Spectra of some invertible weighted composition operators on Hardy and weighted Bergman spaces in the unit ball

In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_\alpha^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit ball of the $N$-dimensional complex space. By taking $N=1$, $\mathbb{B}_N=\mathbb{D}$ the unit disc, we also complete the discussion about the spectrum of a weighted composition operator when it is invertible on $H^2(\mathbb{D})$ or $A_\alpha^2(\mathbb{D})$.Comment: 23 Page

Layer Antiferromagnetic State in Bilayer Graphene : A First-Principle Investigation

The ground state of bilayer graphene is investigated by the density functional calculations with local spin density approximation. We find a ground state with layer antiferromagnetic ordering, which has been suggested by former studies based on simplified model. The calculations prove that the layer antiferromagnetic state (LAF) is stable even if the remote hopping and nonlocal Coulomb interaction are included. The gap of the LAF state is about 1.8 meV, comparable to the experimental value. The surface magnetism in BLG is of the order of $10^{-2} \mu_B /nm^2$

Anderson Impurity in Helical Metal

We use a trial wave function to study the spin-1/2 Kondo effect of a helical metal on the surface of a three-dimensional topological insulator. While the impurity spin is quenched by conduction electrons, the spin-spin correlation of the conduction electron and impurity is strongly anisotropic in both spin and spatial spaces. As a result of strong spin-orbit coupling, the out-of-plane component of the impurity spin is found to be fully screened by the orbital angular momentum of the conduction electrons.Comment: The published versio

Numerical Ranges of Composition Operators with Elliptic Automorphism Symbols

In this paper we investigate the numerical ranges of composition operators whose symbols are elliptic automorphisms of finite orders, on the Hilbert Hardy space $H^2(D)$.Comment: 14 Page