Localization in a quantum spin Hall system

Localization problem of electronic states in a two-dimensional quantum spin Hall system (QSH - a symplectic model with a non-trivial topological structure) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair-annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent $\nu$ for the divergence of the localization length is estimated as $\nu \cong 1.6$ which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. This strongly suggests a different universality class related to the non-trivial topology of the QSH system.Comment: 5 pages, 4 figures, REVTe

Negative 4-Probe Conductances of Mesoscopic Superconducting Wires

We analyze the longitudinal 4-probe conductance of mesoscopic normal and superconducting wires and predict that in the superconducting case, large negative values can arise for both the weakly disordered and localized regimes. This contrasts sharply with the behaviour of the longitudinal 4-probe conductance of normal wires, which in the localized limit is always exponentially small and positive.Comment: Latex, 3 figures available on request to [email protected] (Simon Robinson

Two Conditions for Galaxy Quenching: Compact Centres and Massive Haloes

We investigate the roles of two classes of quenching mechanisms for central and satellite galaxies in the SDSS ($z<0.075$): those involving the halo and those involving the formation of a compact centre. For central galaxies with inner compactness $\Sigma_{\rm 1kpc} \sim 10^{9-9.4}M_{\odot} {\rm kpc}^{-2}$, the quenched fraction $f_{q}$ is strongly correlated with $\Sigma_{\rm 1kpc}$ with only weak halo mass $M_{\rm h}$ dependence. However, at higher and lower $\Sigma_{\rm 1kpc}$, sSFR is a strong function of $M_{\rm h}$ and mostly independent of $\Sigma_{\rm 1kpc}$. In other words, $\Sigma_{\rm 1kpc} \sim 10^{9-9.4} M_{\odot} {\rm kpc}^{-2}$ divides galaxies into those with high sSFR below and low sSFR above this range. In both the upper and lower regimes, increasing $M_{\rm h}$ shifts the entire sSFR distribtuion to lower sSFR without a qualitative change in shape. This is true even at fixed $M_{*}$, but varying $M_{*}$ at fixed $M_{\rm h}$ adds no quenching information. Most of the quenched centrals with $M_{\rm h} > 10^{11.8}M_{\odot}$ are dense ($\Sigma_{\rm 1kpc} > 10^{9}~ M_{\odot} {\rm kpc}^{-2}$), suggesting compaction-related quenching maintained by halo-related quenching. However, 21% are diffuse, indicating only halo quenching. For satellite galaxies in the outskirts of halos, quenching is a strong function of compactness and a weak function of host $M_{\rm h}$. In the inner halo, $M_{\rm h}$ dominates quenching, with $\sim 90\%$ of the satellites being quenched once $M_{\rm h} > 10^{13}M_{\odot}$. This regional effect is greatest for the least massive satellites. As demonstrated via semi-analytic modelling with simple prescriptions for quenching, the observed correlations can be explained if quenching due to central compactness is rapid while quenching due to halo mass is slow.Comment: 16 pages, 11 figures, MNRAS accepte

Rigorous upper bound for the persistent current in systems with toroidal geometry

It is shown that the absolute value of the persistent current in a system with toroidal geometry is rigorously less than or equal to $e \hbar N /4 \pi m r_0^2$, where $N$ is the number of electrons, and $r_0^{-2} = \langle r_i^{-2}\rangle$ is the equilibrium average of the inverse of the square of the distance of an electron from an axis threading the torus. This result is valid in three and two dimensions for arbitrary interactions, impurity potentials, and magnetic fields.Comment: 10 pages + 1 figure available by request, Revte

Wiener Reconstruction of Large-Scale Structure from Peculiar Velocities

We present an alternative, Bayesian method for large-scale reconstruction from observed peculiar velocity data. The method stresses a rigorous treatment of the random errors and it allows extrapolation into poorly sampled regions in real space or in k-space. A likelihood analysis is used to determine the fluctuation power spectrum, followed by a Wiener Filter (WF) analysis to obtain the minimum-variance mean fields of velocity and mass density. Constrained Realizations (CR) are then used to sample the statistical scatter about the WF mean field. The WF/CR method is applied as a demonstration to the Mark III data with 1200 km/s, 900 km/s, and 500 km/s resolutions. The main reconstructed structures are consistent with those extracted by the POTENT method. A comparison with the structures in the distribution of IRAS 1.2Jy galaxies yields a general agreement. The reconstructed velocity field is decomposed into its divergent and tidal components relative to a cube of +/-8000 km/s centered on the Local Group. The divergent component is very similar to the velocity field predicted from the distribution of IRAS galaxies. The tidal component is dominated by a bulk flow of 194 +/- 32 km/s towards the general direction of the Shapley concentration, and it also indicates a significant quadrupole.Comment: 28 pages and 8 GIF figures, Latex (aasms4.sty), submitted to ApJ. Postscript version of the figures can be obtained by anonymous ftp from: ftp://alf.huji.ac.il/pub/saleem