Coherent States of the q--Canonical Commutation Relations

For the $q$-deformed canonical commutation relations $a(f)a^\dagger(g) = (1-q)\,\langle f,g\rangle{\bf1}+q\,a^\dagger(g)a(f)$ for $f,g$ in some Hilbert space ${\cal H}$ we consider representations generated from a vector $\Omega$ satisfying $a(f)\Omega=\langle f,\phi\rangle\Omega$, where $\phi\in{\cal H}$. We show that such a representation exists if and only if $\Vert\phi\Vert\leq1$. Moreover, for $\Vert\phi\Vert<1$ these representations are unitarily equivalent to the Fock representation (obtained for $\phi=0$). On the other hand representations obtained for different unit vectors $\phi$ are disjoint. We show that the universal C*-algebra for the relations has a largest proper, closed, two-sided ideal. The quotient by this ideal is a natural $q$-analogue of the Cuntz algebra (obtained for $q=0$). We discuss the Conjecture that, for $d<\infty$, this analogue should, in fact, be equal to the Cuntz algebra itself. In the limiting cases $q=\pm1$ we determine all irreducible representations of the relations, and characterize those which can be obtained via coherent states.Comment: 19 pages, Plain Te

Water in low-mass star-forming regions with Herschel: HIFI spectroscopy of NGC1333

'Water In Star-forming regions with Herschel' (WISH) is a key programme dedicated to studying the role of water and related species during the star-formation process and constraining the physical and chemical properties of young stellar objects. The Heterodyne Instrument for the Far-Infrared (HIFI) on the Herschel Space Observatory observed three deeply embedded protostars in the low-mass star-forming region NGC1333 in several H2-16O, H2-18O, and CO transitions. Line profiles are resolved for five H16O transitions in each source, revealing them to be surprisingly complex. The line profiles are decomposed into broad (>20 km/s), medium-broad (~5-10 km/s), and narrow (<5 km/s) components. The H2-18O emission is only detected in broad 1_10-1_01 lines (>20 km/s), indicating that its physical origin is the same as for the broad H2-16O component. In one of the sources, IRAS4A, an inverse P Cygni profile is observed, a clear sign of infall in the envelope. From the line profiles alone, it is clear that the bulk of emission arises from shocks, both on small (<1000 AU) and large scales along the outflow cavity walls (~10 000 AU). The H2O line profiles are compared to CO line profiles to constrain the H2O abundance as a function of velocity within these shocked regions. The H2O/CO abundance ratios are measured to be in the range of ~0.1-1, corresponding to H2O abundances of ~10-5-10-4 with respect to H2. Approximately 5-10% of the gas is hot enough for all oxygen to be driven into water in warm post-shock gas, mostly at high velocities.Comment: Accepted for publication in the A&A HIFI special issu

Peculiar Motions in the Region of the Ursa Major Supercluster of Galaxies

We have investigated the peculiar motions of clusters of galaxies in the Ursa Major (UMa) supercluster and its neighborhood. Based on SDSS (Sloan Digital Sky Survey) data, we have compiled a sample of early-type galaxies and used their fundamental plane to determine the cluster distances and peculiar velocities. The samples of early-type galaxies in the central regions (within R_200) of 12 UMa clusters of galaxies, in three main subsystems of the supercluster -- the filamentary structures connecting the clusters, and in nine clusters from the nearest UMa neighborhood have similar parameters. The fairly high overdensity (3 by the galaxy number and 15 by the cluster number) suggests that the supercluster as a whole is gravitationally bound, while no significant peculiar motions have been found: the peculiar velocities do not exceed the measurement errors by more than a factor of 1.5-2. The mean random peculiar velocities of clusters and the systematic deviations from the overall Hubble expansion in the supercluster are consistent with theoretical estimates. For the possible approach of the three UMa subsystems to be confirmed, the measurement accuracy must be increased by a factor of 2-3.Comment: 21 pages, 4 tables, 7 figure

Tunable few-electron double quantum dots and Klein tunnelling in ultra-clean carbon nanotubes

Quantum dots defined in carbon nanotubes are a platform for both basic scientific studies and research into new device applications. In particular, they have unique properties that make them attractive for studying the coherent properties of single electron spins. To perform such experiments it is necessary to confine a single electron in a quantum dot with highly tunable barriers, but disorder has until now prevented tunable nanotube-based quantum-dot devices from reaching the single-electron regime. Here, we use local gate voltages applied to an ultra-clean suspended nanotube to confine a single electron in both a single quantum dot and, for the first time, in a tunable double quantum dot. This tunability is limited by a novel type of tunnelling that is analogous to that in the Klein paradox of relativistic quantum mechanics.Comment: 21 pages including supplementary informatio

Statistical Mechanics of Glass Formation in Molecular Liquids with OTP as an Example

We extend our statistical mechanical theory of the glass transition from examples consisting of point particles to molecular liquids with internal degrees of freedom. As before, the fundamental assertion is that super-cooled liquids are ergodic, although becoming very viscous at lower temperatures, and are therefore describable in principle by statistical mechanics. The theory is based on analyzing the local neighborhoods of each molecule, and a statistical mechanical weight is assigned to every possible local organization. This results in an approximate theory that is in very good agreement with simulations regarding both thermodynamical and dynamical properties

Annihilation of low energy antiprotons in silicon

The goal of the AE$\mathrm{\bar{g}}$IS experiment at the Antiproton Decelerator (AD) at CERN, is to measure directly the Earth's gravitational acceleration on antimatter. To achieve this goal, the AE$\mathrm{\bar{g}}$IS collaboration will produce a pulsed, cold (100 mK) antihydrogen beam with a velocity of a few 100 m/s and measure the magnitude of the vertical deflection of the beam from a straight path. The final position of the falling antihydrogen will be detected by a position sensitive detector. This detector will consist of an active silicon part, where the annihilations take place, followed by an emulsion part. Together, they allow to achieve 1$$ precision on the measurement of $\bar{g}$ with about 600 reconstructed and time tagged annihilations. We present here, to the best of our knowledge, the first direct measurement of antiproton annihilation in a segmented silicon sensor, the first step towards designing a position sensitive silicon detector for the AE$\mathrm{\bar{g}}$IS experiment. We also present a first comparison with Monte Carlo simulations (GEANT4) for antiproton energies below 5 MeVComment: 21 pages in total, 29 figures, 3 table