On nn-superharmonic functions and some geometric applications

In this paper we study asymptotic behavior of $n$-superharmonic functions at isolated singularity using the Wolff potential and $n$-capacity estimates in nonlinear potential theory. Our results are inspired by and extend those of Arsove-Huber and Taliaferro in 2 dimensions. To study $n$-superharmonic functions we use a new notion of $n$-thinness by $n$-capacity motivated by a type of Wiener criterion in Arsove-Huber's paper. To extend Taliaferro's work, we employ the Adams-Moser-Trudinger inequality for the Wolff potential, which is inspired by the one used by Brezis-Merle. For geometric applications, we study the asymptotic end behavior of complete conformally flat manifolds as well as complete properly embedded hypersurfaces in hyperbolic space. In both geometric applications the strong $n$-capacity lower bound estimate of Gehring in 1961 is brilliantly used. These geometric applications seem to elevate the importance of $n$-Laplace equations and make a closer tie to the classic analysis developed in conformal geometry in general dimensions.Comment: 46 page

Quarkonium Production in an Improved Color Evaporation Model

We propose an improved version of the color evaporation model to describe heavy quarkonium production. In contrast to the traditional color evaporation model, we impose the constraint that the invariant mass of the intermediate heavy quark-antiquark pair to be larger than the mass of produced quarkonium. We also introduce a momentum shift between heavy quark-antiquark pair and the quarkonium. Numerical calculations show that our model can describe the charmonium yields as well as ratio of $\psi^\prime$ over $J/\psi$ better than the traditional color evaporation model.Comment: 6 pages, 4 figure

Quantum Monte Carlo Study of Pairing Symmetry and Correlation in Iron-based Superconductors

We perform a systematic quantum Monte Carlo study of the pairing correlation in the $S_4$ symmetric microscopic model for iron-based superconductors. It is found that the pairing with an extensive s-wave symmetry robustly dominates over other pairings at low temperature in reasonable parameter region. The pairing susceptibility, the effective pairing interaction and the $(\pi,0)$antiferromagnetic correlation strongly increase as the on-site Coulomb interaction increases, indicating the importance of the effect of electron-electron correlation. Our non-biased numerical results provide a unified understanding of superconducting mechanism in iron-pnictides and iron-chalcogenides and demonstrate that the superconductivity is driven by strong electron-electron correlation effects.Comment: Accepted for publication as a Letter in Physical Review Letters, and more discussions are adde