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

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

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

Triggering and Delivery Algorithms for AGN Feedback

We compare several common sub-grid implementations of AGN feedback, focusing on the effects of different triggering mechanisms and the differences between thermal and kinetic feedback. Our main result is that pure thermal feedback that is centrally injected behaves differently from feedback with even a small kinetic component. Specifically, pure thermal feedback results in excessive condensation and smothering of the AGN by cold gas because the feedback energy does not propagate to large enough radii. We do not see large differences between implementations of different triggering mechanisms, as long as the spatial resolution is sufficiently high, probably because all of the implementations tested here trigger strong AGN feedback under similar conditions. In order to assess the role of resolution, we vary the size of the "accretion zone" in which properties are measured to determine the AGN accretion rate and resulting feedback power. We find that a larger accretion zone results in steadier jets but can also allow too much cold-gas condensation in simulations with a Bondi-like triggering algorithm. We also vary the opening angle of jet precession and find that a larger precession angle causes more of the jet energy to thermalize closer to the AGN, thereby producing results similar to pure thermal feedback. Our simulations confirm that AGN can regulate the thermal state of cool-core galaxy clusters and maintain the core in a state that is marginally susceptable to thermal instability and precipitation.Comment: 17 pages, 12 figures, submitted to Ap

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

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

Unusual electronic ground state of a prototype cuprate: band splitting of single CuO_2-plane Bi_2 Sr_(2-x) La_x CuO_(6+delta)

By in-situ change of polarization a small splitting of the Zhang-Rice singlet state band near the Fermi level has been resolved for optimum doped (x=0.4) Bi$_{2}$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta}$ at the (pi,0)-point (R.Manzke et al. PRB 63, R100504 (2001). Here we treat the momentum dependence and lineshape of the split band by photoemission in the EDC-mode with very high angular and energy resolution. The splitting into two destinct emissions could also be observed over a large portion of the major symmetry line $\Gamma$M, giving the dispersion for the individual contributions. Since bi-layer effects can not be present in this single-layer material the results have to be discussed in the context of one-particle removal spectral functions derived from current theoretical models. The most prominent are microscopic phase separation including striped phase formation, coexisting antiferromagnetic and incommensurate charge-density-wave critical fluctuations coupled to electrons (hot spots) or even spin charge separation within the Luttinger liquid picture, all leading to non-Fermi liquid like behavior in the normal state and having severe consequences on the way the superconducting state forms. Especially the possibilty of observing spinon and holon excitations is discussed.Comment: 5 pages, 4 figure

The spectral weight of the Hubbard model through cluster perturbation theory

We calculate the spectral weight of the one- and two-dimensional Hubbard models, by performing exact diagonalizations of finite clusters and treating inter-cluster hopping with perturbation theory. Even with relatively modest clusters (e.g. 12 sites), the spectra thus obtained give an accurate description of the exact results. Thus, spin-charge separation (i.e. an extended spectral weight bounded by singularities) is clearly recognized in the one-dimensional Hubbard model, and so is extended spectral weight in the two-dimensional Hubbard model.Comment: 4 pages, 5 figure