Multidimensional Heisenberg convolutions and product formulas for multivariate Laguerre polynomials

Let $p,q$ 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 $p\times q$-matrices. The associated orbit spaces may be identified with \Pi_q\times \b R and \Xi_q\times \b R respectively with the cone $\Pi_q$ 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 $p$. Moreover, we extend these convolutions by analytic continuation to series of convolution structures for arbitrary parameters $p\ge 2q-1$. This leads for $q\ge 2$ 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 $\Pi_q$ and $\Xi_q$. In particular, we give a non-positive product formula for these Laguerre functions on $\Xi_q$. The paper extends the known case $q=1$ due to Koornwinder, Trimeche, and others as well as the group case with integers $p$ 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 $z_L$ measure the overlap between the unique ground state and an excited state. Insulators are characterized by $z_{\infty}\neq 0$. We identify $z_L$ 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