Experimental simulation of quantum graphs by microwave networks

We present the results of experimental and theoretical study of irregular, tetrahedral microwave networks consisting of coaxial cables (annular waveguides) connected by T-joints. The spectra of the networks were measured in the frequency range 0.0001-16 GHz in order to obtain their statistical properties such as the integrated nearest neighbor spacing distribution and the spectral rigidity. The comparison of our experimental and theoretical results shows that microwave networks can simulate quantum graphs with time reversal symmetry. In particular, we use the spectra of the microwave networks to study the periodic orbits of the simulated quantum graphs. We also present experimental study of directional microwave networks consisting of coaxial cables and Faraday isolators for which the time reversal symmetry is broken. In this case our experimental results indicate that spectral statistics of directional microwave networks deviate from predictions of Gaussian orthogonal ensembles (GOE) in random matrix theory approaching, especially for small eigenfrequency spacing s, results for Gaussian unitary ensembles (GUE). Experimental results are supported by the theoretical analysis of directional graphs.Comment: 16 pages, 7 figures, to be published in Phys. Rev.

Photometric identification of blue horizontal branch stars

We investigate the performance of some common machine learning techniques in identifying BHB stars from photometric data. To train the machine learning algorithms, we use previously published spectroscopic identifications of BHB stars from SDSS data. We investigate the performance of three different techniques, namely k nearest neighbour classification, kernel density estimation and a support vector machine (SVM). We discuss the performance of the methods in terms of both completeness and contamination. We discuss the prospect of trading off these values, achieving lower contamination at the expense of lower completeness, by adjusting probability thresholds for the classification. We also discuss the role of prior probabilities in the classification performance, and we assess via simulations the reliability of the dataset used for training. Overall it seems that no-prior gives the best completeness, but adopting a prior lowers the contamination. We find that the SVM generally delivers the lowest contamination for a given level of completeness, and so is our method of choice. Finally, we classify a large sample of SDSS DR7 photometry using the SVM trained on the spectroscopic sample. We identify 27,074 probable BHB stars out of a sample of 294,652 stars. We derive photometric parallaxes and demonstrate that our results are reasonable by comparing to known distances for a selection of globular clusters. We attach our classifications, including probabilities, as an electronic table, so that they can be used either directly as a BHB star catalogue, or as priors to a spectroscopic or other classification method. We also provide our final models so that they can be directly applied to new data.Comment: To appear in A&A. 19 pages, 22 figures. Tables 7, A3 and A4 available electronically onlin

Distant field BHB stars and the mass of the Galaxy II: Photometry and spectroscopy of UKST candidates 16<B<19.5, 11<R<52 kpc

This is the second in a series of papers presenting a new calculation of the mass of the Galaxy based on radial velocities and distances for a sample of faint 16 < B < 21.3 field blue horizontal-branch (BHB) stars. We present accurate BV CCD photometry and spectra for 142 candidate A-type stars selected from ub_jr photometry of UK Schmidt telescope plates in six high-Galactic-latitude fields. Classification of these candidates produces a sample of 60 BHB stars at distances of 11-52 kpc from the Sun (mean 28 kpc), with heliocentric line-of-sight velocities accurate to 15 km/s, and distance errors < 10%. We provide a summary table listing coordinates and velocities of these stars. The measured dispersion of the radial component of the Galactocentric velocity for this sample is 108+-10 km/s, in agreement with a recent study of the distant halo by Sirko and coworkers. Measurements of the Ca II K line indicate that nearly all the stars are metal-poor with a mean [Fe/H] = -1.8 with dispersion 0.5. Subsequent papers will describe a second survey of BHBs to heliocentric distances 70 < R < 125 kpc and present a new estimate of the mass of the Galaxy.Comment: 16 pages, 15 figures. Accepted for publication in MNRA

Combinatorial identities for binary necklaces from exact ray-splitting trace formulae

Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (P\'olya necklaces).Comment: 15 page

Exact trace formulae for a class of one-dimensional ray-splitting systems

Based on quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992)) is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested.Comment: 14 pages, 3 figure

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Non-universal correlations due to localization are observed in statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities. Varying energy {E} and mean free path {l} enable us to experimentally tune from localized to delocalized states. Large level-to-level Inverse Participation Ratio (IPR I_{2}) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The density auto-correlations of eigenfunctions are shown to decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma-models.Comment: 4 pages, LaTex, 5 .jpg figures. This paper with 5 embedded postscript figures available (PS,PDF) at http://sagar.physics.neu.edu/preprints

One-dimensional quantum chaos: Explicitly solvable cases

We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansions for each individual energy level.Comment: 9 pages and 4 figure

Spectroscopy of Bright QUEST RR Lyrae Stars: Velocity Substructures toward Virgo

Using a sample of 43 bright (V<16.1, distance <13 kpc) RR Lyrae stars (RRLS) from the QUEST survey with spectroscopic radial velocities and metallicities, we find that several separate halo substructures contribute to the Virgo overdensity (VOD). While there is little evidence for halo substructure in the spatial distribution of these stars, their distribution in radial velocity reveals two moving groups. These results are reinforced when the sample is combined with a sample of blue horizontal branch stars that were identified in the SDSS, and the combined sample provides evidence for one additional moving group. These groups correspond to peaks in the radial velocity distribution of a sample of F type main-sequence stars that was recently observed in the same directon by SEGUE, although in one case the RRLS and F star groups may not lie at the same distance. One of the new substructures has a very narrow range in metallicity, which is more consistent with it being the debris from a destroyed globular cluster than from a dwarf galaxy. A small concentration of stars have radial velocities that are similar to the Virgo Stellar Stream (VSS) that was identified previously in a fainter sample of RRLS. Our results suggest that this feature extends to distances as short as ~12 kpc from its previous detection at ~19 kpc. None of the new groups and only one star in the sample have velocities that are consistent with membership in the leading tidal stream from the Sagittarius Dwarf Spheroidal Galaxy, which some authors have suggested is the origin of the VOD.Comment: Accepted for publication in the A

Explicitly solvable cases of one-dimensional quantum chaos

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit and exact

Spectra of regular quantum graphs

We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow a detailed investigation of both classical and quantum regimes. Despite their classical chaoticity, these systems exhibit a ``nonintegrable analog'' of the Einstein-Brillouin-Keller quantization formula which provides their spectra explicitly, state by state, by means of convergent periodic orbit expansions.Comment: 32 pages, 10 figure