Symplectic duality of Symmetric Spaces

We show that between symmetric spaces of different types there exists a bi-symplectic map. We compute the duality map explicitely by using the theory of Jordan Algebra

Polarization fields in nitride nanostructures: ten points to think about

Macroscopic polarization, both of intrinsic and piezoelectric nature, is unusually strong in III-V nitrides, and the built in electric fields in the layers of nitride-based nanostructures, stemming from polarization changes at heterointerfaces, have a major impact on the properties of single and multiple quantum wells, high mobility transistors, and thin films. The concepts involved in the theory and applications of polarization in nitrides have encountered some resistance in the field. Here we discuss critically ten ``propositions'' aimed at clarifying the main controversial issues.Comment: RevTeX 5 pages, 2 embedded figure

De-contamination of cosmological 21-cm maps

We present a method for extracting the expected cosmological 21-cm signal from the epoch of reionization, taking into account contaminating radiations and random instrumental noise. The method is based on the maximum a-posteriori probability (MAP) formalism and employs the coherence of the contaminating radiation along the line-of-sight and the three-dimensional correlations of the cosmological signal. We test the method using a detailed and comprehensive modeling of the cosmological 21-cm signal and the contaminating radiation. The signal is obtained using a high resolution N-body simulation where the gas is assumed to trace the dark matter and is reionized by stellar radiation computed from semi-analytic galaxy formation recipes. We model contaminations to the cosmological signal from synchrotron and free-free galactic foregrounds and extragalactic sources including active galactic nuclei, radio haloes and relics, synchrotron and free-free emission from star forming galaxies, and free-free emission from dark matter haloes and the intergalactic medium. We provide tests of the reconstruction method for several rms values of instrumental noise from $\sigma_{N}=1$ to 250 mK. For low instrumental noise, the recovered signal, along individual lines-of-sight, fits the true cosmological signal with a mean rms difference of $d_{rms}\approx 1.7\pm 0.6$ for $\sigma_{N}=1$ mK, and $d_{rms}\approx 4.2\pm 0.4$ for $\sigma_{N}=5$ mK. The one-dimensional power spectrum is nicely reconstructed for all values of $\sigma_{N}$ considered here, while the reconstruction of the two-dimensional power spectrum and the Minkowski functionals is good only for noise levels of the order of few mK.Comment: 19 pages, 17 figures, accepted for publication in MNRA

Electronic Properties of Ultra-Thin Aluminum Nanowires

We have carried out first principles electronic structure and total energy calculations for a series of ultrathin aluminum nanowires, based on structures obtained by relaxing the model wires of Gulseren et al. The number of conducting channels is followed as the wires radius is increased. The results suggest that pentagonal wires should be detectable, as the only ones who can yield a channel number between 8 and 10.Comment: 9 pages + 3 figures, to appear on Surface Scienc

The Puzzling Stability of Monatomic Gold Wires

We have examined theoretically the spontaneous thinning process of tip-suspended nanowires, and subsequently studied the structure and stability of the monatomic gold wires recently observed by Transmission Electron Microscopy (TEM). The methods used include thermodynamics, classical many-body force simulations, Local Density (LDA) and Generalized Gradient (GGA) electronic structure calculations as well as ab-initio simulations including the two tips. The wire thinning is well explained in terms of a thermodynamic tip suction driving migration of surface atoms from the wire to the tips. For the same reason the monatomic wire becomes progressively stretched. Surprisingly, however, all calculations so far indicate that the stretched monatomic gold wire should be unstable against breaking, contrary to the apparent experimental stability. The possible reasons for the observed stability are discussed.Comment: 4 figure

The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology

A simple, combinatorial construction of the sl(n)-WZNW fusion ring, also known as Verlinde algebra, is given. As a byproduct of the construction one obtains an isomorphism between the fusion ring and a particular quotient of the small quantum cohomology ring of the Grassmannian Gr(k,k+n). We explain how our approach naturally fits into known combinatorial descriptions of the quantum cohomology ring, by establishing what one could call a `Boson-Fermion-correspondence' between the two rings. We also present new recursion formulae for the structure constants of both rings, the fusion coefficients and the Gromov-Witten invariants.Comment: 61 pages, 2 eps figures; revised version accepted for publication in Advances in Mathematics: some minor typos removed, rewording of the proof to Corollary 6.9 and figure in Example 8.3 change

Effects of macroscopic polarization in III-V nitride multi-quantum-wells

Huge built-in electric fields have been predicted to exist in wurtzite III-V nitrides thin films and multilayers. Such fields originate from heterointerface discontinuities of the macroscopic bulk polarization of the nitrides. Here we discuss the background theory, the role of spontaneous polarization in this context, and the practical implications of built-in polarization fields in nitride nanostructures. To support our arguments, we present detailed self-consistent tight-binding simulations of typical nitride QW structures in which polarization effects are dominant.Comment: 11 pages, 9 figures, uses revtex/epsf. submitted to PR

Te covered Si(001): a variable surface reconstruction

At a given temperature, clean and adatom covered silicon surfaces usually exhibit well-defined reconstruction patterns. Our finite temperature ab-initio molecular dynamics calculations show that the tellurium covered Si(001) surface is an exception. Soft longitudinal modes of surface phonons due to the strongly anharmonic potential of the bridged tellurium atoms prevent the reconstruction structure from attaining any permanent, two dimensional periodic geometry. This explains why experiments attempting to find a definite model for the reconstruction have reached conflicting conclusions.Comment: 4 pages, 3 gif figure

Quantum interference with beamlike type-II spontaneous parametric down-conversion

We implement experimentally a method to generate photon-number$-$path and polarization entangled photon pairs using ``beamlike'' type-II spontaneous parametric down-conversion (SPDC), in which the signal-idler photon pairs are emitted as two separate circular beams with small emission angles rather than as two diverging cones.Comment: 4 pages, two-colum