Superconductivity in the Three-Fold Charge-Ordered Metal of the Triangular-Lattice Extended Hubbard Model

The quarter-filling extended Hubbard model on the triangular lattice is studied to explore pairing instability in the three-fold charge-ordered (CO) metal. We derive a second-order strong-coupling effective Hamiltonian of doped carriers into the three-fold CO insulator at electron density of $n=2/3$, and then study the $f$- and $d_{xy}$-wave superconductivities down to $n=1/2$ by using the BCS mean-field approximation. It is found that the triplet $f$-wave pairing is more stable than the $d_{xy}$-wave one. We also point out that this coexisting state of the charge ordering and superconductivity is possible to have critical temperature $T_c \sim 0.01 t$.Comment: 4 pages, 7 figure

A detailed study of quasinormal frequencies of the Kerr black hole

We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure

Superconductivity in Na_xCoO_2yH_2O by charge fluctuation

A new mechanism for superconductivity in the newly discovered Co-based oxide is proposed by using charge fluctuation. A single-band extended Hubbard model on the triangular lattice is studied within random phase approximation. $f$-wave triplet superconductivity is stabilized in the vicinity of charge-density-wave instability, which is in sharp contrast with the square-lattice case. The physical origin of the realization of the $f$-wave triplet state as well as the relevance to experiments are discussed

Reduction in cardiovascular disease events in patients with type 2 diabetes mellitus treated with a sodium–glucose cotransporter 2 inhibitor versus a dipeptidyl peptidase-4 inhibitor: A real-world retrospective administrative database analysis in Japan

AIMS/INTRODUCTION: To evaluate the benefit of sodium–glucose cotransporter 2 inhibitors (SGLT2i) versus dipeptidyl peptidase-4 inhibitors (DPP4i) in reducing cardiovascular disease (CVD) events in patients with type 2 diabetes mellitus with and without a CVD history.MATERIALS AND METHODS: This retrospective cohort study used Japanese hospital administrative data from the Medical Data Vision database (January 2015 to April 2020). Patients with type 2 diabetes mellitus (n=625,739) who were new users of an SGLT2i (n=57,070; 9.1%) or DPP4i (n=568,669; 90.9%) were included. Outcomes included hospitalization for heart failure (hHF), all-cause death (ACD) and the composite of hHF or ACD. Hazard ratios (HR) were calculated using the inverse probability weighting Cox proportional hazards model to compare CVD event risks between treatment groups.RESULTS: Compared with DPP4i, SGLT2i was associated with a significant reduction in hHF risk among patients without a CVD history (HR 0.507, 95% confidence interval 0.283–0.907), but not in the full cohort or those with a CVD history. SGLT2i was associated with a significant risk reduction of ACD (HR 0.592, 95% confidence interval 0.481–0.729) and the composite of hHF or ACD (HR 0.712, 95% confidence interval 0.613–0.826), compared with DPP4i in the full cohort; similar results were observed among patients with and without a CVD history.CONCLUSION: In this real-world study, SGLT2i versus DPP4i was associated with a significant reduction in hHF, ACD and hHF or ACD events in patients with type 2 diabetes mellitus without a CVD history

Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach

We study characteristic (quasinormal) modes of a $D$-dimensional Schwarzshild black hole. It proves out that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\sim D r_{0}^{-1}$. The asymptotic formula for large multipole number $l$ and arbitrary $D$ is derived. In addition the WKB formula for computing QN modes, developed to the 3rd order beyond the eikonal approximation, is extended to the 6th order here. This gives us an accurate and economic way to compute quasinormal frequencies.Comment: 15 pages, 6 figures, the 6th order WKB formula for computing QNMs in Mathematica is available from https://goo.gl/nykYG

Area Spectrum of Kerr and extremal Kerr Black Holes from Quasinormal Modes

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form $m\Omega$ where $\Omega$ is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to $\ln 3$. Therefore, it does not give support to Hod's statement that the area spectrum $A_{n}=(4l^{2}_{p}ln 3)n$ should be valid for a generic Kerr-Newman black hole.Comment: 10 pages, no figure, LaTeX; v2: 12 pages, clarifying comments and an Appendix are added, version to appear in Mod. Phys. Lett.

Highly Damped Quasinormal Modes of Kerr Black Holes: A Complete Numerical Investigation

We compute for the first time very highly damped quasinormal modes of the (rotating) Kerr black hole. Our numerical technique is based on a decoupling of the radial and angular equations, performed using a large-frequency expansion for the angular separation constant_{s}A_{l m}. This allows us to go much further in overtone number than ever before. We find that the real part of the quasinormal frequencies approaches a non-zero constant value which does not depend on the spin s of the perturbing field and on the angular index l: \omega_R=m\varpi(a). We numerically compute \varpi(a). Leading-order corrections to the asymptotic frequency are likely to be of order 1/\omega_I. The imaginary part grows without bound, the spacing between consecutive modes being a monotonic function of a.Comment: 5 pages, 3 figure

Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

Using a recently developed perturbation theory for uasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasi-static perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.Comment: Published in PR