Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe Strip

The Bethe Strip of width $m$ is the cartesian product \B\times\{1,...,m\}, where \B is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have "extended states" for small disorder. More precisely, we consider Anderson-like Hamiltonians \;H_\lambda=\frac12 \Delta \otimes 1 + 1 \otimes A + \lambda \Vv on a Bethe strip with connectivity $K \geq 2$, where $A$ is an $m\times m$ symmetric matrix, \Vv is a random matrix potential, and $\lambda$ is the disorder parameter. Given any closed interval $I\subset (-\sqrt{K}+a_{\mathrm{max}},\sqrt{K}+a_{\mathrm{min}})$, where $a_{\mathrm{min}}$ and $a_{\mathrm{max}}$ are the smallest and largest eigenvalues of the matrix $A$, we prove that for $\lambda$ small the random Schr\"odinger operator $\;H_\lambda$ has purely absolutely continuous spectrum in $I$ with probability one and its integrated density of states is continuously differentiable on the interval $I$

An improvement of an inequality of Fiedler leading to a new conjecture on nonnegative matrices

summary:Suppose that $A$ is an $n\times n$ nonnegative matrix whose eigenvalues are $\lambda = \rho (A), \lambda _2,\ldots , \lambda _n$. Fiedler and others have shown that $\det (\lambda I - A) \le \lambda ^n - \rho ^n$, for all $\lambda > \rho$, with equality for any such $\lambda$ if and only if $A$ is the simple cycle matrix. Let $a_i$ be the signed sum of the determinants of the principal submatrices of $A$ of order $i\times i$, $i = 1,\ldots ,n - 1$. We use similar techniques to Fiedler to show that Fiedler’s inequality can be strengthened to: $\det (\lambda I - A) + \sum _{i = 1}^{n - 1} \rho ^{n - 2i}|a_i|(\lambda - \rho )^i \le \lambda ^n -\rho ^n$, for all $\lambda \ge \rho$. We use this inequality to derive the inequality that: $\prod _{2}^{n}(\rho - \lambda _i) \le \rho ^{n - 2}\sum _{i = 2}^{n}(\rho - \lambda _i)$. In the spirit of a celebrated conjecture due to Boyle-Handelman, this inequality inspires us to conjecture the following inequality on the nonzero eigenvalues of $A$: If $\lambda _1 = \rho (A),\lambda _2,\ldots , \lambda _k$ are (all) the nonzero eigenvalues of $A$, then $\prod _{2}^{k}(\rho - \lambda _i) \le \rho ^{k-2}\sum _{i = 2}^{k}(\rho -\lambda )$. We prove this conjecture for the case when the spectrum of $A$ is real

Chemical abundances for Hf 2-2, a planetary nebula with the strongest known heavy element recombination lines

We present high quality optical spectroscopic observations of the planetary nebula (PN) Hf 2-2. The spectrum exhibits many prominent optical recombination lines (ORLs) from heavy element ions. Analysis of the H {\sc i} and He {\sc i} recombination spectrum yields an electron temperature of $\sim 900$ K, a factor of ten lower than given by the collisionally excited [O {\sc iii}] forbidden lines. The ionic abundances of heavy elements relative to hydrogen derived from ORLs are about a factor of 70 higher than those deduced from collisionally excited lines (CELs) from the same ions, the largest abundance discrepancy factor (adf) ever measured for a PN. By comparing the observed O {\sc ii} $\lambda$4089/$\lambda$4649 ORL ratio to theoretical value as a function of electron temperature, we show that the O {\sc ii} ORLs arise from ionized regions with an electron temperature of only $\sim 630$ K. The current observations thus provide the strongest evidence that the nebula contains another previously unknown component of cold, high metallicity gas, which is too cool to excite any significant optical or UV CELs and is thus invisible via such lines. The existence of such a plasma component in PNe provides a natural solution to the long-standing dichotomy between nebular plasma diagnostics and abundance determinations using CELs on the one hand and ORLs on the other.Comment: 12 pages, 5 figures, accepted for publication in the Monthly Notices of the Royal Astronomical Societ

Spectra of binaries classified as lambda Boo stars

High angular resolution observations have shown that some stars classified as lambda Boo are binaries with low values of angular separation and magnitude difference of the components; therefore the observed spectrum of these objects is a combination of those of the two components. These composite spectra have been used to define spectroscopic criteria able to detect other binaries among stars classified as lambda Boo. The application of this method to HD 111786 is presented: the contribution of 5 components to the observed spectrum is demonstrated by the shape of the O I 7774 Angstrom feature. This result makes unreliable any attempt to perform an abundance analysis of this object which therefore must be definitely rejected from the class of the peculiar lambda Boo stars. This approach allowed us also to recognize that the SB2 star HD 153808 is in reality a triple system.Comment: Accepted for publication by A&

An Optical Time-Delay for the Lensed BAL Quasar HE2149-2745

We present optical V and i-band light curves of the gravitationally lensed BAL quasar HE2149-2745. The data, obtained with the 1.5m Danish Telescope (ESO-La Silla) between October 1998 and December 2000, are the first from a long-term project aimed at monitoring selected lensed quasars in the Southern Hemisphere. A time delay of 103+/-12 days is determined from the light curves. In addition, VLT/FORS1 spectra of HE2149-2745 are deconvolved in order to obtain the spectrum of the faint lensing galaxy, free of any contamination by the bright nearby two quasar images. By cross-correlating the spectrum with galaxy-templates we obtain a tentative redshift estimate of z=0.495+/-0.01. Adopting this redshift, a Omega=0.3, Lambda=0.7 cosmology, and a chosen analytical lens model, our time-delay measurement yields a Hubble constant of H_0=66+/-8 km/s/Mpc with an estimated systematic error of +/-3 km/s/Mpc. Using non-parametric models yields H_0=65+/-8 km/s/Mpc and confirms that the lens exhibits a very dense/concentrated mass profile.Comment: 11 pages, accepted for publication in Astronomy & Astrophysic