1,765 research outputs found
Multidimensional Heisenberg convolutions and product formulas for multivariate Laguerre polynomials
Let positive integers. The groups U_p(\b C) and U_p(\b C)\times
U_q(\b C) act on the Heisenberg group H_{p,q}:=M_{p,q}(\b C)\times \b R
canonically as groups of automorphisms where M_{p,q}(\b C) is the vector
space of all complex -matrices. The associated orbit spaces may be
identified with \Pi_q\times \b R and \Xi_q\times \b R respectively with the
cone of positive semidefinite matrices and the Weyl chamber
\Xi_q={x\in\b R^q: x_1\ge...\ge x_q\ge 0}.
In this paper we compute the associated convolutions on \Pi_q\times \b R
and \Xi_q\times \b R explicitly depending on . Moreover, we extend these
convolutions by analytic continuation to series of convolution structures for
arbitrary parameters . This leads for to continuous series
of noncommutative hypergroups on \Pi_q\times \b R and commutative hypergroups
on \Xi_q\times \b R. In the latter case, we describe the dual space in terms
of multivariate Laguerre and Bessel functions on and . In
particular, we give a non-positive product formula for these Laguerre functions
on .
The paper extends the known case due to Koornwinder, Trimeche, and
others as well as the group case with integers due to Faraut, Benson,
Jenkins, Ratcliff, and others. Moreover, it is closely related to product
formulas for multivariate Bessel and other hypergeometric functions of
R\"osler
Development of a relatchable cover mechanism for a cryogenic IR-sensor
A cover mechanism for use on the Infrared Background Signature Survey (IBSS) cryostat was developed. The IBSS IR-instrument is scheduled for STS launch in early 1991 as a payload of the Shuttle Payload Satellite (SPS) 2. The cover is hinged, with a motorized rope drive. During ground processing, launch, entry, and landing, the cryostat, which houses the IR-instrument, is required to be a sealed vacuum tight container for cooling purposes and contamination prevention. When on orbit, the cover is opened to provide an unobstructed field of view for the IR-instrument. A positive seal is accomplished through the use of latch mechanism. The cover and the latch are driven by a common redundant actuator consisting of dc motors, spur gears, and a differential gear. Hall probe limit switches and position sensors (rotary variable transformer) are used to determine the position of the cover and the latch. The cover mechanism was successfully qualified for thermal vacuum (-25 to 35 C), acoustic noise, vibration (6 Gs sine, 9.7 G RMS) and life cycles. Constricting requirements, mechanical and electronic control design, specific design details, test results of functional performance, and environmental and life tests are described
High redshift X-ray galaxy clusters. II. The L_X-T relationship revisited
In this paper we re-visit the observational relation between X-ray luminosity
and temperature for high-z galaxy clusters and compare it with the local L_X-T
and with theoretical models. To these ends we use a sample of 17 clusters
extracted from the Chandra archive supplemented with additional clusters from
the literature, either observed by Chandra or XMM-Newton, to form a final
sample of 39 high redshift (0.25 < z < 1.3) objects. Different statistical
approaches are adopted to analyze the L_X-T relation. The slope of the L_X-T
relation of high redshift clusters is steeper than expected from the
self-similar model predictions and steeper, even though still compatible within
the errors, than the local L_X-T slope. The distant cluster L_X-T relation
shows a significant evolution with respect to the local Universe: high-z
clusters are more luminous than the local ones by a factor ~2 at any given
temperature. The evolution with redshift of the L_X-T relation cannot be
described by a single power law nor by the evolution predicted by the
self-similar model. We find a strong evolution, similar or stronger than the
self-similar model, from z = 0 to z <0.3 followed by a much weaker, if any,
evolution at higher redshift. The weaker evolution is compatible with
non-gravitational models of structure formation. According to us a
statistically significant sample of nearby clusters (z < 0.25) should be
observed with the current available X-ray telescopes to completely exclude
observational effects due to different generation detectors and to understand
this novel result.Comment: 14 pages, 10 postscript figures. Accepted for publication in
Astronomy & Astrophysics. Corrected typo
Conduction States with Vanishing Dimerization in Pt Nanowires on Ge(001) Observed with Scanning Tunneling Microscopy
