Redshift estimate of a gravitational lens from the observed reddening of a multiply imaged quasar

Light rays from a multiply imaged quasar usually sample different path lengths across the deflector. Extinction in the lensing galaxy may thus lead to a differential obscuration and reddening between the observed macro-lensed QSO images. These effects naturally depend on the precise shape of the extinction law and on the redshift of the lens. By means of numerical Monte-Carlo simulations, using a least-squares fitting method and assuming an extinction law similar to that observed in the Galaxy, we show how accurate photometric observations of multiply imaged quasars obtained in several spectral bands could lead to the estimate of the lens redshift, irrespective of the visibility of the deflector. Observational requirements necessary to apply this method to real cases are thoroughly discussed. If extinction laws turn out to be too different from galaxy to galaxy, we find out that more promising observations should consist in getting high signal-to-noise low resolution spectra of at least three distinct images of a lensed quasar, over a spectral range as wide as possible, from which it should be straightforward to extract the precise shape of the redshifted extinction law. Very high signal-to-noise, low spectral resolution, VLT observations of H1413+117 and MG 0414+0534 should enable one to derive such a redshifted extinction law.Comment: 7 pages, 11 figures, to appear in Astronomy and Astrophysics (also available at http://vela.astro.ulg.ac.be/preprint/

Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities

We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which the optimal constants are achieved by extremal functions. The comparison of these optimal constants with the optimal constants of Gagliardo-Nirenberg interpolation inequalities and Gross' logarithmic Sobolev inequality, both without weights, gives a general criterion for such an existence result in some particular cases.Comment: Proc. Edinburgh A (2012) To appea

Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants

This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities. These results have been obtained in a series of papers in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas and are presented from a new viewpoint

Pure emitter dephasing : a resource for advanced solid-state single photon sources

We have computed the spectrum emitted spontaneously by a quantum dot coupled to an arbitrarily detuned single mode cavity, taking into account pure dephasing processes. We show that if the emitter is incoherent, the cavity can efficiently emit photons with its own spectral characteristics. This effect opens unique opportunities for the development of devices exploiting both cavity quantum electrodynamics effects and pure dephasing, such as wavelength stabilized single photon sources robust against spectral diffusion.Comment: 5 pages, 3 figure

Insights on the physics of SNIa obtained from their gamma-ray emission

Type Ia supernovae are thought to be the outcome of the thermonuclear explosion of a carbon/oxygen white dwarf in a close binary system. Their optical light curve is powered by thermalized gamma-rays produced by the radioactive decay of $^{56}$Ni, the most abundant isotope present in the debris. Gamma-rays escaping the ejecta can be used as a diagnostic tool for studying the structure of the exploding star and the characteristics of the explosion. The fluxes of the $^{56}$Ni lines and the continuum obtained by INTEGRAL from SN2014J in M82, the first ever gamma-detected SNIa, around the time of the maximum of the optical light curve strongly suggest the presence of a plume of $^{56}$Ni in the outermost layers moving at high velocities. If this interpretation was correct, it could have important consequences on our current understanding of the physics of the explosion and on the nature of the systems that explode.Comment: Proceedings of the 11th INTEGRAL Conference Gamma-Ray AStrophysics in Multi-Wavelength Perspectiv

Infinite products involving binary digit sums

Let $(u_n)_{n\ge 0}$ denote the Thue-Morse sequence with values $\pm 1$. The Woods-Robbins identity below and several of its generalisations are well-known in the literature \begin{equation*}\label{WR}\prod_{n=0}^\infty\left(\frac{2n+1}{2n+2}\right)^{u_n}=\frac{1}{\sqrt 2}.\end{equation*} No other such product involving a rational function in $n$ and the sequence $u_n$ seems to be known in closed form. To understand these products in detail we study the function \begin{equation*}f(b,c)=\prod_{n=1}^\infty\left(\frac{n+b}{n+c}\right)^{u_n}.\end{equation*} We prove some analytical properties of $f$. We also obtain some new identities similar to the Woods-Robbins product.Comment: Accepted in Proc. AMMCS 2017, updated according to the referees' comment