Andreev Edge State on Semi-Infinite Triangular Lattice: Detecting the Pairing Symmetry in Na_0.35CoO_2.yH_2O

We study the Andreev edge state on the semi-infinite triangular lattice with different pairing symmetries and boundary topologies. We find a rich phase diagram of zero energy Andreev edge states that is a unique fingerprint of each of the possible pairing symmetries. We propose to pin down the pairing symmetry in recently discovered Na_xCoO_2 material by the Fourier-transformed scanning tunneling spectroscopy for the edge state. A surprisingly rich phase diagram is found and explained by a general gauge argument and mapping to 1D tight-binding model. Extensions of this work are discussed at the end.Comment: 4 pages, 1 table, 4 figure

Permutation Symmetric Critical Phases in Disordered Non-Abelian Anyonic Chains

Topological phases supporting non-abelian anyonic excitations have been proposed as candidates for topological quantum computation. In this paper, we study disordered non-abelian anyonic chains based on the quantum groups $SU(2)_k$, a hierarchy that includes the $\nu=5/2$ FQH state and the proposed $\nu=12/5$ Fibonacci state, among others. We find that for odd $k$ these anyonic chains realize infinite randomness critical {\it phases} in the same universality class as the $S_k$ permutation symmetric multi-critical points of Damle and Huse (Phys. Rev. Lett. 89, 277203 (2002)). Indeed, we show that the pertinent subspace of these anyonic chains actually sits inside the ${\mathbb Z}_k \subset S_k$ symmetric sector of the Damle-Huse model, and this ${\mathbb Z}_k$ symmetry stabilizes the phase.Comment: 13 page

The ordered K-theory of a full extension

Let A be a C*-algebra with real rank zero which has the stable weak cancellation property. Let I be an ideal of A such that I is stable and satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a full extension if and only if the extension is stenotic and K-lexicographic. As an immediate application, we extend the classification result for graph C*-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely K-theoretical description of when an essential extension of two simple and stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9 is not correct as stated. See arXiv:1505.05951 for more details. Since Theorem 4.9 is an application to the main results of the paper, the main results of this paper are not affected by the error. Version III comments: Some typos and errors corrected. Some references adde

Low Redshift QSO Lyman alpha Absorption Line Systems Associated with Galaxies

In this paper we present Monte-Carlo simulations of Lyman alpha absorption systems which originate in galactic haloes, galaxy discs and dark matter (DM) satellites around big central haloes. It is found that for strong Lyman alpha absorption lines galactic haloes and satellites can explain ~20% and 40% of the line number density of QSO absorption line key project respectively. If big galaxies indeed possess such large numbers of DM satellites and they possess gas, these satellites may play an important role for strong Lyman alpha lines. However the predicted number density of Lyman-limit systems by satellites is \~0.1 (per unit redshift), which is four times smaller than that by halo clouds. Including galactic haloes, satellites and HI discs of spirals, the predicted number density of strong lines can be as much as 60% of the HST result. The models can also predict all of the observed Lyman-limit systems. The average covering factor within 250 kpc/h is estimated to be ~0.36. And the effective absorption radius of a galaxy is estimated to be ~150 kpc/h. The models predict W_r propto rho^{-0.5} L_B^{0.15} (1+z)^{-0.5}. We study the selection effects of selection criteria similar to the imaging and spectroscopic surveys. We simulate mock observations through known QSO lines-of-sight and find that selection effects can statistically tighten the dependence of line width on projected distance. (abridged)Comment: 23 pages, 9 postscript figures; references updated, minor change in section

Mass Spectrum and Bounds on the Couplings in Yukawa Models With Mirror-Fermions

The $\rm SU(2)_L\otimes SU(2)_R$ symmetric Yukawa model with mirror-fermions in the limit where the mirror-fermion is decoupled is studied both analytically and numerically. The bare scalar self-coupling $\lambda$ is fixed at zero and infinity. The phase structure is explored and the relevant phase transition is found to be consistent with a second order one. The fermionic mass spectrum close to that transition is discussed and a first non-perturbative estimate of the influence of fermions on the upper and lower bounds on the renormalized scalar self-coupling is given. Numerical results are confronted with perturbative predictions.Comment: 7 (Latex) page