Transmission Coefficient as a Three-Point Retarded Function

We show that the transmission probability through a small interacting region connected to noninteracting leads, can be written in terms of a retarded product of a three-point correlation function defined in the real time. Our proof is based on the Kubo formalism, and uses an Eliashberg theory for analytic properties of vertex functions. The aim of this short report is to add a new viewpoint to the transport theory described in the previous paper: A.O., J. Phys. Soc. Jpn. 70 (2001) 2666.Comment: 2 pages, 2 figures, submitted to J. Phys. Soc. Jp

SDSS J131339.98+515128.3: A new gravitationally lensed quasar selected based on near-infrared excess

We report the discovery of a new gravitationally lensed quasar, SDSS J131339.98+515128.3, at a redshift of 1.875 with an image separation of 1.24". The lensing galaxy is clearly detected in visible-light follow-up observations. We also identify three absorption-line doublets in the spectra of the lensed quasar images, from which we measure the lens redshift to be 0.194. Like several other known lenses, the lensed quasar images have different continuum slopes. This difference is probably the result of reddening and microlensing in the lensing galaxy. The lensed quasar was selected by correlating Sloan Digital Sky Survey (SDSS) spectroscopic quasars with Two Micron All Sky Survey (2MASS) sources and choosing quasars that show near-infrared (IR) excess. The near-IR excess can originate, for example, from the contribution of the lensing galaxy at near-IR wavelengths. We show that the near-IR excess technique is indeed an efficient method to identify lensed systems from a large sample of quasars.Comment: Accepted to MNRAS, 8 pages, 7 figure

Electron transport through a strongly correlated monoatomic chain

We study transport properties of a strongly correlated monoatomic chain coupled to metallic leads. Our system is described by tight binding Hubbard-like model in the limit of strong on-site electron-electron interactions in the wire. The equation of motion technique in the slave boson representation has been applied to obtain analytical and numerical results. Calculated linear conductance of the system shows oscillatory behavior as a function of the wire length. We have also found similar oscillations of the electron charge in the system. Moreover our results show spontaneous spin polarization in the wire. Finally, we compare our results with those for non-interacting chain and discuss their modifications due to the Coulomb interactions in the system.Comment: 7 pages, 5 figure

Perturbation Study of the Conductance through an Interacting Region Connected to Multi-Mode Leads

We study the effects of electron correlation on transport through an interacting region connected to multi-mode leads based on the perturbation expansion with respect to the inter-electron interaction. At zero temperature the conductance defined in the Kubo formalism can be written in terms of a single-particle Green's function at the Fermi energy, and it can be mapped onto a transmission coefficient of the free quasiparticles described by an effective Hamiltonian. We apply this formulation to a two-dimensional Hubbard model of finite size connected to two noninteracting leads. We calculate the conductance in the electron-hole symmetric case using the order $U^2$ self-energy. The conductance shows several maximums in the $U$ dependence in some parameter regions of $t_y/t_x$, where $t_x$ ($t_y$) is the hopping matrix element in the $x$- ($y$-) directions. This is caused by the resonance occurring in some of the subbands, and is related with the $U$ dependence of the eigenvalues of the effective Hamiltonian.Comment: 17 pages, 12 figures, to be published in J.Phys.Soc.Jpn. 71(2002)No.

Determination of the phase shifts for interacting electrons connected to reservoirs

We describe a formulation to deduce the phase shifts, which determine the ground-state properties of interacting quantum-dot systems with the inversion symmetry, from the fixed-point eigenvalues of the numerical renormalization group (NRG). Our approach does not assume the specific form of the Hamiltonian nor the electron-hole symmetry, and it is applicable to a wide class of quantum impurities connected to noninteracting leads. We apply the method to a triple dot which is described by a three-site Hubbard chain connected to two noninteracting leads, and calculate the dc conductance away from half-filling. The conductance shows the typical Kondo plateaus of Unitary limit in some regions of the gate voltages, at which the total number of electrons N_el in the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance shows a wide minimum in the gate voltages corresponding to even number of electrons, N_el = 2 and 4. We also discuss the parallel conductance of the triple dot connected transversely to four leads, and show that it can be deduced from the two phase shifts defined in the two-lead case.Comment: 9 pages, 12 figures: Fig. 12 has been added to discuss T_

The Sloan Digital Sky Survey Quasar Lens Search. I. Candidate Selection Algorithm

We present an algorithm for selecting an uniform sample of gravitationally lensed quasar candidates from low-redshift (0.6<z<2.2) quasars brighter than i=19.1 that have been spectroscopically identified in the SDSS. Our algorithm uses morphological and color selections that are intended to identify small- and large-separation lenses, respectively. Our selection algorithm only relies on parameters that the SDSS standard image processing pipeline generates, allowing easy and fast selection of lens candidates. The algorithm has been tested against simulated SDSS images, which adopt distributions of field and quasar parameters taken from the real SDSS data as input. Furthermore, we take differential reddening into account. We find that our selection algorithm is almost complete down to separations of 1'' and flux ratios of 10^-0.5. The algorithm selects both double and quadruple lenses. At a separation of 2'', doubles and quads are selected with similar completeness, and above (below) 2'' the selection of quads is better (worse) than for doubles. Our morphological selection identifies a non-negligible fraction of single quasars: To remove these we fit images of candidates with a model of two point sources and reject those with unusually small image separations and/or large magnitude differences between the two point sources. We estimate the efficiency of our selection algorithm to be at least 8% at image separations smaller than 2'', comparable to that of radio surveys. The efficiency declines as the image separation increases, because of larger contamination from stars. We also present the magnification factor of lensed images as a function of the image separation, which is needed for accurate computation of magnification bias.Comment: 15 pages, 17 figures, 4 tables, accepted for publication in A

The strongest gravitational lenses: I. The statistical impact of cluster mergers

For more than a decade now, it has been controversial whether or not the high rate of giant gravitational arcs and the largest observed Einstein radii are consistent with the standard cosmological model. Recent studies indicate that mergers provide an efficient mechanism to substantially increase the strong-lensing efficiency of individual clusters. Based on purely semi-analytic methods, we investigated the statistical impact of cluster mergers on the distribution of the largest Einstein radii and the optical depth for giant gravitational arcs of selected cluster samples. Analysing representative all-sky realizations of clusters at redshifts z < 1 and assuming a constant source redshift of z_s = 2.0, we find that mergers increase the number of Einstein radii above 10 arcsec (20 arcsec) by ~ 35 % (~ 55 %). Exploiting the tight correlation between Einstein radii and lensing cross sections, we infer that the optical depth for giant gravitational arcs with a length-to-width ratio > 7.5 of those clusters with Einstein radii above 10 arcsec (20 arcsec) increases by ~ 45 % (85 %). Our findings suggest that cluster mergers significantly influence in particular the statistical lensing properties of the strongest gravitational lenses. We conclude that semi-analytic studies must inevitably take these events into account before questioning the standard cosmological model on the basis of the largest observed Einstein radii and the statistics of giant gravitational arcs.Comment: 23 pages, 18 figures; accepted for publication in Astronomy and Astrophysics; v2: minor corrections (added clarifying comments; added Fig. 19) to match the accepted versio