Hypercommutative operad as a homotopy quotient of BV

We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/$\Delta$ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive an equivalence of Hycomm-algebras and BV-algebras enhanced with a homotopy that trivializes the BV-operator. These formulas are given in terms of the Givental graphs, and are proved in two different ways. One proof uses the Givental group action, and the other proof goes through a chain of explicit formulas on resolutions of Hycomm and BV. The second approach gives, in particular, a homological explanation of the Givental group action on Hycomm-algebras.Comment: minor corrections added, to appear in Comm.Math.Phy

The Hamburg/SAO survey for low metallicity blue compact/HII-galaxies (HSS-LM). I. The first list of 46 strong-lined galaxies

We present the description and the first results of a new project devoted to the search for extremely metal-deficient blue compact/HII-galaxies (BCGs) and to the creation of a well selected large BCG sample with strong emission lines. Such galaxies should be suitable for reliable determination of their oxygen abundance through the measurement of the faint [OIII]4363A line. The goals of the project are two-fold: a) to discover a significant number of new extremely metal-poor galaxies (Z <= 1/20 Zo), and b) to study the metallicity distribution of local BCGs. Selection of candidates for follow-up slit spectroscopy is performed on the database of objective prism spectra of the Hamburg Quasar Survey. The sky region is limited by delta >= 0 deg. and b^ii <= -30 deg. In this paper we present the results of the follow-up spectroscopy conducted with the Russian 6m telescope. The list of observed candidates contained 52 objects, of which 46 were confirmed as strong-lined BCGs (EW([OIII]5007) >= 100 A). The remaining five lower excitation ELGs include three BCGs, and two galaxies classified as SBN (Starburst Nucleus) and DANS (Dwarf Amorphous Nucleus Starburst). One object is identified as a quasar with a strong Ly_alpha emission line near 5000 A (z~3). We provide a list with coordinates, measured radial velocities, B-magnitudes, equivalent widths EW([OIII]5007) and EW(H_beta) and for the 46 strong-lined BCGs the derived oxygen abundances 12+log(O/H). The abundances range between 7.42 and 8.4 (corresponding to metallicities between 1/30 and 1/3 Zo). The sample contains four galaxies with Z < 1/20 Zo, of which three are new discoveries.Comment: 19 pages, 13 figures, accepted for publication in A&A, corrected typos, reference

Approximating multi-dimensional Hamiltonian flows by billiards

Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ to the original billiard, and provide asymptotic expansion of the smooth Hamiltonian solution in terms of these billiard approximations. The asymptotic expansion includes error estimates in the $C^{r}$ norm and an iteration scheme for improving this approximation. Applying this theory to smooth potentials which limit to the multi-dimensional close to ellipsoidal billiards, we predict when the separatrix splitting persists for various types of potentials

Spectroscopic and photometric studies of low-metallicity star-forming dwarf galaxies. I. SBS 1129+576

Spectroscopy and V,I CCD photometry of the dwarf irregular galaxy SBS 1129+576 are presented for the first time. The CCD images reveal a chain of compact H II regions within the elongated low-surface-brightness (LSB) component of the galaxy. Star formation takes place mainly in two high-surface-brightness H II regions. The mean (V-I) colour of the LSB component in the surface brightness interval between 23 and 26 mag/sq.arcsec is relatively blue ~0.56+/-0.03 mag, as compared to the (V-I)~0.9-1.0 for the majority of known dwarf irregular and blue compact dwarf (BCD) galaxies. Spectroscopy shows that the galaxy is among the most metal-deficient galaxies with an oxygen abundance 12+log(O/H)= 7.36+/-0.10 in the brightest H II region and 7.48+/-0.12 in the second brightest H II region, or 1/36 and 1/28 of the solar value, respectively. Hbeta and Halpha emission lines and Hdelta and Hgamma absorption lines are detected in a large part of the LSB component. We use two extinction-insensitive methods based on the equivalent widths of (1) emission and (2) absorption Balmer lines to put constraints on the age of the stellar populations in the galaxy. In addition, we use two extinction-dependent methods based on (3) the spectral energy distribution (SED) and (4) the (V-I) colour. The observed properties of the LSB component can be reproduced by a stellar population forming continuously since 10 Gyr ago, provided that the star formation rate has increased during the last 100 Myr by a factor of 6 to 50 and no extinction is present. However, the observational properties of the LSB component can be reproduced equally well by continuous star formation which started not earlier than 100 Myr ago and stopped at 5 Myr, if some extinction is assumed.(Abridged)Comment: 17 pages, 12 figures, Accepted for publication in A&

Sensitivity of the eigenfunctions and the level curvature distribution in quantum billiards

In searching for the manifestations of sensitivity of the eigenfunctions in quantum billiards (with Dirichlet boundary conditions) with respect to the boundary data (the normal derivative) we have performed instead various numerical tests for the Robnik billiard (quadratic conformal map of the unit disk) for 600 shape parameter values, where we look at the sensitivity of the energy levels with respect to the shape parameter. We show the energy level flow diagrams for three stretches of fifty consecutive (odd) eigenstates each with index 1,000 to 2,000. In particular, we have calculated the (unfolded and normalized) level curvature distribution and found that it continuously changes from a delta distribution for the integrable case (circle) to a broad distribution in the classically ergodic regime. For some shape parameters the agreement with the GOE von Oppen formula is very good, whereas we have also cases where the deviation from GOE is significant and of physical origin. In the intermediate case of mixed classical dynamics we have a semiclassical formula in the spirit of the Berry-Robnik (1984) surmise. Here the agreement with theory is not good, partially due to the localization phenomena which are expected to disappear in the semiclassical limit. We stress that even for classically ergodic systems there is no global universality for the curvature distribution, not even in the semiclassical limit.Comment: 19 pages, file in plain LaTeX, 15 figures available upon request Submitted to J. Phys. A: Math. Ge

