Symmetry insights for design of supercomputer network topologies: roots and weights lattices

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

Color Dependence on Thickness in Topaz Crystal from Brazil

It is well known that crystals of topaz from the Eastern Brazilian Pegmatite Province may turn blue by the irradiation with Co-60 gamma rays followed by heat treatment. Also, it is known that the sensation of color changes with the thickness of these crystals. The dependence of the color, given by 1931 CIE chromaticity coordinates, with the thickness of the crystal was analyzed. The absorbance used in the calculation of these coordinates was given by the sum of Gaussian lines. The parameters of these lines were determined through the decomposition of the optical absorption spectra in the ultraviolet and visible regions. The decomposition revealed several lines, whose assignment was made considering studies in spodumene and beryl crystals and highly accurate quantum mechanical calculations. The transmittance becomes very narrow with increasing thickness, and the CIE chromaticity coordinates converge to the borderline of the CIE Chromaticity Diagram at the wavelength of maximum transmittance. Furthermore, the purity of color increases with increasing thickness, and the dominant wavelength reaches the wavelength of maximum transmittance.

LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga-Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density-density correlation due to umklapp scattering in lattice models.

Signatures of quantum phase transitions in parallel quantum dots: Crossover from local moment to underscreened spin-1 Kondo physics

We study a strongly interacting "quantum dot 1" and a weakly interacting "dot 2" connected in parallel to metallic leads. Gate voltages can drive the system between Kondo-quenched and non-Kondo free-moment phases separated by Kosterlitz-Thouless quantum phase transitions. Away from the immediate vicinity of the quantum phase transitions, the physical properties retain signatures of first-order transitions found previously to arise when dot 2 is strictly noninteracting. As interactions in dot 2 become stronger relative to the dot-lead coupling, the free moment in the non-Kondo phase evolves smoothly from an isolated spin-one-half in dot 1 to a many-body doublet arising from the incomplete Kondo compensation by the leads of a combined dot spin-one. These limits, which feature very different spin correlations between dot and lead electrons, can be distinguished by weak-bias conductance measurements performed at finite temperatures.