406 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
Interacting holographic tachyon model of dark energy
We propose a holographic tachyon model of dark energy with interaction
between the components of the dark sector. The correspondence between the
tachyon field and the holographic dark energy densities allows the
reconstruction of the potential and the dynamics of the tachyon scalar field in
a flat Friedmann-Robertson-Walker universe. We show that this model can
describe the observed accelerated expansion of our universe with a parameter
space given by the most recent observational results.Comment: 7 pages, 8 figures, accepted for publication in IJMP
Strong Brane Gravity and the Radion at Low Energies
For the 2-brane Randall-Sundrum model, we calculate the bulk geometry for
strong gravity, in the low matter density regime, for slowly varying matter
sources. This is relevant for astrophysical or cosmological applications. The
warped compactification means the radion can not be written as a homogeneous
mode in the orbifold coordinate, and we introduce it by extending the
coordinate patch approach of the linear theory to the non-linear case. The
negative tension brane is taken to be in vacuum. For conformally invariant
matter on the positive tension brane, we solve the bulk geometry as a
derivative expansion, formally summing the `Kaluza-Klein' contributions to all
orders. For general matter we compute the Einstein equations to leading order,
finding a scalar-tensor theory with ,
and geometrically interpret the radion. We comment that this radion scalar may
become large in the context of strong gravity with low density matter.
Equations of state allowing to be negative, can exhibit behavior
where the matter decreases the distance between the 2 branes, which we
illustrate numerically for static star solutions using an incompressible fluid.
For increasing stellar density, the branes become close before the upper mass
limit, but after violation of the dominant energy condition. This raises the
interesting question of whether astrophysically reasonable matter, and initial
data, could cause branes to collide at low energy, such as in dynamical
collapse.Comment: 24 pages, 3 figure
Non-spherical shapes of capsules within a fourth-order curvature model
We minimize a discrete version of the fourth-order curvature based Landau
free energy by extending Brakke's Surface Evolver. This model predicts
spherical as well as non-spherical shapes with dimples, bumps and ridges to be
the energy minimizers. Our results suggest that the buckling and faceting
transitions, usually associated with crystalline matter, can also be an
intrinsic property of non-crystalline membranes.Comment: 6 pages, 4 figures (LaTeX macros EPJ), accepted for publication in
EPJ
Gravitational lensing as a contaminant of the gravity wave signal in CMB
Gravity waves (GW) in the early universe generate B-type polarization in the
cosmic microwave background (CMB), which can be used as a direct way to measure
the energy scale of inflation. Gravitational lensing contaminates the GW signal
by converting the dominant E polarization into B polarization. By
reconstructing the lensing potential from CMB itself one can decontaminate the
B mode induced by lensing. We present results of numerical simulations of B
mode delensing using quadratic and iterative maximum-likelihood lensing
reconstruction methods as a function of detector noise and beam. In our
simulations we find the quadratic method can reduce the lensing B noise power
by up to a factor of 7, close to the no noise limit. In contrast, the iterative
method shows significant improvements even at the lowest noise levels we
tested. We demonstrate explicitly that with this method at least a factor of 40
noise power reduction in lensing induced B power is possible, suggesting that
T/S=10^-6 may be achievable in the absence of sky cuts, foregrounds, and
instrumental systematics. While we do not find any fundamental lower limit due
to lensing, we find that for high-sensitivity detectors residual lensing noise
dominates over the detector noise.Comment: 6 pages, 2 figures, submitted to PR
Virus shapes and buckling transitions in spherical shells
We show that the icosahedral packings of protein capsomeres proposed by
Caspar and Klug for spherical viruses become unstable to faceting for
sufficiently large virus size, in analogy with the buckling instability of
disclinations in two-dimensional crystals. Our model, based on the nonlinear
physics of thin elastic shells, produces excellent one parameter fits in real
space to the full three-dimensional shape of large spherical viruses. The
faceted shape depends only on the dimensionless Foppl-von Karman number
\gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the
protein shell, \kappa is its bending rigidity and R is the mean virus radius.
