448 research outputs found
Distinguishing Marks of Simply-connected Universes
A statistical quantity suitable for distinguishing simply-connected
Robertson-Walker (RW) universes is introduced, and its explicit expressions for
the three possible classes of simply-connected RW universes with an uniform
distribution of matter are determined. Graphs of the distinguishing mark for
each class of RW universes are presented and analyzed.There sprout from our
results an improvement on the procedure to extract the topological signature of
multiply-connected RW universes, and a refined understanding of that
topological signature of these universes studied in previous works.Comment: 13 pages, 4 figures, LaTeX2e. To appear in Int. J. Mod. Phys. D
(2000
The exit-time problem for a Markov jump process
The purpose of this paper is to consider the exit-time problem for a
finite-range Markov jump process, i.e, the distance the particle can jump is
bounded independent of its location. Such jump diffusions are expedient models
for anomalous transport exhibiting super-diffusion or nonstandard normal
diffusion. We refer to the associated deterministic equation as a
volume-constrained nonlocal diffusion equation. The volume constraint is the
nonlocal analogue of a boundary condition necessary to demonstrate that the
nonlocal diffusion equation is well-posed and is consistent with the jump
process. A critical aspect of the analysis is a variational formulation and a
recently developed nonlocal vector calculus. This calculus allows us to pose
nonlocal backward and forward Kolmogorov equations, the former equation
granting the various moments of the exit-time distribution.Comment: 15 pages, 7 figure
Can We See the Shape of the Universe?
This is a written version of a talk given at the Fifth Friedmann Seminar on
recent work in Observational Cosmic Topology done in partial collaboration with
Armando Bernui. We address three relevant questions related to the search for
the size and shape of our Universe: (i) How do the actual observation of
multiple images of certain cosmic objects, e.g. galaxy clusters, constrain the
possible models for the shape of our Universe?, (ii) What kind of predictions
can be done once a pair of cosmic objects have been identified to be
topological images related by a translation?, and (iii) Is it possible to
determine if two regions of space are topologically identified, even when
distortions on the distributions of cosmic sources due to observational
limitations are not negligible? We give examples answering the first two
questions using the suggestion of Roukema and Edge that the clusters RXJ
1347.5-1145 and CL 09104+4109 might be topological images of the Coma cluster.
For the third question, we suggest a method based on the analysis of PSH's
noise correlations which seems to give a positive answer.Comment: 6 pages, latex2e, contribution to the 5th Alexander Friedmann Seminar
on Gravitation and Cosmology, to appear in Int. J. Mod. Phys. A (2002).
Macros: ws-ijmpa.cl
Wave function statistics at the symplectic 2D Anderson transition: bulk properties
The wavefunction statistics at the Anderson transition in a 2d disordered
electron gas with spin-orbit coupling is studied numerically. In addition to
highly accurate exponents (), we report three qualitative results: (i) the anomalous dimensions are
invariant under which is in agreement with a recent analytical
prediction and supports the universality hypothesis. (ii) The multifractal
spectrum is not parabolic and therefore differs from behavior suspected, e.g.,
for (integer) quantum Hall transitions in a fundamental way. (iii) The critical
fixed point satisfies conformal invariance.Comment: 4 pages, 3 figure
Abundance of Ground States with Positive Parity
We investigate analytically and numerically a random-matrix model for m
fermions occupying l1 single-particle states with positive parity and l2
single-particle states with negative parity and interacting through random
two-body forces that conserve parity. The single-particle states are completely
degenerate and carry no further quantum numbers. We compare spectra of
many-body states with positive and with negative parity. We show that in the
dilute limit, ground states with positive and with negative parity occur with
equal probability. Differences in the ground-state probabilities are, thus, a
finite-size effect and are mainly due to different dimensions of the Hilbert
spaces of either parity.Comment: 12 pages, 1 figur
GRBs and the 511 keV emission of the Galactic bulge
We consider the phenomenology of the 511 keV emission in the Galactic bulge,
as recently observed by INTEGRAL, and propose a model is which the positrons
are produced by gamma-ray bursts (GRB) associated with mini starbursts in the
central molecular zone (CMZ). We show that the positrons can easily diffuse
across the bulge on timescales of about 10^7 yr, and that their injection rate
by GRBs is compatible with the observed fluxes if the mean time between two
GRBs in the bulge is about 8 10^4 yr x E_GRB_51. We also explain the low
disk-to-bulge emission ratio by noting that positrons from GRBs in the Galactic
disk should annihilate on timescales of < 10^4 yr in the dense shell of the
underlying supernova remnant, after the radiative transition, while the
remnants of GRBs occurring in the hot, low-density medium produced by recurrent
starbursts in the CMZ become subsonic before they can form a radiative shell,
allowing the positrons to escape and fill the whole Galactic bulge. If the mean
time between GRBs is smaller than 10^4 E_51 yr, INTEGRAL should be able to
detect the (localized) 511 keV emission associated with one or a few GRB
explosions in the disk.Comment: 6 pages, accepted for publication in A&
Spikes in Cosmic Crystallography
If the universe is multiply connected and small the sky shows multiple images
of cosmic objects, correlated by the covering group of the 3-manifold used to
model it. These correlations were originally thought to manifest as spikes in
pair separation histograms (PSH) built from suitable catalogues. Using
probability theory we derive an expression for the expected pair separation
histogram (EPSH) in a rather general topological-geometrical-observational
setting. As a major consequence we show that the spikes of topological origin
in PSH's are due to translations, whereas other isometries manifest as tiny
deformations of the PSH corresponding to the simply connected case. This result
holds for all Robertson-Walker spacetimes and gives rise to two basic
corollaries: (i) that PSH's of Euclidean manifolds that have the same
translations in their covering groups exhibit identical spike spectra of
topological origin, making clear that even if the universe is flat the
topological spikes alone are not sufficient for determining its topology; and
(ii) that PSH's of hyperbolic 3-manifolds exhibit no spikes of topological
origin. These corollaries ensure that cosmic crystallography, as originally
formulated, is not a conclusive method for unveiling the shape of the universe.
We also present a method that reduces the statistical fluctuations in PSH's
built from simulated catalogues.Comment: 25 pages, LaTeX2e. References updated. To appear in Int. J. Mod.
Phys. D (2002) in the present for
- âŠ