1,731 research outputs found
Penrose Quantum Antiferromagnet
The Penrose tiling is a perfectly ordered two dimensional structure with
fivefold symmetry and scale invariance under site decimation. Quantum spin
models on such a system can be expected to differ significantly from more
conventional structures as a result of its special symmetries. In one
dimension, for example, aperiodicity can result in distinctive quantum
entanglement properties. In this work, we study ground state properties of the
spin-1/2 Heisenberg antiferromagnet on the Penrose tiling, a model that could
also be pertinent for certain three dimensional antiferromagnetic
quasicrystals. We show, using spin wave theory and quantum Monte Carlo
simulation, that the local staggered magnetizations strongly depend on the
local coordination number z and are minimized on some sites of five-fold
symmetry. We present a simple explanation for this behavior in terms of
Heisenberg stars. Finally we show how best to represent this complex
inhomogeneous ground state, using the "perpendicular space" representation of
the tiling.Comment: 4 pages, 5 figure
Dynamical vacuum energy, holographic quintom, and the reconstruction of scalar-field dark energy
When taking the holographic principle into account, the vacuum energy will
acquire dynamical property that its equation of state is evolving. The current
available observational data imply that the holographic vacuum energy behaves
as quintom-type dark energy. We adopt the viewpoint of that the scalar field
models of dark energy are effective theories of an underlying theory of dark
energy. If we regard the scalar field model as an effective description of such
a holographic vacuum theory, we should be capable of using the scalar field
model to mimic the evolving behavior of the dynamical vacuum energy and
reconstructing this scalar field model according to the fits of the
observational dataset. We find the generalized ghost condensate model is a good
choice for depicting the holographic vacuum energy since it can easily realize
the quintom behavior. We thus reconstruct the function of the
generalized ghost condensate model using the best-fit results of the
observational data.Comment: 13 pages, 3 figures; references updated, accepted for publication in
Phys. Rev.
Coupled quintessence and curvature-assisted acceleration
Spatially homogeneous models with a scalar field non-minimally coupled to the
space-time curvature or to the ordinary matter content are analysed with
respect to late-time asymptotic behaviour, in particular to accelerated
expansion and isotropization. It is found that a direct coupling to the
curvature leads to asymptotic de Sitter expansion in arbitrary exponential
potentials, thus yielding a positive cosmological constant although none is
apparent in the potential. This holds true regardless of the steepness of the
potential or the smallness of the coupling constant. For matter-coupled scalar
fields, the asymptotics are obtained for a large class of positive potentials,
generalizing the well-known cosmic no-hair theorems for minimal coupling. In
this case it is observed that the direct coupling to matter does not impact the
late-time dynamics essentially.Comment: 17 pages, no figures. v2: typos correcte
Inflationary spacetimes are not past-complete
Many inflating spacetimes are likely to violate the weak energy condition, a
key assumption of singularity theorems. Here we offer a simple kinematical
argument, requiring no energy condition, that a cosmological model which is
inflating -- or just expanding sufficiently fast -- must be incomplete in null
and timelike past directions. Specifically, we obtain a bound on the integral
of the Hubble parameter over a past-directed timelike or null geodesic. Thus
inflationary models require physics other than inflation to describe the past
boundary of the inflating region of spacetime.Comment: We improve the basic argument to apply to a wider class of
spacetimes, use a better title and add a discussion of cyclic models. 4
pages, 1 figure, RevTe
Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs
Computing reachability probabilities is a fundamental problem in the analysis
of probabilistic programs. This paper aims at a comprehensive and comparative
account on various martingale-based methods for over- and under-approximating
reachability probabilities. Based on the existing works that stretch across
different communities (formal verification, control theory, etc.), we offer a
unifying account. In particular, we emphasize the role of order-theoretic fixed
points---a classic topic in computer science---in the analysis of probabilistic
programs. This leads us to two new martingale-based techniques, too. We give
rigorous proofs for their soundness and completeness. We also make an
experimental comparison using our implementation of template-based synthesis
algorithms for those martingales
Cosmological scaling solutions of minimally coupled scalar fields in three dimensions
We examine Friedmann-Robertson-Walker models in three spacetime dimensions.
The matter content of the models is composed of a perfect fluid, with a
-law equation of state, and a homogeneous scalar field minimally
coupled to gravity with a self-interacting potential whose energy density
red-shifts as , where a denotes the scale factor. Cosmological
solutions are presented for different range of values of and .
The potential required to agree with the above red-shift for the scalar field
energy density is also calculated.Comment: LaTeX2e, 11 pages, 4 figures. To be published in Classical and
Quantum Gravit
Reconstructing a String-Inspired Non-minimally Coupled Quintom Model
Motivated by the recent work of Zhang and Chen \cite{bin}, we generalize
their work to the non-minimally coupled case. We consider a quintom model of
dark energy with a single scalar field given by a Lagrangian which inspired
by tachyonic Lagrangian in string theory. We consider non-minimal coupling of
tachyon field to the scalar curvature, then we reconstruct this model in the
light of three forms of parametrization for dynamical dark energy.Comment: 12 pages, 5 figure
Can black holes be torn up by phantom dark energy in cyclic cosmology?
Infinitely cyclic cosmology is often frustrated by the black hole problem. It
has been speculated that this obstacle in cyclic cosmology can be removed by
taking into account a peculiar cyclic model derived from loop quantum cosmology
or the braneworld scenario, in which phantom dark energy plays a crucial role.
In this peculiar cyclic model, the mechanism of solving the black hole problem
is through tearing up black holes by phantom. However, using the theory of
fluid accretion onto black holes, we show in this paper that there exists
another possibility: that black holes cannot be torn up by phantom in this
cyclic model. We discussed this possibility and showed that the masses of black
holes might first decrease and then increase, through phantom accretion onto
black holes in the expanding stage of the cyclic universe.Comment: 6 pages, 2 figures; discussions adde
Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals
The quasi-unit cell picture describes the atomic structure of quasicrystals
in terms of a single, repeating cluster which overlaps neighbors according to
specific overlap rules. In this paper, we discuss the precise relationship
between a general atomic decoration in the quasi-unit cell picture atomic
decorations in the Penrose tiling and in related tiling pictures. Using these
relations, we obtain a simple, practical method for determining the density,
stoichiometry and symmetry of a quasicrystal based on the atomic decoration of
the quasi-unit cell taking proper account of the sharing of atoms between
clusters.Comment: 14 pages, 8 figure
Quintessence and cosmic acceleration
A cosmological model with perfect fluid and self-interacting quintessence
field is considered in the framework of the spatially flat
Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical
quantities depend on the volume scale factor of the Universe, the general
solution of the gravitational field equations can be expressed in an exact
parametric form. The quintessence field is a free parameter. With an
appropriate choice of the scalar field a class of exact solutions is obtained,
with an exponential type scalar field potential fixed via the gravitational
field equations. The general physical behavior of the model is consistent with
the recent cosmological scenario favored by supernova Type Ia observations,
indicating an accelerated expansion of the Universe.Comment: 6 pages, 3 figures, to appear in Int. J. Mod. Phys.
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