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

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

Transport through a finite Hubbard chain connected to reservoirs

The dc conductance through a finite Hubbard chain of size N coupled to two noninteracting leads is studied at T = 0 in an electron-hole symmetric case. Assuming that the perturbation expansion in U is valid for small N (=1,2,3,...) owing to the presence of the noninteracting leads, we obtain the self-energy at \omega = 0 analytically in the real space within the second order in U. Then, we calculate the inter-site Green's function which connects the two boundaries of the chain, G_{N1}, solving the Dyson equation. The conductance can be obtained through G_{N1}, and the result shows an oscillatory behavior as a function of N. For odd N, a perfect transmission occurs independent of U. This is due to the inversion and electron-hole symmetries, and is attributed to a Kondo resonance appearing at the Fermi level. On the other hand, for even N, the conductance is a decreasing function of N and U.Comment: 11 pages, RevTeX, 6 figures, to be published in Phys. Rev. B 59 (1999

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.

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

Arc sensitivity to cluster ellipticity, asymmetries and substructures

We investigate how ellipticity, asymmetries and substructures separately affect the ability of galaxy clusters to produce strong lensing events, i.e. gravitational arcs, and how they influence the arc morphologies and fluxes. This is important for those studies aiming, for example, at constraining cosmological parameters from statistical lensing, or at determining the inner structure of galaxy clusters through gravitational arcs. We do so by creating two-dimensional gradually smoothed, differently elliptical and asymmetric versions of some numerical models. On average, we find that the contributions of ellipticity, asymmetries and substructures amount to ~40%, ~10% and ~30% of the total strong lensing cross section, respectively. However, our analysis shows that substructures play a more important role in less elliptical and asymmetric clusters, even if located at large distances from the cluster centers (~1Mpc/h). Conversely, their effect is less important in highly asymmetric lenses. The morphology, position and flux of individual arcs are strongly affected by the presence of substructures in the clusters. Removing substructures on spatial scales <~50kpc/h, roughly corresponding to mass scales <~5 10^{10}M_\odot/h, alters the image multiplicity of ~35% of the sources used in the simulations and causes position shifts larger than 5'' for ~40% of the arcs longer than 5''. We conclude that any model for cluster lens cannot neglect the effects of ellipticity, asymmetries and substructures. On the other hand, the high sensitivity of gravitational arcs to deviations from regular, smooth and symmetric mass distributions suggests that strong gravitational lensing is potentially a powerfull tool to measure the level of substructures and asymmetries in clusters.Comment: 16 pages, 18 figures. Accepted version. Version with full resolution images can be found at http://www.ita.uni-heidelberg.de/~massimo/sub/publications.htm

The Kondo crossover in shot noise of a single quantum dot with orbital degeneracy

We investigate out of equilibrium transport through an orbital Kondo system realized in a single quantum dot, described by the multiorbital impurity Anderson model. Shot noise and current are calculated up to the third order in bias voltage in the particle-hole symmetric case, using the renormalized perturbation theory. The derived expressions are asymptotically exact at low energies. The resulting Fano factor of the backscattering current $F_b$ is expressed in terms of the Wilson ratio $R$ and the orbital degeneracy $N$ as $F_b =\frac{1 + 9(N-1)(R-1)^2}{1 + 5(N-1)(R-1)^2}$ at zero temperature. Then, for small Coulomb repulsions $U$, we calculate the Fano factor exactly up to terms of order $U^5$, and also carry out the numerical renormalization group calculation for intermediate $U$ in the case of two- and four-fold degeneracy ($N=2,\,4$). As $U$ increases, the charge fluctuation in the dot is suppressed, and the Fano factor varies rapidly from the noninteracting value $F_b=1$ to the value in the Kondo limit $F_b=\frac{N+8}{N+4}$, near the crossover region $U\sim \pi \Gamma$, with the energy scale of the hybridization $\Gamma$.Comment: 10 pages, 4 figure

Can the Steep Mass Profile of A1689 Be Explained by a Triaxial Dark Halo?

The steep mass profile of A1689 derived from recent detailed lensing observations is not readily reconciled with the low concentration halos predicted by the standard CDM model. However, halo triaxiality may act to bias the profile constraints derived assuming a spherically symmetric mass distribution, since lensing relates only to the projected mass distribution. A degree of halo triaxiality is inherent to the CDM structure formation, arising from the collision-less nature of the dark matter. Here we compare the CDM-based model predictions of triaxial halo with the precise lensing measurements of A1689 based on the ACS/HST and Subaru data, over a wide range of 10kpc<r<2Mpc. The model lensing profiles cover the intrinsic spread of halo mass and shape, and are projected over all inclinations when comparing with the data. We show that the model parameters are only weakly constrained and strongly degenerate mainly because of the lack of information along the line of sight. In particular, the limits on the concentration parameter become less restrictive with increasing triaxiality. Yet, by comparing the obtained constraints with expected probability distributions for the axis ratio and concentration parameters computed from numerical simulations, we find that ~6% of cluster-size halos in the CDM model can match the A1689 lensing observations at the 2-sigma level, corresponding to cases where the major-axis of the halo is aligned with the line of sight. Thus halo triaxiality could reduce the apparent discrepancy between theory and observation. This hypothesis needs to be further explored by a statistical lensing study for other clusters as well as by complementary three-dimensional information derived using X-ray, kinematics, and SZ effect observations.Comment: 7 pages, 6 figures, accepted for publication in Ap