Polarization Properties of Extragalactic Radio Sources and Their Contribution to Microwave Polarization Fluctuations

We investigate the statistical properties of the polarized emission of extragalactic radio sources and estimate their contribution to the power spectrum of polarization fluctuations in the microwave region. The basic ingredients of our analysis are the NVSS polarization data, the multifrequency study of polarization properties of the B3-VLA sample (Mack et al. 2002) which has allowed us to quantify Faraday depolarization effects, and the 15 GHz survey by Taylor et al. (2001), which has provided strong constraints on the high-frequency spectral indices of sources. The polarization degree of both steep- and flat-spectrum at 1.4 GHz is found to be anti-correlated with the flux density. The median polarization degree at 1.4 GHz of both steep- and flat-spectrum sources brighter than $S(1.4 \hbox{GHz})=80$mJy is $\simeq 2.2$. The data by Mack et al. (2002) indicate a substantial mean Faraday depolarization at 1.4 GHz for steep spectrum sources, while the depolarization is undetermined for most flat/inverted-spectrum sources. Exploiting this complex of information we have estimated the power spectrum of polarization fluctuations due to extragalactic radio sources at microwave frequencies. We confirm that extragalactic sources are expected to be the main contaminant of Cosmic Microwave Background (CMB) polarization maps on small angular scales. At frequencies $< 30$GHz the amplitude of their power spectrum is expected to be comparable to that of the $E$-mode of the CMB. At higher frequencies, however, the CMB dominates.Comment: 10 pages, A&A in pres

Quaternionic Diffusion by a Potential Step

In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential step. In this paper, we restrict our attention to diffusion phenomena. For the group velocity of the wave packet moving in the potential region and for the reflection and transmission times, the study shows a striking difference between the complex and quaternionic formulations which could be matter of further theoretical discussions and could represent the starting point for a possible experimental investigation.Comment: 10 pages, 1 figur

Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles

We consider free lattice fermions subjected to a static bounded potential and a time- and space-dependent electric field. For any bounded convex region $\mathcal{R}\subset \mathbb{R}^{d}$ ($d\geq 1$) of space, electric fields $\mathcal{E}$ within $\mathcal{R}$ drive currents. At leading order, uniformly with respect to the volume $\left| \mathcal{R}\right|$ of $\mathcal{R}$ and the particular choice of the static potential, the dependency on $\mathcal{E}$ of the current is linear and described by a conductivity distribution. Because of the positivity of the heat production, the real part of its Fourier transform is a positive measure, named here (microscopic) conductivity measure of $\mathcal{R}$, in accordance with Ohm's law in Fourier space. This finite measure is the Fourier transform of a time-correlation function of current fluctuations, i.e., the conductivity distribution satisfies Green-Kubo relations. We additionally show that this measure can also be seen as the boundary value of the Laplace-Fourier transform of a so-called quantum current viscosity. The real and imaginary parts of conductivity distributions satisfy Kramers-Kronig relations. At leading order, uniformly with respect to parameters, the heat production is the classical work performed by electric fields on the system in presence of currents. The conductivity measure is uniformly bounded with respect to parameters of the system and it is never the trivial measure $0\,\mathrm{d}\nu$. Therefore, electric fields generally produce heat in such systems. In fact, the conductivity measure defines a quadratic form in the space of Schwartz functions, the Legendre-Fenchel transform of which describes the resistivity of the system. This leads to Joule's law, i.e., the heat produced by currents is proportional to the resistivity and the square of currents

Methane and Nitrous Oxide Emissions from Grazed Grasslands

Key points 1. Emissions of methane (CH4) and nitrous oxide (N2O) from grasslands make a substantial contribution to total agricultural emissions of these two gases. 2. At present practical mitigation options that relate to grazing ruminants and grazed pastures are limited. 3. Research into agricultural greenhouse gas emissions is of low priority in most developed countries. 4. Direct manipulation of the rumen ecosystem provides the best opportunity for large reductions in CH4 in the long term. 5. Reducing the amount of nitrogen (N) excreted by grazing animals is a priority in N2O research, as this source of N2O constitutes almost 90% of the total global N2O emissions from grasslands

Magnetic Field Dependence of the Level Spacing of a Small Electron Droplet

The temperature dependence of conductance resonances is used to measure the evolution with the magnetic field of the average level spacing $\Delta\epsilon$ of a droplet containing $\sim 30$ electrons created by lateral confinement of a two-dimensional electron gas in GaAs. $\Delta\epsilon$ becomes very small ($< 30\mu$eV) near two critical magnetic fields at which the symmetry of the droplet changes and these decreases of $\Delta\epsilon$ are predicted by Hartree-Fock (HF) for charge excitations. Between the two critical fields, however, the largest measured $\Delta\epsilon= 100\mu$eV is an order of magnitude smaller than predicted by HF but comparable to the Zeeman splitting at this field, which suggests that the spin degrees of freedom are important. PACS: 73.20.Dx, 73.20.MfComment: 11 pages of text in RevTeX, 4 figures in Postscript (files in the form of uuencoded compressed tar file

Dynamics of two coupled vortices in a spin valve nanopillar excited by spin transfer torque

We investigate the dynamics of two coupled vortices driven by spin transfer. We are able to independently control with current and perpendicular field, and to detect, the respective chiralities and polarities of the two vortices. For current densities above $J=5.7*10^7 A/cm^2$, a highly coherent signal (linewidth down to 46 kHz) can be observed, with a strong dependence on the relative polarities of the vortices. It demonstrates the interest of using coupled dynamics in order to increase the coherence of the microwave signal. Emissions exhibit a linear frequency evolution with perpendicular field, with coherence conserved even at zero magnetic field

Computational approach to the Schottky problem

We present a computational approach to the classical Schottky problem based on Fay's trisecant identity for genus $g\geq 4$. For a given Riemann matrix $\mathbb{B}\in\mathbb{H}^{g}$, the Fay identity establishes linear dependence of secants in the Kummer variety if and only if the Riemann matrix corresponds to a Jacobian variety as shown by Krichever. The theta functions in terms of which these secants are expressed depend on the Abel maps of four arbitrary points on a Riemann surface. However, there is no concept of an Abel map for general $\mathbb{B} \in \mathbb{H}^{g}$. To establish linear dependence of the secants, four components of the vectors entering the theta functions can be chosen freely. The remaining components are determined by a Newton iteration to minimize the residual of the Fay identity. Krichever's theorem assures that if this residual vanishes within the finite numerical precision for a generic choice of input data, then the Riemann matrix is with this numerical precision the period matrix of a Riemann surface. The algorithm is compared in genus 4 for some examples to the Schottky-Igusa modular form, known to give the Jacobi locus in this case. It is shown that the same residuals are achieved by the Schottky-Igusa form and the approach based on the Fay identity in this case. In genera 5, 6 and 7, we discuss known examples of Riemann matrices and perturbations thereof for which the Fay identity is not satisfied