Non-Uniform Cosmological Birefringence and Active Galactic Nuclei

Cosmological birefringence, a rotation by an angle $\alpha$ of the polarization of photons as they propagate over cosmological distances, is constrained by the cosmic microwave background (CMB) to be $|\alpha|\lesssim1^\circ$ ($1\sigma$) out to redshifts $z\simeq1100$ for a rotation that is uniform across the sky. However, the rotation angle $\alpha(\theta,\phi)$ may vary as a function of position $(\theta,\phi)$ on the sky. Here I discuss how a position-dependent rotation can be sought in current and future AGN data. An upper limit \VEV{\alpha^2}^{1/2} \lesssim 3.7^\circ to the scatter in the position-angle--polarization offsets in a sample of only N=9 AGN already constrains the rotation spherical-harmonic coefficients to $(4\pi)^{-1/2} \alpha_{lm}\lesssim 3.7^\circ$ and constrains the power spectrum for $\alpha$ in models where it is a stochastic field. Future constraints can be improved with more sources and by analyzing well-mapped sources with a tensor-harmonic decomposition of the polarization analogous to that used in CMB polarization and weak gravitational lensing.Comment: 5 pages

Metal-insulator transitions in anisotropic 2d systems

Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using transfer matrix techniques. Scaling functions of isotropic systems are recovered once the dimension of the system in each direction is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and that the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system (approximately 7/3). We also calculate the critical value of the scaling function for both the isotropic and the anisotropic system. It is found that the isotropic value equals the geometric mean of the two anisotropic values. Detailed numerical studies of the density of states for the isotropic system reveals that for an appreciable amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review

Credit constraints and the propagation of the Great Depression in Germany

We evaluate the role played by loan supply shocks in the decline of investment and industrial production during the Great Depression in Germany from 1927 to 1932. We identify loan supply shocks in the context of a time varying parameter vector autoregression with stochastic volatility. Our results indicate that credit constraints were a significant driver of industrial production between 1927 and 1932, supporting the view that a structurally weak banking sector was an important contributor to the German Great Depression. We find further that loan supply shocks were an important driver of investment in the early phase of the depression, between 1927 and 1929, but not between 1930 and 1932. We suggest possible explanations for this puzzle and directions for future research