Polynomial-time simulation of pairing models on a quantum computer

We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between the ground and the first excited states and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultrasmall metallic grains.     

On a question of André Verbeure

We show that a non discrete state of van Hove's Universal Receptacle in the fermion case is not unitarily equivalent to any quasi-free state.Centre National de la Recherche Scientifique.     

The morphology of isomorphous substituted hectorites

Small-angle scattering (SAS) is used to investigate geometric structure parameters of isomorphically substituted hectorites. The aluminum content, the layer charge, and the purity of the substituted hectorites are related to the Al supply. The structural information contained in the scattering curves I(h) about the morphology of the samples in four different range orders from 1 nm to 300 nm is analyzed using the theory of the chord length distribution. The geometric structure parameters obtained are compared with results from XRD (L ₀-parameter), N₂-adsorption (L ₁ and mesopore size) and photon-correlation spectroscopy (largest dimension L ₃ and characteristic dimension of the secondary particles). Accepted after revision: 13 November 2001 Electronic Publication     

Molecular Dissociation on the SiC(0001) 3×3 Surface

In the framework of density functional theory, the adsorption of the halogenated polycyclic aromatic hydrocarbon 2,11‐diiodohexabenzocoronene (HBC‐I₂) on the SiC(0001) 3×3 surface has been investigated. Nondissociative and dissociative molecular adsorption is considered, and simulated scanning tunneling microscopy (STM) images are compared with the corresponding experimental observations. Calculations show that dissociative adsorption is favorable and reveal the crucial importance of the extended flat carbon core on molecule–surface interactions in dissociative adsorption; the iodine atom–surface interaction is of minor importance. Indeed, removing iodine atoms does not significantly affect the STM images of the central part of the molecule. This study shows that the dissociation of large halogenated polycyclic aromatic hydrocarbon molecules can occur on the SiC surface. This opens up interesting perspectives in the chemical reactivity and functionalization of wide band gap semiconductors.     

The general dévissage theorem for Witt groups of schemes

Let be a closed subscheme of the noetherian scheme X. We show that if X has a dualizing complex then there exists a dualizing complex of Z such that there is an isomorphism of coherent Witt groups for all . Received: 3 March 2006     

Gosteli-Claisen rearrangement of propargyl vinyl ethers: cascading molecular rearrangements

The ambivalent reactivity of 2-alkoxycarbonyl-substituted propargyl vinyl ethers has been explored. Depending on the conditions, the catalyzed and uncatalyzed Gosteli-Claisen rearrangement triggers downstream transformations that cascade from initially formed γ-allenyl α-keto esters to highly substituted furanes and cyclopentenes. In support of a mechanistic hypothesis, the results of a DFT study using the B1B95 and B3LYP functionals are revealed.     

Pseudomorphy, surface alloys and the role of elementary clusters on the domain orientations in the Cu/Al13Co4(100) system

We have used the pseudo-tenfold surface of the orthorhombic Al(13)Co(4) crystal as a template for the adsorption of Cu thin films of various thicknesses deposited at different temperatures. This study has been carried out by means of low energy electron diffraction (LEED), scanning tunnelling microscopy (STM), x-ray photoelectron spectroscopy (XPS) and x-ray photoelectron diffraction (XPD). From 300 to 573 K, Cu adatoms grow pseudomorphically up to one monolayer. At 300 K, the β-Al(Cu, Co) phase appears for coverages greater than one monolayer. For higher temperature deposition, the β-Al(Cu, Co) phase further transforms into the γ-Al(4)Cu(9) phase. Both β and γ phases grow as two (110) domains rotated by 72° ± 1° from each other. Instead of following the substrate symmetry, it is the orientations of the bipentagonal motifs present on the clean Al(13)Co(4)(100) surface that dictate the growth orientation of these domains. The initial bulk composition and structural complexity of the substrate have a minor role in the formation of the γ-Al(4)Cu(9) phase as long as the amount of Al and the Cu film thickness reach a critical stoichiometry.     

Novel tocopherol derivatives. Part 32: On the bromination of pyrano[3,2-f]chromenes related to γ-tocopherol

While bromination of γ-tocopherol (2) with elemental bromine affords 5-bromo-γ-tocopherol quantitatively (3), the analogous reaction of its truncated model compound, 2,2,7,8-tetramethylchromanol (2a) is known to be accompanied by side reactions and to produce hitherto unknown byproducts. These compounds originate from pyrano[3,2-f]chromene (6), a byproduct in the synthesis of model compound 2a, which affords bromochromene 7 as the major product. The reaction mechanism was shown to proceed via chromene 8 and its 1,2-dibromo addition compound 9, which eliminates HBr in an E1 process to finally afford 7. Analytical data including crystal structures of both 6 and 7 are reported.