143 research outputs found
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/ (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 , which, in the limit
, become a singular hard-wall potential of a multi-dimensional
billiard. We define auxiliary billiard domains that asymptote, as
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 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 makes into a Lie algebra object in
, the bounded below derived category of coherent sheaves on .
Furthermore Kapranov proved that, for a K\"ahler manifold , the Dolbeault
resolution of is an
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 , i.e. a
Lie algebroid together with a Lie subalgebroid , we define the Atiyah
class of an -module (relative to ) as the obstruction to
the existence of an -compatible -connection on . We prove that the
Atiyah classes and respectively make and
into a Lie algebra and a Lie algebra module in the bounded below
derived category , where is the abelian
category of left -modules and is the universal
enveloping algebra of . Moreover, we produce a homotopy Leibniz algebra and
a homotopy Leibniz module stemming from the Atiyah classes of and ,
and inducing the aforesaid Lie structures in .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
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