3,868 research outputs found
Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics
Finding the eigenvalues of a Sturm-Liouville problem can be a computationally
challenging task, especially when a large set of eigenvalues is computed, or
just when particularly large eigenvalues are sought. This is a consequence of
the highly oscillatory behaviour of the solutions corresponding to high
eigenvalues, which forces a naive integrator to take increasingly smaller
steps. We will discuss some techniques that yield uniform approximation over
the whole eigenvalue spectrum and can take large steps even for high
eigenvalues. In particular, we will focus on methods based on coefficient
approximation which replace the coefficient functions of the Sturm-Liouville
problem by simpler approximations and then solve the approximating problem. The
use of (modified) Magnus or Neumann integrators allows to extend the
coefficient approximation idea to higher order methods
Average output entropy for quantum channels
We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of
quantum channels. This quantity gives information about the average noisiness
of the channel output arising from a typical, highly entangled input state in
the limit of infinite dimensions. We find a closed expression for
\beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We
find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking
channels, and also for the qubit depolarizing channel as a
function of the parameter . We prove equality of the two quantities in
some cases, in particular we conclude that for both are
non-analytic functions of the variable .Comment: 32 pages, several plots and figures; positivity condition added for
Theorem on entanglement breaking channels; new result for entrywise positive
channel
The SDSS Damped Lya Survey: Data Release 1
We present the results from an automated search for damped Lya (DLA) systems
in the quasar spectra of Data Release 1 from the Sloan Digital Sky Survey
(SDSS-DR1). At z~2.5, this homogeneous dataset has greater statistical
significance than the previous two decades of research. We derive a statistical
sample of 71 damped Lya systems (>50 previously unpublished) at z>2.1 and
measure HI column densities directly from the SDSS spectra. The number of DLA
systems per unit redshift is consistent with previous measurements and we
expect our survey has >95% completeness. We examine the cosmological baryonic
mass density of neutral gas Omega_g inferred from the damped Lya systems from
the SDSS-DR1 survey and a combined sample drawn from the literature. Contrary
to previous results, the Omega_g values do not require a significant correction
from Lyman limit systems at any redshift. We also find that the Omega_g values
for the SDSS-DR1 sample do not decline at high redshift and the combined sample
shows a (statistically insignificant) decrease only at z>4. Future data
releases from SDSS will provide the definitive survey of DLA systems at z~2.5
and will significantly reduce the uncertainty in Omega_g at higher redshift.Comment: 12 pages, includes color figures. Accepted to PASP, April 20 200
Silicon nanoparticles and interstellar extinction
To examine a recently proposed hypothesis that silicon nanoparticles are the
source of extended red emission (ERE) in the interstellar medium, we performed
a detailed modeling of the mean Galactic extinction in the presence of silicon
nanoparticles. For this goal we used the appropriate optical constants of
nanosized Si, essentially different from those of bulk Si due to quantum
confinement. It was found that a dust mixture of silicon nanoparticles, bare
graphite grains, silicate core-organic refractory mantle grains and three-layer
silicate-water ice-organic refractory grains works well in explaining the
extinction and, in addition, results in the acceptable fractions of UV/visible
photons absorbed by silicon nanoparticles: 0.071-0.081. Since these fractions
barely agree with the fraction of UV/visible photons needed to excite the
observed ERE, we conclude that the intrinsic photon conversion efficiency of
the photoluminescence by silicon nanoparticles must be near 100%, if they are
the source of the ERE.Comment: Latex2e, uses emulateapj.sty (included), multicol.sty, epsf.sty, 6
pages, 3 figures (8 Postscript files), accepted for publication in ApJ
Letters, complete Postscript file is also available at
http://physics.technion.ac.il/~zubko/eb.html#SNP
The Meinunger "Nicht Rote" Objects
Four high-latitude slow variable stars have been noted by Meinunger (1972) as
"nicht rote" ("not red") objects and thus curious. We have previously reported
(Margon & Deutsch 1997) that one of these objects, CC Boo, is in fact a QSO.
Here we present observations demonstrating that the remaining three are also
highly variable active galactic nuclei. The most interesting object of the four
is perhaps S 10765 (= NGP9 F324-0276706), which proves to be a resolved galaxy
at z=0.063. Despite the rapid and large reported variability amplitude (~1.6
mag), the spectrum is that of a perfectly normal galaxy, with no emission lines
or evident nonthermal continuum. We also present new spectroscopic and
photometric observations for AR CVn, suggested by Meinunger to be an RR Lyrae
star despite its very faint magnitude (=19.4). The object is indeed one of
the most distant RR Lyrae stars known, at a galactocentric distance of ~40 kpc.Comment: Accepted for publication in Publications of the Astronomical Society
of the Pacific, Volume 111, January 1999; 14 pages including 4 figures and 1
tabl
Eigenvalue variance bounds for Wigner and covariance random matrices
This work is concerned with finite range bounds on the variance of individual
eigenvalues of Wigner random matrices, in the bulk and at the edge of the
spectrum, as well as for some intermediate eigenvalues. Relying on the GUE
example, which needs to be investigated first, the main bounds are extended to
families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment
Theorem and recent localization results by Erd\"os, Yau and Yin. The case of
real Wigner matrices is obtained from interlacing formulas. As an application,
bounds on the expected 2-Wasserstein distance between the empirical spectral
measure and the semicircle law are derived. Similar results are available for
random covariance matrices
On Hastings' counterexamples to the minimum output entropy additivity conjecture
Hastings recently reported a randomized construction of channels violating
the minimum output entropy additivity conjecture. Here we revisit his argument,
presenting a simplified proof. In particular, we do not resort to the exact
probability distribution of the Schmidt coefficients of a random bipartite pure
state, as in the original proof, but rather derive the necessary large
deviation bounds by a concentration of measure argument. Furthermore, we prove
non-additivity for the overwhelming majority of channels consisting of a Haar
random isometry followed by partial trace over the environment, for an
environment dimension much bigger than the output dimension. This makes
Hastings' original reasoning clearer and extends the class of channels for
which additivity can be shown to be violated.Comment: 17 pages + 1 lin
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