The shape can be parameterized more quantitatively in terms of a spherical
harmonic expansion. We also investigate elastic shell theory for extremely
large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral
shapes of large vesicles studied with freeze fracture and electron microscopy.Comment: 11 pages, 12 figure
Spin waves and local magnetizations on the Penrose tiling
We consider a Heisenberg antiferromagnet on the Penrose tiling, a
quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin
wave energies and wavefunctions are studied in the linear spin wave
approximation. A linear dispersion law is found at low energies, as in other
bipartite antiferromagnets, with an effective spin wave velocity lower than in
the square lattice. Spatial properties of eigenmodes are characterized in
several different ways. At low energies, eigenstates are relatively extended,
and show multifractal scaling. At higher energies, states are more localized,
and, depending on the energy, confined to sites of a specified coordination
number. The ground state energy of this antiferromagnet, and local staggered
magnetizations are calculated. Perpendicular space projections are presented in
order to show the underlying simplicity of this "complex" ground state. A
simple analytical model, the two-tier Heisenberg star, is presented to explain
the staggered magnetization distribution in this antiferromagnetic system.Comment: 14 pages, 21 figure
Reconstructing generalized ghost condensate model with dynamical dark energy parametrizations and observational datasets
Observations of high-redshift supernovae indicate that the universe is
accelerating at the present stage, and we refer to the cause for this cosmic
acceleration as ``dark energy''. In particular, the analysis of current data of
type Ia supernovae (SNIa), cosmic large-scale structure (LSS), and the cosmic
microwave background (CMB) anisotropy implies that, with some possibility, the
equation-of-state parameter of dark energy may cross the cosmological-constant
boundary () during the recent evolution stage. The model of ``quintom''
has been proposed to describe this crossing behavior for dark energy. As
a single-real-scalar-field model of dark energy, the generalized ghost
condensate model provides us with a successful mechanism for realizing the
quintom-like behavior. In this paper, we reconstruct the generalized ghost
condensate model in the light of three forms of parametrization for dynamical
dark energy, with the best-fit results of up-to-date observational data.Comment: 8 pages, 3 figures; references added; accepted for publication in
Mod. Phys. Lett.
A Tracker Solution for a Holographic Dark Energy Model
We investigate a kind of holographic dark energy model with the future event
horizon the IR cutoff and the equation of state -1. In this model, the
constraint on the equation of state automatically specifies an interaction
between matter and dark energy. With this interaction included, an accelerating
expansion is obtained as well as the transition from deceleration to
acceleration. It is found that there exists a stable tracker solution for the
numerical parameter , and smaller than one will not lead to a physical
solution. This model provides another possible phenomenological framework to
alleviate the cosmological coincidence problem in the context of holographic
dark energy. Some properties of the evolution which are relevant to
cosmological parameters are also discussed.Comment: 10 pages, 3 figures; accepted for publication in Int.J.Mod.Phys.
Equation of State of Oscillating Brans-Dicke Scalar and Extra Dimensions
We consider a Brans-Dicke scalar field stabilized by a general power law
potential with power index at a finite equilibrium value. Redshifting
matter induces oscillations of the scalar field around its equilibrium due to
the scalar field coupling to the trace of the energy momentum tensor. If the
stabilizing potential is sufficiently steep these high frequency oscillations
are consistent with observational and experimental constraints for arbitrary
value of the Brans-Dicke parameter . We study analytically and
numerically the equation of state of these high frequency oscillations in terms
of the parameters and and find the corresponding evolution of the
universe scale factor. We find that the equation of state parameter can be
negative and less than -1 but it is not related to the evolution of the scale
factor in the usual way. Nevertheless, accelerating expansion is found for a
certain parameter range. Our analysis applies also to oscillations of the size
of extra dimensions (the radion field) around an equilibrium value. This
duality between self-coupled Brans-Dicke and radion dynamics is applicable for
where D is the number of extra dimensions.Comment: 10 two-column pages, RevTex4, 8 figures. Added clarifying
discussions, new references. Accepted in Phys. Rev. D (to appear
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