Damping of Neutron Star Shear Modes by Superfluid Friction

The forced motion of superfluid vortices in shear oscillations of rotating solid neutron star matter produces damping of the mode. A simple model of the unpinning and repinning processes is described, with numerical calculations of the consequent energy decay times. These are of the order of 1 s or more for typical anomalous X-ray pulsars but become very short for the general population of radio pulsars. The superfluid friction processes considered here may also be significant for the damping of r-modes in rapidly rotating neutron stars.Comment: 7 LaTeX pages, 4 eps figures; accepted for publication in MNRA

A renormalization approach for the 2D Anderson model at the band edge: Scaling of the localization volume

We study the localization volumes $V$ (participation ratio) of electronic wave functions in the 2d-Anderson model with diagonal disorder. Using a renormalization procedure, we show that at the band edges, i.e. for energies $E\approx \pm 4$, $V$ is inversely proportional to the variance \var of the site potentials. Using scaling arguments, we show that in the neighborhood of $E=\pm 4$, $V$ scales as V=\var^{-1}g((4-\ve E\ve)/\var) with the scaling function $g(x)$. Numerical simulations confirm this scaling ansatz

Sufficient Conditions for Topological Order in Insulators

We prove the existence of low energy excitations in insulating systems at general filling factor under certain conditions, and discuss in which cases these may be identified as topological excitations. This proof is based on previously proven locality results. In the case of half-filling it provides a significantly shortened proof of the recent higher dimensional Lieb-Schultz-Mattis theorem.Comment: 7 pages, no figure

Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux

Absence of localization is demonstrated analytically to leading order in weak disorder in a one-dimensional Anderson model of a ring threaded by an Aharonov-Bohm (A-B) flux. The result follows from adapting an earlier perturbation treatment of disorder in a superconducting ring subjected to an imaginary vector potential proportional to a depinning field for flux lines bound to random columnar defects parallel to the axis of the ring. The absence of localization in the ring threaded by an A-B flux for sufficiently weak disorder is compatible with large free electron type persistent current obtained in recent studies of the above model

Nonlinear Schr\"odinger Equation for Superconductors

Using the Hartree-Fock-Bogoliubov factorization of the density matrix and the Born-Oppenheimer approximation we show that the motion of the condensate satisfies a nonlinear Schr\"odinger equation in the zero temperature limit. The Galilean invariance of the equation is explicitly manifested. {}From this equation some general properties of a superconductor, such as Josephson effects, the Magnus force, and the Bogoliubov-Anderson mode can be obtained readily.Comment: Latex, 12 page

Hierarchical Structure of Azbel-Hofstader Problem: Strings and loose ends of Bethe Ansatz

We present numerical evidence that solutions of the Bethe Ansatz equations for a Bloch particle in an incommensurate magnetic field (Azbel-Hofstadter or AH model), consist of complexes-"strings". String solutions are well-known from integrable field theories. They become asymptotically exact in the thermodynamic limit. The string solutions for the AH model are exact in the incommensurate limit, where the flux through the unit cell is an irrational number in units of the elementary flux quantum. We introduce the notion of the integral spectral flow and conjecture a hierarchical tree for the problem. The hierarchical tree describes the topology of the singular continuous spectrum of the problem. We show that the string content of a state is determined uniquely by the rate of the spectral flow (Hall conductance) along the tree. We identify the Hall conductances with the set of Takahashi-Suzuki numbers (the set of dimensions of the irreducible representations of $U_q(sl_2)$ with definite parity). In this paper we consider the approximation of noninteracting strings. It provides the gap distribution function, the mean scaling dimension for the bandwidths and gives a very good approximation for some wave functions which even captures their multifractal properties. However, it misses the multifractal character of the spectrum.Comment: revtex, 30 pages, 6 Figs, 8 postscript files are enclosed, important references are adde

Topological winding properties of spin edge states in Kane-Mele graphene model

We study the spin edge states in the quantum spin-Hall (QSH) effect on a single-atomic layer graphene ribbon system with both intrinsic and Rashba spin-orbit couplings. The Harper equation for solving the energies of the spin edge states is derived. The results show that in the QSH phase, there are always two pairs of gapless spin-filtered edge states in the bulk energy gap, corresponding to two pairs of zero points of the Bloch function on the complex-energy Riemann surface (RS). The topological aspect of the QSH phase can be distinguished by the difference of the winding numbers of the spin edge states with different polarized directions cross the holes of the RS, which is equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys. Rev. Lett. 95, 146802 (2005)].Comment: 9 pages, 10 figure

Ensemble Averaged Conductance Fluctuations in Anderson Localized Systems

We demonstrate the presence of energy dependent fluctuations in the localization length, which depend on the disorder distribution. These fluctuations lead to Ensemble Averaged Conductance Fluctuations (EACF) and are enhanced by large disorder. For the binary distribution the fluctuations are strongly enhanced in comparison to the Gaussian and uniform distributions. These results have important implications on ensemble averaged quantities, such as the transmission through quantum wires, where fluctuations can subsist to very high temperatures. For the non-fluctuating part of the localization length in one dimension we obtained an improved analytical expression valid for all disorder strengths by averaging the probability density.Comment: 4 page