scale of the collapse are studied. Finally, we describe possible observational tests of our model, especially, the periodicity of the collapses and the gravitational wave associated with them.Comment: 21 pages, 5 figure

Large-scale mapping observations of the CI(3P1-3P0) and CO(J=3-2) lines toward the Orion A molecular cloud

Large scale mapping observations of the 3P1-3P0 fine structure transition of atomic carbon (CI, 492 GHz) and the J=3-2 transition of CO (346 GHz) toward the Orion A molecular cloud have been carried out with the Mt. Fuji submillimeter-wave telescope. The observations cover 9 square degrees, and include the Orion nebula M42 and the L1641 dark cloud complex. The CI emission extends over almost the entire region of the Orion A cloud and is surprisingly similar to that of 13CO(J=1-0).The CO(J=3-2) emission shows a more featureless and extended distribution than CI.The CI/CO(J=3-2) integrated intensity ratio shows a spatial gradient running from the north (0.10) to the south (1.2) of the Orion A cloud, which we interpret as a consequence of the temperature gradient. On the other hand, the CI/13CO(J=1-0) intensity ratio shows no systematic gradient. We have found a good correlation between the CI and 13CO(J=1-0) intensities over the Orion A cloud. This result is discussed on the basis of photodissociation region models.Comment: Text file is 13 pages long, and 3 figure files (pdf format). NRO Report No. 508 (1999). University of Tokyo, Resceu 41/9

Swarm-Oscillators

Nonlinear coupling between inter- and intra-element dynamics appears as a collective behaviour of elements. The elements in this paper denote symptoms such as a bacterium having an internal network of genes and proteins, a reactive droplet, a neuron in networks, etc. In order to elucidate the capability of such systems, a simple and reasonable model is derived. This model exhibits the rich patterns of systems such as cell membrane, cell fusion, cell growing, cell division, firework, branch, and clustered clusters (self-organized hierarchical structure, modular network). This model is extremely simple yet powerful; therefore, it is expected to impact several disciplines.Comment: 9 pages, 4 figure

Quantum Markov Process on a Lattice

We develop a systematic description of Weyl and Fano operators on a lattice phase space. Introducing the so-called ghost variable even on an odd lattice, odd and even lattices can be treated in a symmetric way. The Wigner function is defined using these operators on the quantum phase space, which can be interpreted as a spin phase space. If we extend the space with a dichotomic variable, a positive distribution function can be defined on the new space. It is shown that there exits a quantum Markov process on the extended space which describes the time evolution of the distribution function.Comment: Lattice2003(theory

Unambiguous pure state identification without classical knowledge

We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are presented. By the unambiguous identification, we mean that we are not allowed to make a mistake but our measurement can produce an inconclusive result. Assuming the two reference states are independently distributed over the whole pure state space in a unitary invariant way, we determine the optimal mean success probability for an arbitrary number of copies of the reference states and a general dimension of the state space. It is explicitly shown that the obtained optimal mean success probability asymptotically approaches that of the unambiguous discrimination as the number of the copies of the reference states increases.Comment: v3: 8 pages, minor corrections, journal versio