The Born Oscillator

The paper studies the properties of an oscillator whose Hamiltonian is $[(1+q^2)(1+p^2)]^{1/2}-1$. It can be deduced from the nonlinear theory of electrodynamics originally proposed by Max Born in 1934. The quantization of such oscillator represents a possible regularization of the Barry and Keating's Hamiltonian, which has been proposed in the framework of the theory of non-trivial zeros of the Riemann's $\zeta$ function

The zCOSMOS 10k-Bright Spectroscopic Sample

We present spectroscopic redshifts of a large sample of galaxies with I_(AB) < 22.5 in the COSMOS field, measured from spectra of 10,644 objects that have been obtained in the first two years of observations in the zCOSMOS-bright redshift survey. These include a statistically complete subset of 10,109 objects. The average accuracy of individual redshifts is 110 km s^(–1), independent of redshift. The reliability of individual redshifts is described by a Confidence Class that has been empirically calibrated through repeat spectroscopic observations of over 600 galaxies. There is very good agreement between spectroscopic and photometric redshifts for the most secure Confidence Classes. For the less secure Confidence Classes, there is a good correspondence between the fraction of objects with a consistent photometric redshift and the spectroscopic repeatability, suggesting that the photometric redshifts can be used to indicate which of the less secure spectroscopic redshifts are likely right and which are probably wrong, and to give an indication of the nature of objects for which we failed to determine a redshift. Using this approach, we can construct a spectroscopic sample that is 99% reliable and which is 88% complete in the sample as a whole, and 95% complete in the redshift range 0.5 < z < 0.8. The luminosity and mass completeness levels of the zCOSMOS-bright sample of galaxies is also discussed

Mass and environment as drivers of galaxy evolution in SDSS and zCOSMOS and the origin of the Schechter function

We explore the inter-relationships between mass, star-formation rate and environment in the SDSS, zCOSMOS and other surveys. The differential effects of mass and environment are completely separable to z ~ 1, indicating that two distinct processes are operating, "mass-quenching" and "environment-quenching". Environment-quenching, at fixed over-density, evidently does not change with epoch to z ~ 1, suggesting that it occurs as large-scale structure develops in the Universe. The observed constancy of the mass-function shape for star-forming galaxies, demands that the mass-quenching of galaxies around and above M*, must be proportional to their star-formation rates at all z < 2. We postulate that this simple mass-quenching law also holds over a much broader range of stellar mass and epoch. These two simple quenching processes, plus some additional quenching due to merging, then naturally produce (a) a quasi-static Schechter mass function for star-forming galaxies with a value of M* that is set by the proportionality between the star-formation and mass-quenching rates, (b) a double Schechter function for passive galaxies with two components: the dominant one is produced by mass-quenching and has exactly the same M* as the star-forming galaxies but an alpha shallower by +1, while the other is produced by environment effects and has the same M* and alpha as the star-forming galaxies, and is larger in high density environments. Subsequent merging of quenched galaxies modifies these predictions somewhat in the denser environments, slightly increasing M* and making alpha more negative. All of these detailed quantitative relationships between the Schechter parameters are indeed seen in the SDSS, lending strong support to our simple empirically-based model. The model naturally produces for passive galaxies the "anti-hierarchical" run of mean ages and alpha-element abundances with mass.Comment: 66 pages, 19 figures, 1 movie, accepted for publication in ApJ. The movie is also available at http://www.exp-astro.phys.ethz.ch/zCOSMOS/MF_simulation_d1_d4.mo

Derivation of the Green's function of the linear transport equation from the discrete-ordinate solution

A new, simple way to calculate the Green's function of the linear transport equation in a homogeneous, infinite medium is presented. The solution resorts to the corresponding Green's function for the discrete-ordinate method, which is readily obtainable, by using a suitable procedure to calculate the limit when the number of discrete directions tends to infinity

A∞ and AN formulations of the linear transport equation in heterogeneous media

The aim of the paper is to provide a contribution for the extension to heterogeneous media of the A1 and AN formulations for the linear transport equation. A new approach is proposed, in which the exponential of the optical length is decomposed in a sum of pure exponential terms, as in a homogeneous medium; in this way, a set of coupled diffusion-like equations is obtained. Different approximations are presented and their validity is discussed

Study on the extension of AN and SPN methods to the analysis of heterogeneous media

The AN and SPN methods to solve the linear transport equation are rigorously valid for a finite, homoge- neous medium or for heterogeneous, one-dimensional problems. In the present work, two distinct cases are considered, each of them close to one of these situations, and it is shown that the correct equations that take into account for the heterogeneity and the multidimensionality can be obtained by adding suitable extra terms to the model