Perturbation study of the conductance through a finite Hubbard chain

Transport through a Hubbard chain of size N (=1,2,3,...) connected to reservoirs is studied at T = 0 in an electron-hole symmetric case based on the second-order perturbation theory in U. The result shows a typical even-odd property corresponding to a Kondo or Mott-Hubbard physics. In this report, specifically, we study the dependence of the conductance on the coupling between the chain and reservoirs, which was not examined in detail in our previous report [Phy. Rev. B 59, 12240 (1999)].Comment: 2 pages, LaTeX, submitted to LT22 (Physica B

Transmission probability through small interacting systems: application to a series of quantum dots

We apply a theory for the transmission probability of small interacting systems, which was formulated based on the Kubo formalism in our previous study, to a series of quantum dots described by the N-impurity Anderson model. In this report, we present the transmission pobability for the system of N=2 calculated using the order $U^2$ self-energy and vertex corrections. Particularly, we examine the features in the two typical parameter regions, $t\Gamma$, where the Kondo effect or the inter-dot correlation dominates. Here, $t$ is the inter-dot transfer and $\Gamma$ is the level broadening caused by the coupling with the noninteracting leads.Comment: 2 pages, 2 figures: proccedings of LT23 (Hiroshima, August, 2002

Kondo screening of a high-spin Nagaoka state in a triangular quantum dot

We study transport through a triangle triple quantum dot connected to two noninteracting leads using the numerical renormalization group (NRG). The triangle has a high-spin ground state of S=1 caused by a Nagaoka ferromagnetism, when it is isolated and has one extra electron introduced into a half-filling. The results show that the conduction electrons screen the local moment via two separate stages with different energy scales. The half of the S=1 is screened first by one of the channel degrees, and then at very low temperature the remaining half is fully screened to form a Kondo singlet. The transport is determined by two phase shifts for quasi-particles with even and odd parities, and then a two-terminal conductance in the series configuration is suppressed $g_{\rm series} \simeq 0$, while plateau of a four-terminal parallel conductance reaches a Unitary limit value $g_{\rm parallel} \simeq 4e^2/h$ of two conducting modes.Comment: 2pages, 2figures: fig1 is revised to show a narrow dip found in the series conductanc

The Mass Distribution of SDSS J1004+4112 Revisited

We present a strong lens analysis of SDSS J1004+4112, a unique quasar lens produced by a massive cluster of galaxies at z=0.68, using a newly developed software for gravitational lensing. We find that our parametric mass model well reproduces all observations including the positions of quasar images as well as those of multiply imaged galaxies with measured spectroscopic redshifts, time delays between quasar images, and the positions of faint central images. The predicted large total magnification of \mu ~ 70 suggests that the lens system is indeed a useful site for studying the fine structure of a distant quasar and its host galaxy. The dark halo component is found to be unimodal centered on the brightest cluster galaxy and the Chandra X-ray surface brightness profile. In addition, the orientation of the halo component is quite consistent with those of the brightest cluster galaxy and member galaxy distribution, implying that the lensing cluster is a relaxed system. The radial profile of the best-fit mass model is in good agreement with a mass profile inferred from the X-ray observation. While the inner radial slope of the dark halo component is consistent with being -1, a clear dependence of the predicted A-D time delay on the slope indicates that an additional time delay measurement will improve constraints on the mass model.Comment: 9 pages, 5 figures, accepted for publication in PASJ. The lens software presented in the paper available at http://www.slac.stanford.edu/~oguri/glafic

Self-Calibrated Cluster Counts as a Probe of Primordial Non-Gaussianity

We show that the ability to probe primordial non-Gaussianity with cluster counts is drastically improved by adding the excess variance of counts which contains information on the clustering. The conflicting dependences of changing the mass threshold and including primordial non-Gaussianity on the mass function and biasing indicate that the self-calibrated cluster counts well break the degeneracy between primordial non-Gaussianity and the observable-mass relation. Based on the Fisher matrix analysis, we show that the count variance improves constraints on f_NL by more than an order of magnitude. It exhibits little degeneracy with dark energy equation of state. We forecast that upcoming Hyper Suprime-cam cluster surveys and Dark Energy Survey will constrain primordial non-Gaussianity at the level \sigma(f_NL) \sim 8, which is competitive with forecasted constraints from next-generation cosmic microwave background experiments.Comment: 4 pages, 3 figures, accepted for publication in PR

Is There a Quad Problem among Optical Gravitational Lenses?

Most of optical gravitational lenses recently discovered in the Sloan Digital Sky Survey Quasar Lens Search (SQLS) have two-images rather than four-images, in marked contrast to radio lenses for which the fraction of four-image lenses (quad fraction) is quite high. We revisit the quad fraction among optical lenses by taking the selection function of the SQLS into account. We find that the current observed quad fraction in the SQLS is indeed lower than, but consistent with, the prediction of our theoretical model. The low quad fraction among optical lenses, together with the high quad fraction among radio lenses, implies that the quasar optical luminosity function has a relatively shallow faint end slope.Comment: 9 pages, 4 figures, invited contribution to appear in New Journal of Physics (Focus on Gravitational Lensing