The low-energy electronic properties of one-dimensional nanowires formed by
Pt atoms on Ge(001) are studied with scanning tunneling microscopy down to the
millivolt-regime. The chain structure exhibits various dimerized elements at
high tunneling bias, indicative of a substrate bonding origin rather than a
charge density wave. Unexpectedly, this dimerization becomes vanishingly small
when imaging energy windows close to the Fermi level with adequately low
tunneling currents. Evenly spaced nanowire atoms emerge which are found to
represent conduction states. Implications for the metallicity of the chains are
discussed.Comment: 4 pages, 4 figure
The mass-L_x relation for moderate luminosity X-ray clusters
We present measurements of the masses of a sample of 25 moderate X-ray
luminosity clusters of galaxies from the 160 square degree ROSAT survey. The
masses were obtained from a weak lensing analysis of deep F814W images obtained
using the Advanced Camera for Surveys (ACS). We present an accurate empirical
correction for the effect of charge transfer (in)efficiency on the shapes of
faint galaxies. A significant lensing signal is detected around most of the
clusters. The lensing mass correlates tightly with the cluster richness. We
measured the intrinsic scatter in the scaling relation between M_2500 and L_X
and find the best fit power law slope and normalisation to be alpha=0.68+-0.07
and M_X=(1.2+-0.12)10^14M_sun (for L_X=2x10^44 erg/s). These results agree well
with a number of recent studies, but the normalisation is lower compared to the
study of Rykoff et al. (2008b). One explanation for this difference may be the
fact that (sub)structures projected along the line-of-sight boost both the
galaxy counts and the lensing mass. Such superpositions lead to an increased
mass at a given L_X when clusters are binned by richness.Comment: accepted for publication in the Astrophysical Journal; 15 pages, 11
figure
Assessment of the GW Approximation using Hubbard Chains
We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. GW and exchange-only calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable
Does Luttinger liquid behaviour survive in an atomic wire on a surface?
We form a highly simplified model of an atomic wire on a surface by the
coupling of two one-dimensional chains, one with electron-electron interactions
to represent the wire and and one with no electron-electron interactions to
represent the surface. We use exact diagonalization techniques to calculate the
eigenstates and response functions of our model, in order to determine both the
nature of the coupling and to what extent the coupling affects the Luttinger
liquid properties we would expect in a purely one-dimensional system. We find
that while there are indeed Luttinger liquid indicators present, some residual
Fermi liquid characteristics remain.Comment: 14 pages, 7 figures. Submitted to J Phys
On the Intracluster Medium in Cooling Flow & Non-Cooling Flow Clusters
Recent X-ray observations have highlighted clusters that lack entropy cores.
At first glance, these results appear to invalidate the preheated ICM models.
We show that a self-consistent preheating model, which factors in the effects
of radiative cooling, is in excellent agreement with the observations.
Moreover, the model naturally explains the intrinsic scatter in the L-T
relation, with ``cooling flow'' and ``non-cooling flow'' systems corresponding
to mildly and strongly preheated systems, respectively. We discuss why
preheating ought to be favoured over merging as a mechanism for the origin of
``non-cooling flow'' clusters.Comment: 4 pages, to appear in the proceedings of the "Multiwavelength
Cosmology" Conference held in Mykonos, Greece, June 2003, ed. M. Plionis
(Kluwer
Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
In one dimension, the exponential position operators introduced in a theory
of polarization are identified with the twisting operators appearing in the
Lieb-Schultz-Mattis argument, and their finite-size expectation values
measure the overlap between the unique ground state and an excited state.
Insulators are characterized by . We identify with
ground-state expectation values of vertex operators in the sine-Gordon model.
This allows an accurate detection of quantum phase transitions in the
universality classes of the Gaussian model. We apply this theory to the
half-filled extended Hubbard model and obtain agreement with the level-crossing
approach.Comment: 4 pages, 3 figure
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