Time and Geometric Quantization

In this paper we briefly review the functional version of the Koopman-von Neumann operatorial approach to classical mechanics. We then show that its quantization can be achieved by freezing to zero two Grassmannian partners of time. This method of quantization presents many similarities with the one known as Geometric Quantization.Comment: Talk given by EG at "Spacetime and Fundamental Interactions: Quantum Aspects. A conference to honour A.P.Balachandran's 65th birthday

The Visibility of Galactic Bars and Spiral Structure At High Redshifts

We investigate the visibility of galactic bars and spiral structure in the distant Universe by artificially redshifting 101 B-band CCD images of local spiral galaxies from the Ohio State University Bright Spiral Galaxy Survey. Our artificially redshifted images correspond to Hubble Space Telescope I-band observations of the local galaxy sample seen at z=0.7, with integration times matching those of both the very deep Northern Hubble Deep Field data, and the much shallower Flanking Field observations. The expected visibility of galactic bars is probed in two ways: (1) using traditional visual classification, and (2) by charting the changing shape of the galaxy distribution in "Hubble space", a quantitative two-parameter description of galactic structure that maps closely on to Hubble's original tuning fork. Both analyses suggest that over 2/3 of strongly barred luminous local spirals i.e. objects classified as SB in the Third Reference Catalog) would still be classified as strongly barred at z=0.7 in the Hubble Deep Field data. Under the same conditions, most weakly barred spirals (classified SAB in the Third Reference Catalog) would be classified as regular spirals. The corresponding visibility of spiral structure is assessed visually, by comparing luminosity classifications for the artificially redshifted sample with the corresponding luminosity classifications from the Revised Shapley Ames Catalog. We find that for exposures times similar to that of the Hubble Deep Field spiral structure should be detectable in most luminous low-inclination spiral galaxies at z=0.7 in which it is present. [ABRIDGED]Comment: Accepted for publication in The Astronomical Journa

Variability of GRB Afterglows Due to Interstellar Turbulence

Gamma-Ray Burst (GRB) afterglows are commonly interpreted as synchrotron emission from a relativistic blast wave produced by a point explosion in an ambient medium, plausibly the interstellar medium of galaxies. We calculate the amplitude of flux fluctuations in the lightcurve of afterglows due to inhomogeneities in the surrounding medium. Such inhomogeneities are an inevitable consequence of interstellar turbulence, but could also be generated by variability and anisotropy in a precursor wind from the GRB progenitor. Detection of their properties could provide important clues about the environments of GRB sources. We apply our calculations to GRB990510, where an rms scatter of 2% was observed for the optical flux fluctuations on the 0.1--2 hour timescale during the first day of the afterglow, consistent with it being entirely due to photometric noise (Stanek et al. 1999). The resulting upper limits on the density fluctuations on scales of 20-200 AU around the source of GRB990510, are lower than the inferred fluctuation amplitude on similar scales in the Galactic interstellar medium. Hourly monitoring of future optical afterglows might therefore reveal fractional flux fluctuations at the level of a few percent.Comment: 18 pages, submitted to Ap

Identifying the Environment and Redshift of GRB Afterglows from the Time-Dependence of Their Absorption Spectra

The discovery of Gamma-Ray Burst (GRB) afterglows revealed a new class of variable sources at optical and radio wavelengths. At present, the environment and precise redshift of the detected afterglows are still unknown. We show that if a GRB source resides in a compact (<100pc) gas-rich environment, the afterglow spectrum will show time-dependent absorption features due to the gradual ionization of the surrounding medium by the afterglow radiation. Detection of this time-dependence can be used to constrain the size and density of the surrounding gaseous system. For example, the MgII absorption line detected in GRB970508 should have weakened considerably during the first month if the absorption occurred in a gas cloud of size <100pc around the source. The time-dependent HI or metal absorption features provide a precise determination of the GRB redshift.Comment: 13 pages, 4 figures, submitted to ApJ

The Pierre Auger Observatory: Results on Ultra-High Energy Cosmic Rays

The focus of this article is on recent results on ultra-high energy cosmic rays obtained with the Pierre Auger Observatory. The world's largest instrument of this type and its performance are described. The observations presented here include the energy spectrum, the primary particle composition, limits on the fluxes of photons and neutrinos and a discussion of the anisotropic distribution of the arrival directions of the most energetic particles. Finally, plans for the construction of a Northern Auger Observatory in Colorado, USA, are discussed.Comment: Proceedings of the International Workshop on Advances in Cosmic Ray Science, Waseda University, Shinjuku, Tokyo, Japan, March 2008; to be published in the Journal of the Physical Society of Japan (JPSJ) supplemen

