An O(M(n) log n) algorithm for the Jacobi symbol

The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n) log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and Zimmermann. Our implementation - which to our knowledge is the first to run in time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010

Challenges for creating magnetic fields by cosmic defects

We analyse the possibility that topological defects can act as a source of magnetic fields through the Harrison mechanism in the radiation era. We give a detailed relativistic derivation of the Harrison mechanism at first order in cosmological perturbations, and show that it is only efficient for temperatures above T ~ 0.2 keV. Our main result is that the vector metric perturbations generated by the defects cannot induce vorticity in the matter fluids at linear order, thereby excluding the production of currents and magnetic fields. We show that anisotropic stress in the matter fluids is required to source vorticity and magnetic fields. Our analysis is relevant for any mechanism whereby vorticity is meant to be transferred purely by gravitational interactions, and thus would also apply to dark matter or neutrinos.Comment: 9 pages, 1 figure; minor corrections and additions; accepted for publication in Physical Review

Ellipsoidal Universe Can Solve The CMB Quadrupole Problem

The recent three-year WMAP data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit \Lambda CDM prediction. We show that, allowing the large-scale spatial geometry of our universe to be plane-symmetric with eccentricity at decoupling or order 10^{-2}, the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy.Comment: 4 pages, 2 figures, minor changes, reference added, to appear in Phys. Rev. Let

Magnetic Helicity Generation from the Cosmic Axion Field

The coupling between a primordial magnetic field and the cosmic axion field generates a helical component of the magnetic field around the time in which the axion starts to oscillate. If the energy density of the seed magnetic field is comparable to the energy density of the universe at that time, then the resulting magnetic helicity is about |H_B| \simeq (10^{-20} G)^2 kpc and remains constant after its generation. As a corollary, we find that the standard properties of the oscillating axion remain unchanged even in the presence of very strong magnetic fields.Comment: 6 pages, 2 figures. Accepted for publication in Phys. Rev. D. Minor revisions and new references adde

Pulsar rotation measures and the magnetic structure of our Galaxy

We have obtained 63 rotation measures (RMs) from polarization observations of southern pulsars, of which 54 are new measurements and 3 are varied from previous values. The new pulsar RM data at high Galactic latitudes are mostly consistent with the antisymmetric RM distribution found previously. For the Galactic disc, evidence for a field reversal near the Perseus arm, and possibly another beyond it, is presented. Inside the Solar Circle, in addition to the two known field reversals in or near the Carina-Sagittartus arm and the Crux-Scutum arm, a further reversal in the Norma arm is tentatively identified. These reversals, together with the pitch angle derived from pulsar RM and stellar polarization distributions, are consistent with bisymmetric spiral (BSS) models for the large-scale magnetic field structure in the disc of our Galaxy. However, discrimination between models is complicated by the presence of smaller-scale irregularities in the magnetic field, as well as uncertainties in the theoretical modelling.Comment: 10pages; 8 figures; Accepted by MNRA

Sharpenings of Li's criterion for the Riemann Hypothesis

Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with $A>0$ and $B$ explicitly given, also for the case of more general zeta or $L$-functions); whereas in the opposite case, $\lambda_n$ has a non-tempered oscillatory form.Comment: 10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text corrections and updated reference

Nonequilibrium Electron Interactions in Metal Films

Ultrafast relaxation dynamics of an athermal electron distribution is investigated in silver films using a femtosecond pump-probe technique with 18 fs pulses in off-resonant conditions. The results yield evidence for an increase with time of the electron-gas energy loss rate to the lattice and of the free electron damping during the early stages of the electron-gas thermalization. These effects are attributed to transient alterations of the electron average scattering processes due to the athermal nature of the electron gas, in agreement with numerical simulations

CMB anisotropies due to cosmological magnetosonic waves

We study scalar mode perturbations (magnetosonic waves) induced by a helical stochastic cosmological magnetic field and derive analytically the corresponding cosmic microwave background (CMB) temperature and polarization anisotropy angular power spectra. We show that the presence of a stochastic magnetic field, or an homogeneous magnetic field, influences the acoustic oscillation pattern of the CMB anisotropy power spectrum, effectively acting as a reduction of the baryon fraction. We find that the scalar magnetic energy density perturbation contribution to the CMB temperature anisotropy is small compared to the contribution to the CMB $E$-polarization anisotropy.Comment: 17 pages, references added, version accepted for publication in Phys. Rev.

Optical Phonon Lasing in Semiconductor Double Quantum Dots

We propose optical phonon lasing for a double quantum dot (DQD) fabricated in a semiconductor substrate. We show that the DQD is weakly coupled to only two LO phonon modes that act as a natural cavity. The lasing occurs for pumping the DQD via electronic tunneling at rates much higher than the phonon decay rate, whereas an antibunching of phonon emission is observed in the opposite regime of slow tunneling. Both effects disappear with an effective thermalization induced by the Franck-Condon effect in a DQD fabricated in a carbon nanotube with a strong electron-phonon coupling.Comment: 8 pages, 4 figure

Testing Lorentz Invariance Violation with WMAP Five Year Data

We consider different renormalizable models of Lorentz invariance violation. We show that the limits on birefringence of the propagation of cosmic microwave background photons from the five year data of the Wilkinson microwave anisotropy probe (WMAP) can be translated into a limit of Lorentz symmetry violation. The obtained limits on Lorentz invariance violation are stronger than other published limits. We also cast them in terms of limits on a birefringent effective photo "mass" and on a polarization dependence of the speed of light.Comment: 5 pages, references and discussions added, results unchanged, accepted for publications in PR