1,464 research outputs found
Wigner molecules in polygonal quantum dots: A density functional study
We investigate the properties of many-electron systems in two-dimensional
polygonal (triangle, square, pentagon, hexagon) potential wells by using the
density functional theory. The development of the ground state electronic
structure as a function of the dot size is of particular interest. First we
show that in the case of two electrons, the Wigner molecule formation agrees
with the previous exact diagonalization studies. Then we present in detail how
the spin symmetry breaks in polygonal geometries as the spin density functional
theory is applied. In several cases with more than two electrons, we find a
transition to the crystallized state, yielding coincidence with the number of
density maxima and the electron number. We show that this transition density,
which agrees reasonably well with previous estimations, is rather insensitive
to both the shape of the dot and the electron number.Comment: 8 pages, 11 figure
Cosmological Solutions in Macroscopic Gravity
In the macroscopic gravity approach to the averaging problem in cosmology,
the Einstein field equations on cosmological scales are modified by appropriate
gravitational correlation terms. We present exact cosmological solutions to the
equations of macroscopic gravity for a spatially homogeneous and isotropic
macroscopic space-time and find that the correlation tensor is of the form of a
spatial curvature term. We briefly discuss the physical consequences of these
results.Comment: 5 page
Light-cone averaging in cosmology: formalism and applications
We present a general gauge invariant formalism for defining cosmological
averages that are relevant for observations based on light-like signals. Such
averages involve either null hypersurfaces corresponding to a family of past
light-cones or compact surfaces given by their intersection with timelike
hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of
these light-cone averages are given. After introducing some adapted "geodesic
light-cone" coordinates, we give explicit expressions for averaging the
redshift to luminosity-distance relation and the so-called "redshift drift" in
a generic inhomogeneous Universe.Comment: 20 pages, 2 figures. Comments and references added, typos corrected.
Version accepted for publication in JCA
Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging
Using a recently proposed gauge invariant formulation of light-cone
averaging, together with adapted "geodesic light-cone" coordinates, we show how
an "induced backreaction" effect emerges, in general, from correlated
fluctuations in the luminosity distance and covariant integration measure.
Considering a realistic stochastic spectrum of inhomogeneities of primordial
(inflationary) origin we find that both the induced backreaction on the
luminosity-redshift relation and the dispersion are larger than naively
expected. On the other hand the former, at least to leading order and in the
linear perturbative regime, cannot account by itself for the observed effects
of dark energy at large-redshifts. A full second-order calculation, or even
better a reliable estimate of contributions from the non-linear regime, appears
to be necessary before firm conclusions on the correct interpretation of the
data can be drawn.Comment: 22 pages, 4 figures. Comments and references added, Fig. 1 modified.
Version accepted for publication in JCA
Gauges and Cosmological Backreaction
We present a formalism for spatial averaging in cosmology applicable to
general spacetimes and coordinates, and allowing the easy incorporation of a
wide variety of matter sources. We apply this formalism to a
Friedmann-LeMaitre-Robertson-Walker universe perturbed to second-order and
present the corrections to the background in an unfixed gauge. We then present
the corrections that arise in uniform curvature and conformal Newtonian gauges.Comment: 13 pages. Updated: reference added, typos corrected, exposition
clarified. Version 3: Replaced with version published by JCA
Light Propagation and Large-Scale Inhomogeneities
We consider the effect on the propagation of light of inhomogeneities with
sizes of order 10 Mpc or larger. The Universe is approximated through a
variation of the Swiss-cheese model. The spherical inhomogeneities are
void-like, with central underdensities surrounded by compensating overdense
shells. We study the propagation of light in this background, assuming that the
source and the observer occupy random positions, so that each beam travels
through several inhomogeneities at random angles. The distribution of
luminosity distances for sources with the same redshift is asymmetric, with a
peak at a value larger than the average one. The width of the distribution and
the location of the maximum increase with increasing redshift and length scale
of the inhomogeneities. We compute the induced dispersion and bias on
cosmological parameters derived from the supernova data. They are too small to
explain the perceived acceleration without dark energy, even when the length
scale of the inhomogeneities is comparable to the horizon distance. Moreover,
the dispersion and bias induced by gravitational lensing at the scales of
galaxies or clusters of galaxies are larger by at least an order of magnitude.Comment: 27 pages, 9 figures, revised version to appear in JCAP, analytical
estimate included, typos correcte
Averaging Robertson-Walker Cosmologies
The cosmological backreaction arises when one directly averages the Einstein
equations to recover an effective Robertson-Walker cosmology, rather than
assuming a background a priori. While usually discussed in the context of dark
energy, strictly speaking any cosmological model should be recovered from such
a procedure. We apply the Buchert averaging formalism to linear
Robertson-Walker universes containing matter, radiation and dark energy and
evaluate numerically the discrepancies between the assumed and the averaged
behaviour, finding the largest deviations for an Einstein-de Sitter universe,
increasing rapidly with Hubble rate to a 0.01% effect for h=0.701. For the LCDM
concordance model, the backreaction is of the order of Omega_eff~4x10^-6, with
those for dark energy models being within a factor of two or three. The impacts
at recombination are of the order of 10^-8 and those in deep radiation
domination asymptote to a constant value. While the effective equations of
state of the backreactions in Einstein-de Sitter, concordance and quintessence
models are generally dust-like, a backreaction with an equation of state
w_eff<-1/3 can be found for strongly phantom models.Comment: 18 pages, 11 figures, ReVTeX. Updated to version accepted by JCA
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