23,798 research outputs found
Occurrence of normal and anomalous diffusion in polygonal billiard channels
From extensive numerical simulations, we find that periodic polygonal
billiard channels with angles which are irrational multiples of pi generically
exhibit normal diffusion (linear growth of the mean squared displacement) when
they have a finite horizon, i.e. when no particle can travel arbitrarily far
without colliding. For the infinite horizon case we present numerical tests
showing that the mean squared displacement instead grows asymptotically as t
log t. When the unit cell contains accessible parallel scatterers, however, we
always find anomalous super-diffusion, i.e. power-law growth with an exponent
larger than 1. This behavior cannot be accounted for quantitatively by a simple
continuous-time random walk model. Instead, we argue that anomalous diffusion
correlates with the existence of families of propagating periodic orbits.
Finally we show that when a configuration with parallel scatterers is
approached there is a crossover from normal to anomalous diffusion, with the
diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures,
additional comments. Some higher quality figures available at
http://www.fis.unam.mx/~dsander
The Topology of Branching Universes
The purpose of this paper is to survey the possible topologies of branching
space-times, and, in particular, to refute the popular notion in the literature
that a branching space-time requires a non-Hausdorff topology
SU(5) Heterotic Standard Model Bundles
We construct a class of stable SU(5) bundles on an elliptically fibered
Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass
fibration, which admits a free involution. The bundles are invariant under the
involution, solve the topological constraint imposed by the heterotic anomaly
equation and give three generations of Standard Model fermions after symmetry
breaking by Wilson lines of the intermediate SU(5) GUT-group to the Standard
Model gauge group. Among the solutions we find some which can be perturbed to
solutions of the Strominger system. Thus these solutions provide a step toward
the construction of phenomenologically realistic heterotic flux
compactifications via non-Kahler deformations of Calabi-Yau geometries with
bundles. This particular class of solutions involves a rank two hidden sector
bundle and does not require background fivebranes for anomaly cancellation.Comment: 17 page
Optical properties of the vibrations in charged C molecules
The transition strengths for the four infrared-active vibrations of charged
C molecules are evaluated in self-consistent density functional theory
using the local density approximation. The oscillator strengths for the second
and fourth modes are strongly enhanced relative to the neutral C
molecule, in good agreement with the experimental observation of ``giant
resonances'' for those two modes. Previous theory, based on a ``charged
phonon'' model, predicted a quadratic dependence of the oscillator strength on
doping, but this is not borne out in our calculations.Comment: 10 pages, RevTeX3.
Heterotic Standard Model Moduli
In previous papers, we introduced a heterotic standard model and discussed
its basic properties. The Calabi-Yau threefold has, generically, three Kahler
and three complex structure moduli. The observable sector of this vacuum has
the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate
fields. The hidden sector has no charged matter in the strongly coupled string
and only minimal matter for weak coupling. Additionally, the spectrum of both
sectors will contain vector bundle moduli. The exact number of such moduli was
conjectured to be small, but was not explicitly computed. In this paper, we
rectify this and present a formalism for computing the number of vector bundle
moduli. Using this formalism, the number of moduli in both the observable and
strongly coupled hidden sectors is explicitly calculated.Comment: 28 pages, LaTeX; v2: typos corrected, references added; v3:
clarifications, references adde
Searching for periodic sources with LIGO. II: Hierarchical searches
The detection of quasi-periodic sources of gravitational waves requires the
accumulation of signal-to-noise over long observation times. If not removed,
Earth-motion induced Doppler modulations, and intrinsic variations of the
gravitational-wave frequency make the signals impossible to detect. These
effects can be corrected (removed) using a parameterized model for the
frequency evolution. We compute the number of independent corrections
required for incoherent search strategies which use stacked
power spectra---a demodulated time series is divided into segments of
length , each segment is FFTed, the power is computed, and the
spectra are summed up. We estimate that the sensitivity of an all-sky search
that uses incoherent stacks is a factor of 2--4 better than would be achieved
using coherent Fourier transforms; incoherent methods are computationally
efficient at exploring large parameter spaces. A two-stage hierarchical search
which yields another 20--60% improvement in sensitivity in all-sky searches for
old (>= 1000 yr) slow (= 40 yr) fast (<=
1000 Hz) pulsars. Assuming 10^{12} flops of effective computing power for data
analysis, enhanced LIGO interferometers should be sensitive to: (i) Galactic
core pulsars with gravitational ellipticities of \epsilon\agt5\times 10^{-6}
at 200 Hz, (ii) Gravitational waves emitted by the unstable r-modes of newborn
neutron stars out to distances of ~8 Mpc, and (iii) neutron stars in LMXB's
with x-ray fluxes which exceed . Moreover,
gravitational waves from the neutron star in Sco X-1 should be detectable is
the interferometer is operated in a signal-recycled, narrow-band configuration.Comment: 22 Pages, 13 Figure
Topology Change and Causal Continuity
The result that, for a scalar quantum field propagating on a ``trousers''
topology in 1+1 dimensions, the crotch singularity is a source for an infinite
burst of energy has been used to argue against the occurrence of topology
change in quantum gravity. We draw attention to a conjecture due to Sorkin that
it may be the particular type of topology change involved in the trousers
transition that is problematic and that other topology changes may not cause
the same difficulties. The conjecture links the singular behaviour to the
existence of ``causal discontinuities'' in the spacetime and relies on a
classification of topology changes using Morse theory. We investigate various
topology changing transitions, including the pair production of black holes and
of topological geons, in the light of these ideas.Comment: Latex, 28 pages, 10 figures, small changes in text (one figure
removed), conclusions remain unchanged. Accepted for publication in Physical
Review
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