Tradeoffs for number-squeezing in collisions of Bose-Einstein condensates

We investigate the factors that influence the usefulness of supersonic collisions of Bose-Einstein condensates as a potential source of entangled atomic pairs by analyzing the reduction of the number difference fluctuations between regions of opposite momenta. We show that non-monochromaticity of the mother clouds is typically the leading limitation on number squeezing, and that the squeezing becomes less robust to this effect as the density of pairs grows. We develop a simple model that explains the relationship between density correlations and the number squeezing, allows one to estimate the squeezing from properties of the correlation peaks, and shows how the multi-mode nature of the scattering must be taken into account to understand the behavior of the pairing. We analyze the impact of the Bose enhancement on the number squeezing, by introducing a simplified low-gain model. We conclude that as far as squeezing is concerned the preferable configuration occurs when atoms are scattered not uniformly but rather into two well separated regions.Comment: 13 pages, 13 figures, final versio

X-ray polarization in relativistic jets

We investigate the polarization properties of Comptonized X-rays from relativistic jets in active galactic nuclei (AGN) using Monte Carlo simulations. We consider three scenarios commonly proposed for the observed X-ray emission in AGN: Compton scattering of blackbody photons emitted from an accretion disc; scattering of cosmic microwave background (CMB) photons and self-Comptonization of intrinsically polarized synchrotron photons emitted by jet electrons. Our simulations show that for Comptonization of disc and CMB photons, the degree of polarization of the scattered photons increases with the viewing inclination angle with respect to the jet axis. In both cases, the maximum linear polarization is ≈20 per cent. In the case of synchrotron self-Comptonization (SSC), we find that the resulting X-ray polarization depends strongly on the seed synchrotron photon injection site, with typical fractional polarizations P≈ 10–20 per cent when synchrotron emission is localized near the jet base, while P≈ 20–70 per cent for the case of uniform emission throughout the jet. These results indicate that X-ray polarimetry may be capable of providing unique clues to identify the location of particle acceleration sites in relativistic jets. In particular, if synchrotron photons are emitted quasi-uniformly throughout a jet, then the observed degree of X-ray polarization may be sufficiently different for each of the competing X-ray emission mechanisms (synchrotron, SSC or external Comptonization) to determine which is the dominant process. However, X-ray polarimetry alone is unlikely to be able to distinguish between disc and CMB Comptonization

Scattering by Interstellar Dust Grains. II. X-Rays

Scattering and absorption of X-rays by interstellar dust is calculated for a model consisting of carbonaceous grains and amorphous silicate grains. The calculations employ realistic dielectric functions with structure near X-ray absorption edges, with resulting features in absorption, scattering, and extinction. Differential scattering cross sections are calculated for energies between 0.3 and 10 keV. The median scattering angle is given as a function of energy, and simple but accurate approximations are found for the X-ray scattering properties of the dust mixture, as well as for the angular distribution of the scattered X-ray halo for dust with simple spatial distributions. Observational estimates of the X-ray scattering optical depth are compared to model predictions. Observations of X-ray halos to test interstellar dust grain models are best carried out using extragalactic point sources.Comment: ApJ, accepted. 27 pages, 12 figures. Much of this material was previously presented in astro-ph/0304060v1,v2,v3 but has been separated into the present article following recommendation by the refere

Analytical Approximations for Calculating the Escape and Absorption of Radiation in Clumpy Dusty Environments

We present analytical approximations for calculating the scattering, absorption and escape of nonionizing photons from a spherically symmetric two-phase clumpy medium, with either a central point source of isotropic radiation, a uniform distribution of isotropic emitters, or uniformly illuminated by external sources. The analytical approximations are based on the mega-grains model of two-phase clumpy media, as proposed by Hobson & Padman, combined with escape and absorption probability formulae for homogeneous media. The accuracy of the approximations is examined by comparison with 3D Monte Carlo simulations of radiative transfer, including multiple scattering. Our studies show that the combined mega-grains and escape/absorption probability formulae provide a good approximation of the escaping and absorbed radiation fractions for a wide range of parameters characterizing the medium. A realistic test is performed by modeling the absorption of a starlike source of radiation by interstellar dust in a clumpy medium, and by calculating the resulting equilibrium dust temperatures and infrared emission spectrum of both the clumps and the interclump medium. In particular, we find that the temperature of dust in clumps is lower than in the interclump medium if clumps are optically thick. Comparison with Monte Carlo simulations of radiative transfer in the same environment shows that the analytic model yields a good approximation of dust temperatures and the emerging UV to FIR spectrum of radiation for all three types of source distributions mentioned above. Our analytical model provides a numerically expedient way to estimate radiative transfer in a variety of interstellar conditions and can be applied to a wide range of astrophysical environments, from star forming regions to starburst galaxies.Comment: 55 pages, 27 figures. ApJ 523 (1999), in press. Corrected equations and text so as to be same as ApJ versio

Coarse coherence of metric spaces and groups and its permanence properties

We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by F. Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. We show that coarse regular coherence implies weak regular coherence, a weakening of regular coherence by G. Carlsson and the first author. The latter was introduced with the same goal as Waldhausen's, in order to perform computations of algebraic K-theory of group rings. However, all groups known to be weakly regular coherent are also coarsely regular coherent. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.Comment: 11 page