7,871 research outputs found
Value distribution of the eigenfunctions and spectral determinants of quantum star graphs
We compute the value distributions of the eigenfunctions and spectral
determinant of the Schrodinger operator on families of star graphs. The values
of the spectral determinant are shown to have a Cauchy distribution with
respect both to averages over bond lengths in the limit as the wavenumber tends
to infinity and to averages over wavenumber when the bond lengths are fixed and
not rationally related. This is in contrast to the spectral determinants of
random matrices, for which the logarithm is known to satisfy a Gaussian limit
distribution. The value distribution of the eigenfunctions also differs from
the corresponding random matrix result. We argue that the value distributions
of the spectral determinant and of the eigenfunctions should coincide with
those of Seba-type billiards.Comment: 32 pages, 9 figures. Final version incorporating referee's comments.
Typos corrected, appendix adde
Intermediate wave-function statistics
We calculate statistical properties of the eigenfunctions of two quantum
systems that exhibit intermediate spectral statistics: star graphs and Seba
billiards. First, we show that these eigenfunctions are not quantum ergodic,
and calculate the corresponding limit distribution. Second, we find that they
can be strongly scarred by short periodic orbits, and construct sequences of
states which have such a limit. Our results are illustrated by numerical
computations.Comment: 4 pages, 3 figures. Final versio
No quantum ergodicity for star graphs
We investigate statistical properties of the eigenfunctions of the
Schrodinger operator on families of star graphs with incommensurate bond
lengths. We show that these eigenfunctions are not quantum ergodic in the limit
as the number of bonds tends to infinity by finding an observable for which the
quantum matrix elements do not converge to the classical average. We further
show that for a given fixed graph there are subsequences of eigenfunctions
which localise on pairs of bonds. We describe how to construct such
subsequences explicitly. These constructions are analogous to scars on short
unstable periodic orbits.Comment: 26 pages, 5 figure
Complete bandgaps in one-dimensional left-handed periodic structures
Artificially fabricated structures with periodically modulated parameters
such as photonic crystals offer novel ways of controlling the flow of light due
to the existence of a range of forbidden frequencies associated with a photonic
bandgap. It is believed that modulation of the refractive index in all three
spatial dimensions is required to open a complete bandgap and prevent the
propagation of electromagnetic waves in all directions. Here we reveal that, in
a sharp contrast to what was known before and contrary to the accepted physical
intuition, a one-dimensional periodic structure containing the layers of
transparent left-handed (or negative-index) metamaterial can trap light in
three-dimensional space due to the existence of a complete bandgap.Comment: 4 pages, 5 figure
Aircraft measurements of electrified clouds at Kennedy Space Center, part 3
Flights made by the Special Purpose Test Vehicle for Atmospheric Research (SPTVAR) airplane during a second deployment to Florida during the summer of 1989 are discussed. The findings based on the data gathered are presented. The progress made during the second year of the project is discussed. The summer 1989 study was carried out with the support and guidance of Col. John Madura, Commander of Detachment 11, 2nd Weather Squadron, USAF, at Patrick Air Force Base (PAFB) and Cape Canaveral Air Force Station. The project goals were to develop and demonstrate techniques for measuring the electric field aloft and locating regions of charge during flight within and near clouds; to characterize the electric conditions that are presently identified as a threat to space launch vehicles; and to study the correlation between the electric field aloft and that at Kennedy Space Center's ground-based electric field mill array for a variety of electrified clouds
Aircraft measurements of electrified clouds at Kennedy Space Center. Part 2: Case study: 4 November 1988 (88309)
During the fall of 1988, a Schweizer airplane equipped to measure electric field and other meteorological parameters flew over Kennedy Space Center (KSC) in a program to study clouds defined in the existing launch restriction criteria. A case study is presented of a single flight over KSC on November 4, 1988. This flight was chosen for two reasons: (1) the clouds were weakly electrified, and no lightning was reported during the flight; and (2) electric field mills in the surface array at KSC indicated field strengths greater than 3 kV/m, yet the aircraft flying directly over them at an altitude of 3.4 km above sea level measured field strengths of less than 1.6 kV/m. A weather summary, sounding description, record of cloud types, and an account of electric field measurements are included
Aircraft measurements of electrified clouds at Kennedy Space Center
The space-vehicle launch commit criteria for weather and atmospheric electrical conditions in us at Cape Canaveral Air Force Station and Kennedy Space Center (KSC) have been made restrictive because of the past difficulties that have arisen when space vehicles have triggered lightning discharge after their launch during cloudy weather. With the present ground-base instrumentation and our limited knowledge of cloud electrification process over this region of Florida, it has not been possible to provide a quantitative index of safe launching conditions. During the fall of 1988, a Schweizer 845 airplane equipped to measure electric field and other meteorological parameters flew over KSC in a program to study clouds defined in the existing launch restriction criteria. All aspects of this program are addressed including planning, method, and results. A case study on the November 4, 1988 flight is also presented
Twenty-One New Light Curves of OGLE-TR-56b: New System Parameters and Limits on Timing Variations
Although OGLE-TR-56b was the second transiting exoplanet discovered, only one
light curve, observed in 2006, has been published besides the discovery data.
