Study of gossamer superconductivity and antiferromagnetism in the t-J-U model

The d-wave superconductivity (dSC) and antiferromagnetism are analytically studied in a renormalized mean field theory for a two dimensional t-J model plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing the $U$ term is to partially impose the no double occupancy constraint by employing the Gutzwiller approximation. The phase diagrams as functions of doping $\delta$ and $U$ are studied. Using the standard value of $t/J=3.0$ and in the large $U$ limit, we show that the antiferromagnetic (AF) order emerges and coexists with the dSC in the underdoped region below the doping $\delta\sim0.1$. The dSC order parameter increases from zero as the doping increases and reaches a maximum near the optimal doping $\delta\sim0.15$. In the small $U$ limit, only the dSC order survives while the AF order disappears. As $U$ increased to a critical value, the AF order shows up and coexists with the dSC in the underdoped regime. At half filing, the system is in the dSC state for small $U$ and becomes an AF insulator for large $U$. Within the present mean field approach, We show that the ground state energy of the coexistent state is always lower than that of the pure dSC state.Comment: 7 pages, 8 figure

Optimal estimation of the mean function based on discretely sampled functional data: Phase transition

The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs. Minimax rates of convergence are established and easily implementable rate-optimal estimators are introduced. The analysis reveals interesting and different phase transition phenomena in the two cases. Under the common design, the sampling frequency solely determines the optimal rate of convergence when it is relatively small and the sampling frequency has no effect on the optimal rate when it is large. On the other hand, under the independent design, the optimal rate of convergence is determined jointly by the sampling frequency and the number of curves when the sampling frequency is relatively small. When it is large, the sampling frequency has no effect on the optimal rate. Another interesting contrast between the two settings is that smoothing is necessary under the independent design, while, somewhat surprisingly, it is not essential under the common design.Comment: Published in at http://dx.doi.org/10.1214/11-AOS898 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive covariance matrix estimation through block thresholding

Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. A fully data-driven block thresholding estimator is proposed. The estimator is constructed by carefully dividing the sample covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding. The estimator is shown to be optimally rate adaptive over a wide range of bandable covariance matrices. A simulation study is carried out and shows that the block thresholding estimator performs well numerically. Some of the technical tools developed in this paper can also be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/12-AOS999 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discussion: "A significance test for the lasso"

Discussion of "A significance test for the lasso" by Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani, Robert Tibshirani [arXiv:1301.7161].Comment: Published in at http://dx.doi.org/10.1214/13-AOS1175B the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Role of Starburst-AGN composites in Luminous Infrared Galaxy Mergers: Insights from the New Optical Classification Scheme

We investigate the fraction of starbursts, starburst-AGN composites, Seyferts, and LINERs as a function of infrared luminosity (L_IR) and merger progress for ~500 infrared-selected galaxies. Using the new optical classifications afforded by the extremely large data set of the Sloan Digital Sky Survey, we find that the fraction of LINERs in IR-selected samples is rare (< 5%) compared with other spectral types. The lack of strong infrared emission in LINERs is consistent with recent optical studies suggesting that LINERs contain AGN with lower accretion rates than in Seyfert galaxies. Most previously classified infrared-luminous LINERs are classified as starburst-AGN composite galaxies in the new scheme. Starburst-AGN composites appear to "bridge" the spectral evolution from starburst to AGN in ULIRGs. The relative strength of the AGN versus starburst activity shows a significant increase at high infrared luminosity. In ULIRGs (L_IR >10^12 L_odot), starburst-AGN composite galaxies dominate at early--intermediate stages of the merger, and AGN galaxies dominate during the final merger stages. Our results are consistent with models for IR-luminous galaxies where mergers of gas-rich spirals fuel both starburst and AGN, and where the AGN becomes increasingly dominant during the final merger stages of the most luminous infrared objects.Comment: 30 pages, 19 figures, 10 tables, ApJ accepte

Are Black Holes Elementary Particles?

Quantum black holes are the smallest and heaviest conceivable elementary particles. They have a microscopic size but a macroscopic mass. Several fundamental types have been constructed with some remarkable properties. Quantum black holes in the neighborhood of the Galaxy could resolve the paradox of ultra-high energy cosmic rays detected in Earth's atmosphere. They may also play a role as dark matter in cosmology.Comment: Lecture delivered in Conference on Particle Physics, Astrophysics and Quantum Field Theory: 75 Years since Solvay, 27 -29 November 2008, Nanyang Executive Centre, Singapore. 10 page

Star Formation and Dust Extinction Properties of Local Galaxies as seen from AKARI and GALEX

An accurate estimation of the star formation-related properties of galaxies is crucial for understanding the evolution of galaxies. In galaxies, ultraviolet (UV) light emitted by recently formed massive stars is attenuated by dust, which is also produced by star formation (SF) activity, and is reemitted at mid- and far- infrared (IR) wavelengths. In this study, we investigate the star formation rate (SFR) and dust extinction using UV and IR data. We selected local galaxies which are detected at AKARI FIS 90 um and matched the IRAS IIFSCz 60 um select catalog. We measured FUV and NUV flux densities from GALEX images. We examined the SF and extinction of Local galaxies using four bands of AKARI. Then, we calculated FUV and total IR luminosities, and obtained the SF luminosity, L_{SF}, the total luminosity related to star formation activity, and the SFR. We find that in most galaxies, L_{SF} is dominated by L_{dust}. We also find that galaxies with higher SF activity have a higher fraction of their SF hidden by dust. In fact, the SF of galaxies with SFRs >20 M_{sun}/yr is almost completely hidden by dust. Our results boast a significantly higher precision with respect to previously published works, due to the use of much larger object samples from the AKARI and GALEX all sky surveys.Comment: 9 pages, 12 figures, accepted for publication in Earth, Planets, and Space, A few minor corrections, and a reference adde