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