Quantum information with Gaussian states

Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states.Comment: 170 pages. Minors of the published version are corrected and listed in the Acknowledgement part of this versio

Gravitational Lens Statistics and The Density Profile of Dark Halos

We investigate the influence of the inner profile of lens objects on gravitational lens statistics taking into account of the effect of magnification bias and both the evolution and the scatter of halo profiles. We take the dark halos as the lens objects and consider the following three models for the density profile of dark halos; SIS (singular isothermal sphere), the NFW (Navarro Frenk White) profile, and the generalized NFW profile which has a different slope at smaller radii. The mass function of dark halos is assumed to be given by the Press-Schechter function. We find that magnification bias for the NFW profile is order of magnitude larger than that for SIS. We estimate the sensitivity of the lensing probability of distant sources to the inner profile of lenses and to the cosmological parameters. It turns out that the lensing probability is strongly dependent on the inner density profile as well as on the cosmological constant. We compare the predictions with the largest observational sample, the Cosmic Lens All-Sky Survey. The absence or presence of large splitting events in larger surveys currently underway such as the 2dF and SDSS could set constraints on the inner density profile of dark halos.Comment: 22 pages, minor changes and references added, accepted for publication in Ap

Enhancement of the Critical Current Density of YBa2Cu3Ox Superconductors under Hydrostatic Pressure

The dependence of the critical current density Jc on hydrostatic pressure to 0.6 GPa is determined for a single 25-degree [001]-tilt grain boundary in a bicrystalline ring of nearly optimally doped melt-textured YBa2Cu3Ox. Jc is found to increase rapidly under pressure at +20 %/GPa. A new diagnostic method is introduced (pressure-induced Jc relaxation) which reveals a sizeable concentration of vacant oxygen sites in the grain boundary region. Completely filling such sites with oxygen anions should lead to significant enhancements in Jc.Comment: revised manuscript, graphic errors in figures correcte

Photometric Observations of Star Formation Activity in Early Type Spirals

We observationally study the current star formation activities of early type spiral galaxies. We construct a complete sample of 15 early type spirals having far-infrared (FIR) to optical B band luminosity ratios, L(FIR)/L(B), larger than the average of the type, and make their CCD imaging of the R and H-alpha bands. The equivalent widths of H-alpha emission increase with increasing L(FIR)/L(B), indicating that L(FIR)/L(B) can be an indicator of star formation for such early type spirals with star formation activities higher than the average. For all of the observed early type spirals, the extended HII regions exist at the central regions with some asymmetric features. H-alpha emission is more concentrated to the galactic center than the R band light, and the degree of the concentration increases with the star formation activity. We also analyze the relation between the star formation activities and the existence of companion galaxies in the sample galaxies and other bright early type spirals. No correlation is found and this suggests that the interaction is not responsible for all of the star formation activities of early type spirals.Comment: LaTex, 23 pages (2 tables included), plus 9 Postscript figures & 1 table. To be published in AJ (November issue

Efficient Computation of CMB anisotropies in closed FRW models

We implement the efficient line of sight method to calculate the anisotropy and polarization of the cosmic microwave background for scalar and tensor modes in almost-Friedmann-Robertson-Walker models with positive spatial curvature. We present new results for the polarization power spectra in such models.Comment: 4 pages, 1 figure. Corrected/updated references. Accepted by ApJ. For the F90 source code see http://www.mrao.cam.ac.uk/~aml1005/cmb

Density waves and star formation in grand design spirals

HII regions in the arms of spiral galaxies are indicators of recent star-forming processes. They may have been caused by the passage of the density wave or simply created by other means near the arms. The study of these regions may give us clues to clarifying the controversy over the existence of a triggering scenario, as proposed in the density wave theory. Using H$\alpha$ direct imaging, we characterize the HII regions from a sample of three grand design galaxies: NGC5457, NGC628 and NGC6946. Broad band images in R and I were used to determine the position of the arms. The HII regions found to be associated with arms were selected for the study. The age and the star formation rate of these HII regions was obtained using measures on the H$\alpha$ line. The distance between the current position of the selected HII regions and the position they would have if they had been created in the centre of the arm is calculated. A parameter, T, which measures whether a region was created in the arm or in the disc, is defined. With the help of the T parameter we determine that the majority of regions were formed some time after the passage of the density wave, with the regions located `behind the arm' (in the direction of the rotation of the galaxy) the zone they should have occupied had they been formed in the centre of the arm. The presence of the large number of regions created after the passage of the arm may be explained by the effect of the density wave, which helps to create the star-forming regions after its passage. There is clear evidence of triggering for NGC5457 and a co-rotation radius is proposed. A more modest triggering seems to exist for NGC628 and non significant evidence of triggering are found for NGC6946.Comment: 10 pages, 20 figures, accepted for publication in A&

Renormalization Group Approach to Einstein Equation in Cosmology

The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the present work we apply the renormalization group to the Einstein equation in cosmology and carry out detailed analysis of renormalization group flow in the vicinity of the scale invariant fixed point in the spherically symmetric and inhomogeneous dust filled universe model.Comment: 16 pages including 2 eps figures, RevTe

Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem

We present a detailed description of the idea and procedure for the newly proposed Monte Carlo algorithm of tuning the critical point automatically, which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we investigate the three-dimensional Ising model and the bond percolation problem. We employ a refined finite-size scaling analysis to make estimates of critical point and exponents. With much less efforts, we obtain the results which are consistent with the previous calculations. We argue several directions for the application of the PCC algorithm.Comment: 6 pages including 8 eps figures, to appear in J. Phys. Soc. Jp