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

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

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

Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins

The Wigner d function, which is the essential part of an irreducible representation of SU(2) and SO(3) parameterized with Euler angles, has been know to suffer from a serious numerical errors at high spins, if it is calculated by means of the Wigner formula as a polynomial of cos and sin of half of the second Euler angle. This paper shows a way to avoid this problem by expressing the d functions as the Fourier series of the half angle. A precise numerical table of the coefficients of the series is obtainable from a web site.Comment: 5 pages, 5 figure

Complete solution for unambiguous discrimination of three pure states with real inner products

Complete solutions are given in a closed analytic form for unambiguous discrimination of three general pure states with real mutual inner products. For this purpose, we first establish some general results on unambiguous discrimination of n linearly independent pure states. The uniqueness of solution is proved. The condition under which the problem is reduced to an (n-1)-state problem is clarified. After giving the solution for three pure states with real mutual inner products, we examine some difficulties in extending our method to the case of complex inner products. There is a class of set of three pure states with complex inner products for which we obtain an analytical solution.Comment: 13 pages, 3 figures, presentation improved, reference adde

A Reversibility Parameter for a Markovian Stepper

Recent experimental studies on the stepwize motion of biological molecular motors have revealed that the ``characteristic distance'' of a step is usually less than the actual step size. This observation implies that the detailed-balance condition for kinetic rates of steps is violated in these motors. In this letter, in order to clarify the significance of the characteristic distance, we study a Langevin model of a molecular motor with a hidden degree of freedom. We find that the ratio of the characteristic distance to the step size is equal to unity if the dominant paths in the state space are one dimensional, while it deviates from unity if the dominant paths are branched. Therefore, this parameter can be utilized to determine the reversibility of a motor even under a restricted observation.Comment: 6 pages, 2 figures - minor revision