Optical properties of current carrying molecular wires

We consider several fundamental optical phenomena involving single molecules in biased metal-molecule-metal junctions. The molecule is represented by its highest occupied and lowest unoccupied molecular orbitals, and the analysis involves the simultaneous consideration of three coupled fluxes: the electronic current through the molecule, energy flow between the molecule and electron-hole excitations in the leads and the incident and/or emitted photon flux. Using a unified theoretical approach based on the non-equilibrium Green function method we derive expressions for the absorption lineshape (not an observable but a ueful reference for considering yields of other optical processes) and for the current induced molecular emission in such junctions. We also consider conditions under which resonance radiation can induce electronic current in an unbiased junction. We find that current driven molecular emission and resonant light induced electronic currents in single molecule junctions can be of observable magnitude under appropriate realizable conditions. In particular, light induced current should be observed in junctions involving molecular bridges that are characterized by strong charge transfer optical transitions. For observing current induced molecular emission we find that in addition to the familiar need to control the damping of molecular excitations into the metal substrate the phenomenon is also sensitive to the way in which the potential bias si distributed on the junction.Comment: 56 pages, 8 figures; submitted to JC

The Star Formation History of the Hubble Sequence: Spatially Resolved Colour Distributions of Intermediate Redshift Galaxies in the Hubble Deep Field

We analyse the spatially resolved colours of distant galaxies of known redshift in the Hubble Deep Field, using a new technique based on matching resolved four-band internal colour data to the predictions of evolutionary synthesis models. We quantify the relative age, dispersion in age, ongoing star-formation rate, star-formation history, and dust content of these galaxies. To demonstrate the potential of the method, we study the near-complete sample of 32 I ~ 0.5 studied by Bouwens et al (1997). The dispersion of the internal colours of a sample of 0.4<z<1 early-type field galaxies in the HDF indicates that ~40% [4/11] show evidence of star formation which must have occurred within the past third of their ages at the epoch of observation. For a sample of well-defined spirals, we similarly exploit the dispersion in colour to analyse the relative histories of bulge and disc stars, in order to resolve the current controversy regarding the ages of galactic bulges. Dust and metallicity gradients are ruled out as major contributors to the colour dispersions we observe in these systems. The median ages of bulge stars are found to be signicantly older than those in galactic discs, and exhibit markedly different star-formation histories. This result is inconsistent with a secular growth of bulges from disc instabilities, but consistent with gradual disc formation by accretion of gas onto bulges, as predicted by hierarchical theories. We extend our technique in order to discuss the star formation history of the entire Bouwens et al sample in the context of earlier studies concerned with global star formation histories.Comment: 8 colour postscript figures plus LaTeX source; submitted to MNRAS. Uses the mnras.sty LaTeX style fil

Observation and inverse problems in coupled cell networks

A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism, economical networks... It consists in a directed graph $G$, each node (or cell) representing an agent of the network and each directed arrow representing which agent acts on which one. It yields a system of differential equations $\dot x(t)=f(x(t))$, where the component $i$ of $f$ depends only on the cells $x_j(t)$ for which the arrow $j\rightarrow i$ exists in $G$. In this paper, we investigate the observation problems in coupled cell networks: can one deduce the behaviour of the whole network (oscillations, stabilisation etc.) by observing only one of the cells? We show that the natural observation properties holds for almost all the interactions $f$

Nonthermal THz to TeV Emission from Stellar Wind Shocks in the Galactic Center

The central parsec of the Galaxy contains dozens of massive stars with a cumulative mass loss rate of ~ 10^{-3} solar masses per year. Shocks among these stellar winds produce the hot plasma that pervades the central part of the galaxy. We argue that these stellar wind shocks also efficiently accelerate electrons and protons to relativistic energies. The relativistic electrons inverse Compton scatter the ambient ultraviolet and far infrared radiation field, producing high energy gamma-rays with a roughly constant luminosity from \~ GeV to ~ 10 TeV. This can account for the TeV source seen by HESS in the Galactic Center. Our model predicts a GLAST counterpart to the HESS source with a luminosity of ~ 10^{35} ergs/s and cooling break at ~ 4 GeV. Synchrotron radiation from the same relativistic electrons should produce detectable emission at lower energies, with a surface brightness ~ 10^{32} B^2_{-3} ergs/s/arcsec^2 from ~ THz to ~ keV, where B_{-3} is the magnetic field strength in units of mG. The observed level of diffuse thermal X-ray emission in the central parsec requires B < 300 micro-G in our models. Future detection of the diffuse synchrotron background in the central parsec can directly constrain the magnetic field strength, providing an important boundary condition for models of accretion onto Sgr A*.Comment: submitted to ApJ Letter