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

Toroidal transformers procedure 902.66-01 Final report

Qualification tests of multi-secondary toroidal transformers and open-construction ratio toroidal transformer

Orbital Orientations of Exoplanets: HAT-P-4b is Prograde and HAT-P-14b is Retrograde

We present observations of the Rossiter-McLaughlin effect for two exoplanetary systems, revealing the orientations of their orbits relative to the rotation axes of their parent stars. HAT-P-4b is prograde, with a sky-projected spin-orbit angle of lambda = -4.9 +/- 11.9 degrees. In contrast, HAT-P-14b is retrograde, with lambda = 189.1 +/- 5.1 degrees. These results conform with a previously noted pattern among the stellar hosts of close-in giant planets: hotter stars have a wide range of obliquities and cooler stars have low obliquities. This, in turn, suggests that three-body dynamics and tidal dissipation are responsible for the short-period orbits of many exoplanets. In addition, our data revealed a third body in the HAT-P-4 system, which could be a second planet or a companion star.Comment: AJ, in press [8 pages

A Prograde, Low-Inclination Orbit for the Very Hot Jupiter WASP-3b

We present new spectroscopic and photometric observations of the transiting exoplanetary system WASP-3. Spectra obtained during two separate transits exhibit the Rossiter-McLaughlin (RM) effect and allow us to estimate the sky-projected angle between the planetary orbital axis and the stellar rotation axis, lambda = 3.3^{+2.5}_{-4.4} degrees. This alignment between the axes suggests that WASP-3b has a low orbital inclination relative to the equatorial plane of its parent star. During our first night of spectroscopic measurements, we observed an unexpected redshift briefly exceeding the expected sum of the orbital and RM velocities by 140 m/s. This anomaly could represent the occultation of material erupting from the stellar photosphere, although it is more likely to be an artifact caused by moonlight scattered into the spectrograph.Comment: 23 pages, 4 figures, Accepted for publication in The Astrophysical Journal, Replacement includes revised citation

Radiation Damage and Recovery Properties of Common Plastics PEN (Polyethylene Naphthalate) and PET (Polyethylene Terephthalate) Using a 137Cs Gamma Ray Source Up To 1 MRad and 10 MRad

Polyethylene naphthalate (PEN) and polyethylene teraphthalate (PET) are cheap and common polyester plastics used throughout the world in the manufacturing of bottled drinks, containers for foodstuffs, and fibers used in clothing. These plastics are also known organic scintillators with very good scintillation properties. As particle physics experiments increase in energy and particle flux density, so does radiation exposure to detector materials. It is therefore important that scintillators be tested for radiation tolerance at these generally unheard of doses. We tested samples of PEN and PET using laser stimulated emission on separate tiles exposed to 1 MRad and 10 MRad gamma rays with a 137Cs source. PEN exposed to 1 MRad and 10 MRad emit 71.4% and 46.7% of the light of an undamaged tile, respectively, and maximally recover to 85.9% and 79.5% after 5 and 9 days, respectively. PET exposed to 1 MRad and 10 MRad emit 35.0% and 12.2% light, respectively, and maximally recover to 93.5% and 80.0% after 22 and 60 days, respectively

Line-profile tomography of exoplanet transits I: The Doppler shadow of HD 189733b

We present a direct method for isolating the component of the starlight blocked by a planet as it transits its host star, and apply it to spectra of the bright transiting planet HD 189733b. We model the global shape of the stellar cross-correlation function as the convolution of a limb-darkened rotation profile and a gaussian representing the Doppler core of the average photospheric line profile. The light blocked by the planet during the transit is a gaussian of the same intrinsic width, whose trajectory across the line profile yields a precise measure of the misalignment angle and an independent measure of v sin I. We show that even when v sin I is less than the width of the intrinsic line profile, the travelling Doppler "shadow" cast by the planet creates an identifiable distortion in the line profiles which is amenable to direct modelling. Direct measurement of the trajectory of the missing starlight yields self-consistent measures of the projected stellar rotation rate, the intrinsic width of the mean local photospheric line profile, the projected spin-orbit misalignment angle, and the system's centre-of-mass velocity. Combined with the photometric rotation period, the results give a geometrical measure of the stellar radius which agrees closely with values obtained from high-precision transit photometry if a small amount of differential rotation is present in the stellar photosphere.Comment: 8 pages, 5 figures, 2 tables; accepted by MNRA