10,465 research outputs found
Measuring the transition to homogeneity with photometric redshift surveys
We study the possibility of detecting the transition to homogeneity using
photometric redshift catalogs. Our method is based on measuring the fractality
of the projected galaxy distribution, using angular distances, and relies only
on observable quantites. It thus provides a way to test the Cosmological
Principle in a model-independent unbiased way. We have tested our method on
different synthetic inhomogeneous catalogs, and shown that it is capable of
discriminating some fractal models with relatively large fractal dimensions, in
spite of the loss of information due to the radial projection. We have also
studied the influence of the redshift bin width, photometric redshift errors,
bias, non-linear clustering, and surveyed area, on the angular homogeneity
index H2 ({\theta}) in a {\Lambda}CDM cosmology. The level to which an upcoming
galaxy survey will be able to constrain the transition to homogeneity will
depend mainly on the total surveyed area and the compactness of the surveyed
region. In particular, a Dark Energy Survey (DES)-like survey should be able to
easily discriminate certain fractal models with fractal dimensions as large as
D2 = 2.95. We believe that this method will have relevant applications for
upcoming large photometric redshift surveys, such as DES or the Large Synoptic
Survey Telescope (LSST).Comment: 14 pages, 14 figure
On the generalized Feng-Rao numbers of numerical semigroups generated by intervals
We give some general results concerning the computation of the generalized
Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup
generated by an interval, a formula for the Feng-Rao number is
obtained.Comment: 23 pages, 6 figure
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
Isocausal spacetimes may have different causal boundaries
We construct an example which shows that two isocausal spacetimes, in the
sense introduced by Garc\'ia-Parrado and Senovilla, may have c-boundaries which
are not equal (more precisely, not equivalent, as no bijection between the
completions can preserve all the binary relations induced by causality). This
example also suggests that isocausality can be useful for the understanding and
computation of the c-boundary.Comment: Minor modifications, including the title, which matches now with the
published version. 12 pages, 3 figure
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