Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length

Electrons on a square lattice with half a flux quantum per plaquette are considered. An effective description for the current loops is given by a two-dimensional Dirac theory with random mass. It is shown that the conductivity and the localization length can be calculated from a product of Dirac Green's functions with the {\it same} frequency. This implies that the delocalization of electrons in a magnetic field is due to a critical point in a phase with a spontaneously broken discrete symmetry. The estimation of the localization length is performed for a generalized model with $N$ fermion levels using a $1/N$--expansion and the Schwarz inequality. An argument for the existence of two Hall transition points is given in terms of percolation theory.Comment: 10 pages, RevTeX, no figure

Internal kinematics of isolated modelled disk galaxies

We present a systematic investigation of rotation curves (RCs) of fully hydrodynamically simulated galaxies, including cooling, star formation with associated feedback and galactic winds. Applying two commonly used fitting formulae to characterize the RCs, we investigate systematic effects on the shape of RCs both by observational constraints and internal properties of the galaxies. We mainly focus on effects that occur in measurements of intermediate and high redshift galaxies. We find that RC parameters are affected by the observational setup, like slit misalignment or the spatial resolution and also depend on the evolution of a galaxy. Therefore, a direct comparison of quantities derived from measured RCs with predictions of semi-analytic models is difficult. The virial velocity V_c, which is usually calculated and used by semi-analytic models can differ significantly from fit parameters like V_max or V_opt inferred from RCs. We find that V_c is usually lower than typical characteristic velocities derived from RCs. V_max alone is in general not a robust estimator for the virial mass.Comment: 9 pages, 15 figures, accepted for publication in A&

BD-22 3467, a DAO-type star exciting the nebula Abell 35

Spectral analyses of hot, compact stars with NLTE (non-local thermodynamical equilibrium) model-atmosphere techniques allow the precise determination of photospheric parameters. The derived photospheric metal abundances are crucial constraints for stellar evolutionary theory. Previous spectral analyses of the exciting star of the nebula A 35, BD-22 3467, were based on He+C+N+O+Si+Fe models only. For our analysis, we use state-of-the-art fully metal-line blanketed NLTE model atmospheres that consider opacities of 23 elements from hydrogen to nickel. For the analysis of high-resolution and high-S/N (signal-to-noise) FUV (far ultraviolet, FUSE) and UV (HST/STIS) observations, we combined stellar-atmosphere models and interstellar line-absorption models to fully reproduce the entire observed UV spectrum. The best agreement with the UV observation of BD-22 3467 is achieved at Teff = 80 +/- 10 kK and log g =7.2 +/- 0.3. While Teff of previous analyses is verified, log g is significantly lower. We re-analyzed lines of silicon and iron (1/100 and about solar abundances, respectively) and for the first time in this star identified argon, chromium, manganese, cobalt, and nickel and determined abundances of 12, 70, 35, 150, and 5 times solar, respectively. Our results partially agree with predictions of diffusion models for DA-type white dwarfs. A combination of photospheric and interstellar line-absorption models reproduces more than 90 % of the observed absorption features. The stellar mass is M ~ 0.48 Msun. BD-22 3467 may not have been massive enough to ascend the asymptotic giant branch and may have evolved directly from the extended horizontal branch to the white dwarf state. This would explain why it is not surrounded by a planetary nebula. However, the star, ionizes the ambient interstellar matter, mimicking a planetary nebula.Comment: 13 pages, 17 figure

Integer Quantum Hall Effect for Lattice Fermions

A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the presence of disorder. It presents an alternative to the continuous picture for the IQHE with Landau levels. The large $N$ limit can be solved: two Hall transitions appear and there is an interpolating behavior between the two Hall plateaux. Although this approach to the IQHE is different from the traditional one with Landau levels because of different symmetries (continuous for Landau levels and discrete here), some characteristic features are reproduced. For instance, the slope of the Hall conductivity is infinite at the transition points and the electronic states are delocalized only at the transitions.Comment: 9 pages, Plain-Te

Internal kinematics of modelled interacting disc galaxies

We present an investigation of galaxy-galaxy interactions and their effects on the velocity fields of disc galaxies in combined N-body/hydrodynamic simulations, which include cooling, star formation with feedback, and galactic winds. Rotation curves (RCs) of the gas are extracted from these simulations in a way that follows the procedure applied to observations of distant, small, and faint galaxies as closely as possible. We show that galaxy-galaxy mergers and fly-bys disturb the velocity fields significantly and hence the RCs of the interacting galaxies, leading to asymmetries and distortions in the RCs. Typical features of disturbed kinematics are significantly rising or falling profiles in the direction of the companion galaxy and pronounced bumps in the RCs. In addition, tidal tails can leave strong imprints on the rotation curve. All these features are observable for intermediate redshift galaxies, on which we focus our investigations. We use a quantitative measure for the asymmetry of rotation curves to show that the appearance of these distortions strongly depends on the viewing angle. We also find in this way that the velocity fields settle back into relatively undisturbed equilibrium states after unequal mass mergers and fly-bys. About 1 Gyr after the first encounter, the RCs show no severe distortions anymore. These results are consistent with previous theoretical and observational studies. As an illustration of our results, we compare our simulated velocity fields and direct images with rotation curves from VLT/FORS spectroscopy and ACS images of a cluster at z=0.53 and find remarkable similarities.Comment: 13 pages, 14 figures, accepted for publication in A&A, some improvements and changes, main conclusions are unaffecte

On the fundamental group of the complement of a complex hyperplane arrangement

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.Comment: 12 pages, Latex2e with AMSLaTeX 1.2, no figures; this last version is almost the same as published in Functional Analysis and its Applications 45:2 (2011), 137-14

Bank Failures: A Study of Georgia Banks

Our study considers why a much large proportion of failed U.S. banks, between the years 2007 through 2018, were located in the State of Georgia. Georgia politicians, and certain local bankers, postulated this was due to overzealous regulators. We reviewed various capital ratios and loan risk indicators in the years prior to failure to analyze bank health. Our study found the indicators for bank health in Georgia were significantly worse as compared to the other failed banks. Georgia bank failures were more likely due to undercapitalization, too much loan risk, and insufficient loan loss reserve, rather than overzealous regulators

Density of states "width parity" effect in d-wave superconducting quantum wires

We calculate the density of states (DOS) in a clean mesoscopic d-wave superconducting quantum wire, i.e. a sample of infinite length but finite width $N$. For open boundary conditions, the DOS at zero energy is found to be zero if $N$ is even, and nonzero if $N$ is odd. At finite chemical potential, all chains are gapped but the qualtitative differences between even and odd $N$ remain.Comment: 7 pages, 8 figures, new figures and extended discussio