Quantum graph as a quantum spectral filter

We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter $\alpha$. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of $\Gamma$ as $\alpha\to\infty$. This effect can be used for a spectral analysis of the given graph $\Gamma$. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where $\Gamma$ is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.Comment: 15 pages, 8 figures. Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physic

Geochemistry of volcanic rocks from the Wawa greenstone belt

The Wawa greenstone belt is located in the District of Algoma and extends east-northeast from Lake Superior to the western part of the Sudbury District in Ontario, Canada. Recent mapping by Attoh has shown that an unconformity at the base of the Dore' Formation and equivalent sedimentary rocks marks a significant stratigraphic break which can be traced throughout the volcanic belt. This break has been used to subdivide the volcanic-sedimentary into pre- and post-Dore' sequences. The pre-Dore' sequence includes at least two cycles of mafic-to-felsic volcanism, each capped by an iron-formation unit. The post-Dore' sequence includes an older mafic-to-felsic unit, which directly overlies sedimentary rocks correlated with the Dore' Formation, and a younger felsic breccia unit interpreted to have formed as debris flows from a felsic volcanic center. In the present study, samples of both the pre-and post-Dore' volcanic sequences were analyzed for major and trace elements, incuding rare earths (REE). This preliminary study is part of an ongoing program to assess the petrogenesis of the volcanic rocks of the Wawa greenstone belt

Rhyolitic components of the Michipicoten greenstone belt, Ontario: Evidence for late Archaen intracontinental rifts or convergent plate margins in the Canadian Shield?

Rhyolitic rocks often are the dominant felsic end member of the biomodal volcanic suites that characterize many late Archean greenstone belts of the Canadian Shield. The rhyolites primarily are pyroclastic flows (ash flow tuffs) emplaced following plinian eruptions, although deposits formed by laval flows and phreatomagmatic eruptions also are presented. Based both on measured tectono-stratigraphic sections and provenance studies of greenstone belt sedimentary sequences, the rhyolites are believed to have been equal in abundance to associated basaltic rocks. In many recent discussions of the tectonic setting of late Archean Canadian greenstone belts, rhyolites have been interpreted as products of intracontinental rifting . A study of the tectono-stratigraphic relationships, rock associations and chemical characteristics of the particularly ell-exposed late Archean rhyolites of the Michipicoten greenstone belt, suggests that convergent plate margin models are more appropriate

Discovery of Reflection Nebulosity Around Five Vega-like Stars

Coronagraphic optical observations of six Vega-like stars reveal reflection nebulosities, five of which were previously unknown. The nebulosities illuminated by HD 4881, HD 23362, HD 23680, HD 26676, and HD 49662 resemble that of the Pleiades, indicating an interstellar origin for dust grains. The reflection nebulosity around HD 123160 has a double-arm morphology, but no disk-like feature is seen as close as 2.5 arcsec from the star in K-band adaptive optics data. We demonstrate that uniform density dust clouds surrounding HD 23362, HD 23680 and HD 123160 can account for the observed 12-100 micron spectral energy distributions. For HD 4881, HD 26676, and HD 49662 an additional emission source, such as from a circumstellar disk or non-equilibrium grain heating, is required to fit the 12-25 micron data. These results indicate that in some cases, particularly for Vega-like stars located beyond the Local Bubble (>100 pc), the dust responsible for excess thermal emission may originate from the interstellar medium rather than from a planetary debris system.Comment: The Astrophysical Journal, in press for March, 2002 (32 pages, 13 figures

Sylvester's question and the Random Acceleration Process

Let n points be chosen randomly and independently in the unit disk. "Sylvester's question" concerns the probability p_n that they are the vertices of a convex n-sided polygon. Here we establish the link with another problem. We show that for large n this polygon, when suitably parametrized by a function r(phi) of the polar angle phi, satisfies the equation of the random acceleration process (RAP), d^2 r/d phi^2 = f(phi), where f is Gaussian noise. On the basis of this relation we derive the asymptotic expansion log p_n = -2n log n + n log(2 pi^2 e^2) - c_0 n^{1/5} + ..., of which the first two terms agree with a rigorous result due to Barany. The nonanalyticity in n of the third term is a new result. The value 1/5 of the exponent follows from recent work on the RAP due to Gyorgyi et al. [Phys. Rev. E 75, 021123 (2007)]. We show that the n-sided polygon is effectively contained in an annulus of width \sim n^{-4/5} along the edge of the disk. The distance delta_n of closest approach to the edge is exponentially distributed with average 1/(2n).Comment: 29 pages, 4 figures; references added and minor change

A double-lined spectroscopic orbit for the young star HD 34700

We report high-resolution spectroscopic observations of the young star HD 34700, which confirm it to be a double-lined spectroscopic binary. We derive an accurate orbital solution with a period of 23.4877 +/- 0.0013 days and an eccentricity of e = 0.2501 +/- 0.0068. The stars are found to be of similar mass (M2/M1 = 0.987 +/- 0.014) and luminosity. We derive also the effective temperatures (5900 K and 5800 K) and projected rotational velocities (28 km/s and 22 km/s) of the components. These values of v sin i are much higher than expected for main-sequence stars of similar spectral type (G0), and are not due to tidal synchronization. We discuss also the indicators of youth available for the object. Although there is considerable evidence that the system is young --strong infrared excess, X-ray emission, Li I 6708 absorption (0.17 Angstroms equivalent width), H alpha emission (0.6 Angstroms), rapid rotation-- the precise age cannot yet be established because the distance is unknown.Comment: 17 pages, including 2 figures and 2 tables. Accepted for publication in AJ, to appear in February 200

The Coronal X-ray Spectrum of the Multiple Weak-Lined T Tauri Star System HD 98800

We present high-resolution X-ray spectra of the multiple (hierarchical quadruple) weak-lined T Tauri star system HD 98800, obtained with the High Energy Transmission Gratings Spectrograph (HETGS) aboard the Chandra X-ray Observatory (CXO). In the zeroth-order CXO/HETGS X-ray image, both principle binary components of HD 98800 (A and B, separation 0.8'') are detected; component A was observed to flare during the observation. The infrared excess (dust disk) component, HD 98800B, is a factor ~4 fainter in X-rays than the apparently ``diskless'' HD 98800A, in quiescence. The line ratios of He-like species (e.g., Ne IX, O VII) in the HD 98800A spectrum indicate that the X-ray-emitting plasma around HD 98800 is in a typical coronal density regime (log n <~ 11). We conclude that the dominant X-ray-emitting component(s) of HD 98800 is (are) coronally active. The sharp spectral differences between HD 98800 and the classical T Tauri star TW Hya demonstrate the potential utility of high-resolution X-ray spectroscopy in providing diagnostics of pre-main sequence accretion processes.Comment: 11 pages, 5 figures; to appear in the Astrophysical Journal (Letters