Commensurations and Metric Properties of Houghton's Groups

We describe the automorphism groups and the abstract commensurators of Houghton's groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding quasi-isometry groups. As a further consequence, we obtain that the Houghton group on two rays is at least quadratically distorted in those with three or more rays

Full two-photon downconversion of just a single photon

We demonstrate, both numerically and analytically, that it is possible to generate two photons from one and only one photon. We characterize the output two photon field and make our calculations close to reality by including losses. Our proposal relies on real or artificial three-level atoms with a cyclic transition strongly coupled to a one-dimensional waveguide. We show that close to perfect downconversion with efficiency over 99% is reachable using state-of-the-art Waveguide QED architectures such as photonic crystals or superconducting circuits. In particular, we sketch an implementation in circuit QED, where the three level atom is a transmon

Quantum stochastic walks on networks for decision-making

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce''s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process'' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making

Galaxy Evolution and Star Formation Efficiency in the Last Half of the Universe

We present the results of a CO(1-0) emission survey with the IRAM 30m of 30 galaxies at moderate redshift (z ~ 0.2-0.6) to explore galaxy evolution and in particular the star formation efficiency, in the redshift range filling the gap between local and very high-z objects. Our detection rate is about 50%. One of the bright objects was mapped at high resolution with the IRAM interferometer, and about 50% of the total emission found in the 27 arcsec (97 kpc) single dish beam is recovered by the interferometer, suggesting the presence of extended emission. The FIR-to-CO luminosity ratio is enhanced, following the increasing trend observed between local and high-z ultra-luminous starbursts.Comment: 6 pages, 5 figures, To appear in the proceedings of "SF2A-2007: Semaine de l'Astrophysique Francaise", (J. Bouvier, A. Chalabaev, and C. Charbonnel eds

Dark matter within high surface brightness spiral galaxies

We present results from a detailed dynamical analysis of five high surface brightness, late type spirals, studied with the aim to quantify the luminous-to-dark matter ratio inside their optical radii. The galaxies' stellar light distribution and gas kinematics have been observed and compared to hydrodynamic gas simulations, which predict the 2D gas dynamics arising in response to empirical gravitational potentials, which are combinations of differing stellar disk and dark halo contributions. The gravitational potential of the stellar disk was derived from near-infrared photometry, color-corrected to constant (M/L); the dark halo was modelled by an isothermal sphere with a core. Hydrodynamic gas simulations were performed for each galaxy for a sequence of five different mass fractions of the stellar disk and for a wide range of spiral pattern speeds. These two parameters mainly determine the modelled gas distribution and kinematics. The agreement between the non-axisymmetric part of the simulated and observed gas kinematics permitted us to conclude that the galaxies with the highest rotation velocities tend to possess near-maximal stellar disks. In less massive galaxies, with v_max<200 km/s, the mass of the dark halo at least equals the stellar mass within 2-3 R_disk. The simulated gas morphology provides a powerful tool to determine the dominant spiral pattern speed. The corotation radius for all galaxies was found to be constant at R_corotation ~ 3 R_disk and encloses the strong part of the stellar spiral in all cases.Comment: 28 pages, 7 figures; to appear in the Astrophysical Journal, Vol. 586, March 200

Molecular gas chemistry in AGN. II. High-resolution imaging of SiO emission in NGC1068: shocks or XDR?

This paper is part of a multi-species survey of line emission from the molecular gas in the circum-nuclear disk (CND) of the Seyfert 2 galaxy NGC1068. Single-dish observations have provided evidence that the abundance of silicon monoxide(SiO) in the CND of NGC1068 is enhanced by 3-4 orders of magnitude with respect to the values typically measured in quiescent molecular gas in the Galaxy. We aim at unveiling the mechanism(s) underlying the SiO enhancement. We have imaged with the IRAM Plateau de Bure interferometer the emission of the SiO(2-1) and CN(2--1) lines in NGC1068 at 150pc and 60pc spatial resolution, respectively. We have also obtained complementary IRAM 30m observations of HNCO and methanol (CH3OH) lines. SiO is detected in a disk of 400pc size around the AGN. SiO abundances in the CND of (1-5)xE-09 are about 1-2 orders of magnitude above those measured in the starburst ring. The overall abundance of CN in the CND is high: (0.2-1)xE-07. The abundances of SiO and CN are enhanced at the extreme velocities of gas associated with non-circular motions close to the AGN (r<70pc). Abundances measured for CN and SiO, and the correlation of CN/CO and SiO/CO ratios with hard X-ray irradiation, suggest that the CND of NGC1068 has become a giant X-ray dominated region (XDR). The extreme properties of molecular gas in the circum-nuclear molecular disk of NGC1068 result from the interplay between different processes directly linked to nuclear activity. Whereas XDR chemistry offers a simple explanation for CN and SiO in NGC1068, the relevance of shocks deserves further scrutiny. The inclusion of dust grain chemistry would help solve the controversy regarding the abundances of other molecular species, like HCN, which are under-predicted by XDR models.Comment: 18 pages, 13 figures, 2 tables; accepted for publication in A&

Tracing high density gas in M 82 and NGC 4038

We present the first detection of CS in the Antennae galaxies towards the NGC 4038 nucleus, as well as the first detections of two high-J (5-4 and 7-6) CS lines in the center of M 82. The CS(7-6) line in M 82 shows a profile that is surprisingly different to those of other low-J CS transitions we observed. This implies the presence of a separate, denser and warmer molecular gas component. The derived physical properties and the likely location of the CS(7-6) emission suggests an association with the supershell in the centre of M 82.Comment: 10 pages, 3 figures, ApJ Letter - ACCEPTE