A Spectroscopic Study of a Large Sample of Wolf-Rayet Galaxies

We analyze long-slit spectral observations of 39 Wolf-Rayet (WR) galaxies with heavy element mass fraction ranging over 2 orders of magnitude, from Zsun/50 to 2Zsun. Nearly all galaxies in our sample show broad WR emission in the blue region of the spectrum (the blue bump) consisting of an unresolved blend of N III 4640, C III 4650, C IV 4658 and He II 4686 emission lines. Broad C IV 5808 emission (the red bump) is detected in 30 galaxies. Additionally, weaker WR emission lines are identified, most often the N III 4512 and Si III 4565 lines, which have very rarely or never been seen and discussed before in WR galaxies. These emission features are characteristic of WN7-WN8 and WN9-WN11 stars respectively. We derive the numbers of early WC (WCE) and late WN (WNL) stars from the luminosities of the red and blue bumps, and the number of O stars from the luminosity of the Hbeta emission line. Additionally, we propose a new technique for deriving the numbers of WNL stars from the N III 4512 and Si III 4565 emission lines. This technique is potentially more precise than the blue bump method because it does not suffer from contamination of WCE and early WN (WNE) stars and nebular gaseous emission. The N(WR)/N(O+WR) ratio decreases with decreasing metallicity, in agreement with predictions of evolutionary synthesis models. The N(WC)/N(WN) ratios and the equivalent widths of the blue bump EW(4650) and of the red bump EW(5808) derived from observations are also in satisfactory agreement with theoretical predictions.Comment: 49 pages, 9 figures, to appear in Astrophys.

From Atiyah Classes to Homotopy Leibniz Algebras

A celebrated theorem of Kapranov states that the Atiyah class of the tangent bundle of a complex manifold $X$ makes $T_X[-1]$ into a Lie algebra object in $D^+(X)$, the bounded below derived category of coherent sheaves on $X$. Furthermore Kapranov proved that, for a K\"ahler manifold $X$, the Dolbeault resolution $\Omega^{\bullet-1}(T_X^{1,0})$ of $T_X[-1]$ is an $L_\infty$ algebra. In this paper, we prove that Kapranov's theorem holds in much wider generality for vector bundles over Lie pairs. Given a Lie pair $(L,A)$, i.e. a Lie algebroid $L$ together with a Lie subalgebroid $A$, we define the Atiyah class $\alpha_E$ of an $A$-module $E$ (relative to $L$) as the obstruction to the existence of an $A$-compatible $L$-connection on $E$. We prove that the Atiyah classes $\alpha_{L/A}$ and $\alpha_E$ respectively make $L/A[-1]$ and $E[-1]$ into a Lie algebra and a Lie algebra module in the bounded below derived category $D^+(\mathcal{A})$, where $\mathcal{A}$ is the abelian category of left $\mathcal{U}(A)$-modules and $\mathcal{U}(A)$ is the universal enveloping algebra of $A$. Moreover, we produce a homotopy Leibniz algebra and a homotopy Leibniz module stemming from the Atiyah classes of $L/A$ and $E$, and inducing the aforesaid Lie structures in $D^+(\mathcal{A})$.Comment: 36 page

Autocorrelation function of eigenstates in chaotic and mixed systems

We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation length. For localized states, like bouncing ball modes or states living on tori, a simple model using only classical input gives good agreement with the exact result. In particular, a prediction for irregular eigenfunctions in mixed systems is derived and tested. For chaotic systems, the expansion of the autocorrelation function can be used to test quantum ergodicity on different length scales.Comment: 30 pages, 12 figures. Some of the pictures are included in low resolution only. For a version with pictures in high resolution see http://www.physik.uni-ulm.de/theo/qc/ or http://www.maths.bris.ac.uk/~maab

Chaotic eigenfunctions in momentum space

We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are derived. We present a detailed numerical study for the stadium and the cardioid billiard, which shows in several cases that the radially integrated momentum distribution is a good indicator of localized eigenstates, such as scars, or bouncing ball modes. We also find examples, where the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally applications and generalizations are discussed.Comment: 30 pages. The figures are included in low resolution only. For a version with figures in high resolution see http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp99-2.htm

Edge Diffraction, Trace Formulae and the Cardioid Billiard

We study the effect of edge diffraction on the semiclassical analysis of two dimensional quantum systems by deriving a trace formula which incorporates paths hitting any number of vertices embedded in an arbitrary potential. This formula is used to study the cardioid billiard, which has a single vertex. The formula works well for most of the short orbits we analyzed but fails for a few diffractive orbits due to a breakdown in the formalism for certain geometries. We extend the symbolic dynamics to account for diffractive orbits and use it to show that in the presence of parity symmetry the trace formula decomposes in an elegant manner such that for the cardioid billiard the diffractive orbits have no effect on the odd spectrum. Including diffractive orbits helps resolve peaks in the density of even states but does not appear to affect their positions. An analysis of the level statistics shows no significant difference between spectra with and without diffraction.Comment: 25 pages, 12 Postscript figures. Published versio