Analytical Study of the Julia Set of a Coupled Generalized Logistic Map

A coupled system of two generalized logistic maps is studied. In particular influence of the coupling to the behaviour of the Julia set in two dimensional complex space is analyzed both analytically and numerically. It is proved analytically that the Julia set disappears from the complex plane uniformly as a parameter interpolates from the chaotic phase to the integrable phase, if the coupling strength satisfies a certain condition.Comment: 30pages, 22figure

Air-core photonic band-gap fibers: the impact of surface modes

We study the dispersion and leakage properties for the recently reported low-loss photonic band-gap fiber by Smith et al. [Nature 424, 657 (2003)]. We find that surface modes have a significant impact on both the dispersion and leakage properties of the fundamental mode. Our dispersion results are in qualitative agreement with the dispersion profile reported recently by Ouzounov et al. [Science 301, 1702 (2003)] though our results suggest that the observed long-wavelength anomalous dispersion is due to an avoided crossing (with surface modes) rather than band-bending caused by the photonic band-gap boundary of the cladding.Comment: 7 pages including 4 figures. Accepted for Optics Expres

Complex Analysis of a Piece of Toda Lattice

We study a small piece of two dimensional Toda lattice as a complex dynamical system. In particular the Julia set, which appears when the piece is deformed, is shown analytically how it disappears as the system approaches to the integrable limit.Comment: 17 pages, LaTe

Effects of a Supermassive Black Hole Binary on a Nuclear Gas Disk

We study influence of a galactic central supermassive black hole (SMBH) binary on gas dynamics and star formation activity in a nuclear gas disk by making three-dimensional Tree+SPH simulations. Due to orbital motions of SMBHs, there are various resonances between gas motion and the SMBH binary motion. We have shown that these resonances create some characteristic structures of gas in the nuclear gas disk, for examples, gas elongated or filament structures, formation of gaseous spiral arms, and small gas disks around SMBHs. In these gaseous dense regions, active star formations are induced. As the result, many star burst regions are formed in the nuclear region.Comment: 19 pages, 11 figures, accepted for publication in Ap

Tidal disruption of dark matter halos around proto-globular clusters

Tidal disruption of dark matter halos around proto-globular clusters in a halo of a small galaxy is studied in the context of the hierarchical clustering scenario by using semi-cosmological N-body/SPH simulations assuming the standard cold dark matter model ($\Omega_0 = 1$). Our analysis on formation and evolution of the galaxy and its substructures archives until $z = 2.0$. In such a high-redshift universe, the Einstein-de Sitter universe is still a good approximation for a recently favored $\Lambda$-dominated universe, and then our results does not depend on the choice of cosmology. In order to resolve small gravitationally-bound clumps around galaxies and consider radiative cooling below $T = 10^4 K$, we adopt a fine mass resolution (m_{\rm SPH} = 1.12 \times 10^3 \Msun). Because of the cooling, each clump immediately forms a `core-halo' structure which consists of a baryonic core and a dark matter halo. The tidal force from the host galaxy mainly strips the dark matter halo from clumps and, as a result, theses clumps get dominated by baryons. Once a clump is captured by the host halo, its mass drastically decreases each pericenter passage. At $z = 2$, more than half of the clumps become baryon dominated systems (baryon mass/total mass $> 0.5$). Our results support the tidal evolution scenario of the formation of globular clusters and baryon dominated dwarf galaxies in the context of the cold dark matter universe.Comment: 9page, 13 figures. Accepted for publication in ApJ. A high-resolution PDF of the paper can be obtained from http://th.nao.ac.jp/~takayuki/ApJ05

Nonclassical correlation in a multipartite quantum system: two measures and evaluation

There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic measures of nonclassical correlation of a multipartite quantum system. One is defined as the minimum uncertainty about a joint system after we collect outcomes of particular local measurements. The other is defined by taking the maximum over all local systems about the minimum distance between a genuine set and a mimic set of eigenvalues of a reduced density matrix of a local system. The latter measure is based on an artificial game to create mimic eigenvalues of a reduced density matrix of a local system from eigenvalues of a density matrix of a global system. Numerical computation of these measures for several examples is performed.Comment: v1: 10 pages, 8 figures, IOPART, v2: introduction modified, figure 7 replaced, v3: 10 pages, 10 figures, RevTeX4, major revision with an additional measure introduced, title changed (previous title: Non-classical correlation in a multi-partite quantum system reconsidered), to appear in Phys. Rev.