Weyl Expansion for Symmetric Potentials

We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the projection operators. For discrete symmetries the expansion yields a formally exact but asymptotic series in $\hbar$, while for the rotational $SO(n)$ symmetries the expansion requires averaging over angular momentum as well as energy. A numerical example is given in two dimensions, in which we calculate the leading terms of the Weyl expansion as well as the leading periodic orbit contributions to the symmetry reduced level density.Comment: Four of the five figures are appended as a postscript file. The fifth figure is available by snail mail

Geometric and Diffractive Orbits in the Scattering from Confocal Hyperbolae

We study the scattering resonances between two confocal hyperbolae and show that the spectrum is dominated by the effect of a single periodic orbit. There are two distinct cases depending on whether the orbit is geometric or diffractive. A generalization of periodic orbit theory allows us to incorporate the second possibility. In both cases we also perform a WKB analysis. Although it is found that the semiclassical approximations work best for resonances with large energies and narrow widths, there is reasonable agreement even for resonances with large widths - unlike the two disk scatterer. We also find agreement with the next order correction to periodic orbit theory.Comment: Written in RevTeX. After \end{document} comes a uuencoded .ps file with two figure

Video head impulse testing: Pitfalls in neurological patients

The video head impulse test (vHIT) assesses the vestibulo-ocular reflex (VOR) during a rapid high-velocity low amplitude (10°–20°) head rotation. Patients with peripheral vestibulopathy have a reduced VOR gain with corrective catch-up saccades during the head turn. There are several pitfalls, mainly technical, which may interfere with interpretation of vHIT data. In addition, intrusive eye movement disorders such as spontaneous nystagmus that affect normal eye position and tracking can affect the vHIT results. To date there has been little study of neurological saccadic eye movements that may interfere with the interpretation of vHIT data. Here, in ten patients with a range of central neurological disorders, we describe oculomotor abnormalities on vHIT in the presence of normal range VOR gain values, recorded at a tertiary vestibular neurology service

Spitzer/IRS Imaging and Spectroscopy of the luminous infrared galaxy NGC 6052 (Mrk 297)

We present photometric and spectroscopic data of the interacting starburst galaxy NGC 6052 obtained with the Spitzer Space Telescope. The mid-infrared (MIR) spectra of the three brightest spatially resolved regions in the galaxy are remarkably similar and are consistent with dust emission from young nearly coeval stellar populations. Analysis of the brightest infrared region of the system, which contributes ~18.5 % of the total 16\micron flux, indicates that unlike similar off-nuclear infrared-bright regions found in Arp 299 or NGC 4038/9, its MIR spectrum is inconsistent with an enshrouded hot dust (T > 300K) component. Instead, the three brightest MIR regions all display dust continua of temperatures less than ~ 200K. These low dust temperatures indicate the dust is likely in the form of a patchy screen of relatively cold material situated along the line of sight. We also find that emission from polycyclic aromatic hydrocarbons (PAHs) and the forbidden atomic lines is very similar for each region. We conclude that the ionization regions are self-similar and come from young (about 6 Myr) stellar populations. A fourth region, for which we have no MIR spectra, exhibits MIR emission similar to tidal tail features in other interacting galaxies.Comment: 20 pages in preprint form, estimated 7 pages in ApJ Aeptember 10, 2007, v666n 2 issue, six encapsulated postscript figure

Characterizing the Rigidly Rotating Magnetosphere Stars HD 345439 and HD 23478

The SDSS III APOGEE survey recently identified two new $\sigma$ Ori E type candidates, HD 345439 and HD 23478, which are a rare subset of rapidly rotating massive stars whose large (kGauss) magnetic fields confine circumstellar material around these systems. Our analysis of multi-epoch photometric observations of HD 345439 from the KELT, SuperWASP, and ASAS surveys reveals the presence of a $\sim$0.7701 day period in each dataset, suggesting the system is amongst the faster known $\sigma$ Ori E analogs. We also see clear evidence that the strength of H-alpha, H I Brackett series lines, and He I lines also vary on a $\sim$0.7701 day period from our analysis of multi-epoch, multi-wavelength spectroscopic monitoring of the system from the APO 3.5m telescope. We trace the evolution of select emission line profiles in the system, and observe coherent line profile variability in both optical and infrared H I lines, as expected for rigidly rotating magnetosphere stars. We also analyze the evolution of the H I Br-11 line strength and line profile in multi-epoch observations of HD 23478 from the SDSS-III APOGEE instrument. The observed periodic behavior is consistent with that recently reported by Sikora and collaborators in optical spectra.Comment: Accepted in ApJ

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure