10,627 research outputs found
Lower bounds on the dilation of plane spanners
(I) We exhibit a set of 23 points in the plane that has dilation at least
, improving the previously best lower bound of for the
worst-case dilation of plane spanners.
(II) For every integer , there exists an -element point set
such that the degree 3 dilation of denoted by in the domain of plane geometric spanners. In the
same domain, we show that for every integer , there exists a an
-element point set such that the degree 4 dilation of denoted by
The
previous best lower bound of holds for any degree.
(III) For every integer , there exists an -element point set
such that the stretch factor of the greedy triangulation of is at least
.Comment: Revised definitions in the introduction; 23 pages, 15 figures; 2
table
Spin systems with dimerized ground states
In view of the numerous examples in the literature it is attempted to outline
a theory of Heisenberg spin systems possessing dimerized ground states (``DGS
systems") which comprises all known examples. Whereas classical DGS systems can
be completely characterized, it was only possible to provide necessary or
sufficient conditions for the quantum case. First, for all DGS systems the
interaction between the dimers must be balanced in a certain sense. Moreover,
one can identify four special classes of DGS systems: (i) Uniform pyramids,
(ii) systems close to isolated dimer systems, (iii) classical DGS systems, and
(iv), in the case of , systems of two dimers satisfying four
inequalities. Geometrically, the set of all DGS systems may be visualized as a
convex cone in the linear space of all exchange constants. Hence one can
generate new examples of DGS systems by positive linear combinations of
examples from the above four classes.Comment: With corrections of proposition 4 and other minor change
Stochastic background from extra-galactic double neutron stars
We present Monte Carlo simulations of the extra galactic population of
inspiralling double neutron stars, and estimate its contribution to the
astrophysical gravitational wave background, in the frequency range of ground
based interferometers, corresponding to the last thousand seconds before the
last stable orbit when more than 96 percent of the signal is released. We show
that sources at redshift z>0.5 contribute to a truly continuous background
which may be detected by correlating third generation interferometers.Comment: 13 pages, 7 figures - proceeding of a talk given at the 11th GWDAW,
to appear in CQ
Hawking Radiation and Unitary evolution
We find a family of exact solutions to the semi-classical equations
(including back-reaction) of two-dimensional dilaton gravity, describing
infalling null matter that becomes outgoing and returns to infinity without
forming a black hole. When a black hole almost forms, the radiation reaching
infinity in advance of the original outgoing null matter has the properties of
Hawking radiation. The radiation reaching infinity after the null matter
consists of a brief burst of negative energy that preserves unitarity and
transfers information faster than the theoretical bound for positive energy.Comment: LaTex file + uuencoded ps version including 4 figure
Aperture synthesis for gravitational-wave data analysis: Deterministic Sources
Gravitational wave detectors now under construction are sensitive to the
phase of the incident gravitational waves. Correspondingly, the signals from
the different detectors can be combined, in the analysis, to simulate a single
detector of greater amplitude and directional sensitivity: in short, aperture
synthesis. Here we consider the problem of aperture synthesis in the special
case of a search for a source whose waveform is known in detail: \textit{e.g.,}
compact binary inspiral. We derive the likelihood function for joint output of
several detectors as a function of the parameters that describe the signal and
find the optimal matched filter for the detection of the known signal. Our
results allow for the presence of noise that is correlated between the several
detectors. While their derivation is specialized to the case of Gaussian noise
we show that the results obtained are, in fact, appropriate in a well-defined,
information-theoretic sense even when the noise is non-Gaussian in character.
The analysis described here stands in distinction to ``coincidence
analyses'', wherein the data from each of several detectors is studied in
isolation to produce a list of candidate events, which are then compared to
search for coincidences that might indicate common origin in a gravitational
wave signal. We compare these two analyses --- optimal filtering and
coincidence --- in a series of numerical examples, showing that the optimal
filtering analysis always yields a greater detection efficiency for given false
alarm rate, even when the detector noise is strongly non-Gaussian.Comment: 39 pages, 4 figures, submitted to Phys. Rev.
Quantum spin models with exact dimer ground states
Inspired by the exact solution of the Majumdar-Ghosh model, a family of
one-dimensional, translationally invariant spin hamiltonians is constructed.
The exchange coupling in these models is antiferromagnetic, and decreases
linearly with the separation between the spins. The coupling becomes
identically zero beyond a certain distance. It is rigorously proved that the
dimer configuration is an exact, superstable ground state configuration of all
the members of the family on a periodic chain. The ground state is two-fold
degenerate, and there exists an energy gap above the ground state. The
Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just
the first member of the family.
The scheme of construction is generalized to two and three dimensions, and
illustrated with the help of some concrete examples. The first member in two
dimensions is the Shastry-Sutherland model. Many of these models have
exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.
Degradabilidade da matéria seca e parâmetros cinéticos da disgestão de cultivares de alfafa avaliados pelo método de produção de gás.
escanearTitulo origina
Near-extremal and extremal quantum-corrected two-dimensional charged black holes
We consider charged black holes within dilaton gravity with
exponential-linear dependence of action coefficients on dilaton and minimal
coupling to quantum scalar fields. This includes, in particular, CGHS and RST
black holes in the uncharged limit. For non-extremal configuration quantum
correction to the total mass, Hawking temperature, electric potential and
metric are found explicitly and shown to obey the first generalized law. We
also demonstrate that quantum-corrected extremal black holes in these theories
do exist and correspond to the classically forbidden region of parameters in
the sense that the total mass ( is a charge). We show that in
the limit (where is the Hawking temperature) the mass and
geometry of non-extremal configuration go smoothly to those of the extremal
one, except from the narrow near-horizon region. In the vicinity of the horizon
the quantum-corrected geometry (however small quantum the coupling parameter
would be) of a non-extremal configuration tends to not the
quantum-corrected extremal one but to the special branch of solutions with the
constant dilaton (2D analog of the Bertotti-Robinson metric) instead.
Meanwhile, if exactly, the near-extremal configuration tends to the
extremal one. We also consider the dilaton theory which corresponds classically
to the spherically-symmetrical reduction from 4D case and show that for the
quantum-corrected extremal black hole .Comment: 25 pages. Typos corrected. To appear in Class. Quant. Gra
Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
The Resonating Valence Bond (RVB) theory for two-dimensional quantum
antiferromagnets is shown to be the correct paradigm for large enough ``quantum
frustration''. This scenario, proposed long time ago but never confirmed by
microscopic calculations, is very strongly supported by a new type of
variational wave function, which is extremely close to the exact ground state
of the Heisenberg model for .
This wave function is proposed to represent the generic spin-half RVB ground
state in spin liquids.Comment: 4 Pages, 5 figures, accepted for publication in PR
Residual entropy and spin gap in a one-dimensional analog of the pyrochlore antiferromagnet
We show that the low-energy sector of the S=1/2, antiferromagnetic Heisenberg
model on a one-dimensional lattice of coupled tetrahedra consists of 2^N
replica of the spectrum of the dimerized Heisenberg chain, where N is the
number of tetrahedra.
This provides a proof of the following properties: i) there is a residual
ground-state entropy per spin equal to 2^{1/4}; ii) there is a singlet-triplet
gap as long as the coupling between the tetrahedra is smaller than the internal
one. These properties are compared to available results on the pyrochlore
lattice.Comment: 4 pages with 3 figure
- …