We present twenty-one light curves of nineteen different transits observed
between July 2003 and July 2009 with the Magellan Telescopes and Gemini South.
The combined analysis of the new light curves confirms a slightly inflated
planetary radius relative to model predictions, with R_p = 1.378 +/- 0.090 R_J.
However, the values found for the transit duration, semimajor axis, and
inclination values differ significantly from the previous result, likely due to
systematic errors. The new semimajor axis and inclination, a = 0.01942 +/-
0.00015 AU and i = 73.72 +/- 0.18 degrees, are smaller than previously
reported, while the total duration, T_14 = 7931 +/- 38 s, is 18 minutes longer.
The transit midtimes have errors from 23 s to several minutes, and no evidence
is seen for transit midtime or duration variations. Similarly, no change is
seen in the orbital period, implying a nominal stellar tidal decay factor of
Q_* = 10^7, with a three-sigma lower limit of 10^5.7.Comment: 14 pages, 5 figures, accepted to Ap
HATS-1b: The First Transiting Planet Discovered by the HATSouth Survey
We report the discovery of HATS-1b, a transiting extrasolar planet orbiting
the moderately bright V=12.05 G dwarf star GSC 6652-00186, and the first planet
discovered by HATSouth, a global network of autonomous wide-field telescopes.
HATS-1b has a period P~3.4465 d, mass Mp~1.86MJ, and radius Rp~1.30RJ. The host
star has a mass of 0.99Msun, and radius of 1.04Rsun. The discovery light curve
of HATS-1b has near continuous coverage over several multi-day periods,
demonstrating the power of using a global network of telescopes to discover
transiting planets.Comment: Submitted to AJ 10 pages, 5 figures, 6 table
Resolving the Surfaces of Extrasolar Planets With Secondary Eclipse Light Curves
We present a method that employs the secondary eclipse light curves of
transiting extrasolar planets to probe the spatial variation of their thermal
emission. This technique permits an observer to resolve the surface of the
planet without the need to spatially resolve its central star. We evaluate the
feasibility of this technique for the HD 209458 system [..]. We consider two
representations of the planetary thermal emission; a simple model parameterized
by a sinusoidal dependence on longitude and latitude, as well as the results of
a three-dimensional dynamical simulation of the planetary atmosphere previously
published by Cooper & Showman. We find that observations of the secondary
eclipse light curve are most sensitive to a longitudinal offset in the
geometric and photometric centroids of the hemisphere of the planet visible
near opposition. To quantify this signal, we define a new parameter, the
``uniform time offset,'' which measures the time lag between the observed
secondary eclipse and that predicted by a planet with a uniform surface flux
distribution. We compare the predicted amplitude of this parameter for HD
209458 with the precision with which it could be measured with IRAC. We find
that IRAC observations at 3.6um a single secondary eclipse should permit
sufficient precision to confirm or reject the Cooper & Showman model of the
surface flux distribution for this planet. We quantify the signal-to-noise
ratio for this offset in the remaining IRAC bands (4.5um, 5.8um, and 8.0um),
and find that a modest improvement in photometric precision (as might be
realized through observations of several eclipse events) should permit a
similarly robust detection.Comment: AASTeX 5.2, 24 pages, 5 figures, accepted for publication in ApJ; v2:
clarifications, updated to version accepted by ApJ; v3: try to reduce spacin
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