Raman study of structural defects in SiO2 aerogels

The structure of the silica aerogels was studied by Raman spectroscopy. The spectra of the solid network resembles that of bulk silica with additional bands related to organic groups and a large amount of OH groups.The typical bands due to ring breathing also called defect bands D ₁ and D ₂ located at 490 and 610 cm^–1 are present. However, the evolution of the D ₂ band compared to that of OH band (980 cm^–1) seems apparently, in contradiction with the results previously reported in the literature. During heat treatments between 25 and 300°C the D ₂ and the OH bands increase simultaneously. Generally, in silica glass the defect band D ₂ grows at the expense of the OH groups.This result is explained by the oxidation of the organic compounds which, in this temperature range, leads to the formation of the both species (OH) and those related to siloxane rings. ²⁹Si MAS NMR results are in agreement with the Raman study.     

π-Nucleus scattering in the Lee model

The scattering operator of a “pion” on two “nucleons” is evaluated in the Lee model and is shown to be identical to the results of Watson's multiple scattering theory.     

Statistical model for intermolecular adhesion in pi-conjugated polymers

We propose an interchain binding mechanism in pi-conjugated polymers based on the intermolecular tunneling of the delocalized electrons occurring at points where the polymers cross. This mechanism predicts specific bound structures of chains that depend on whether they are semiconducting or metallic. Semiconducting chains should form polyacenelike states exhibiting binding at every other site, while (doped) metallic chains can bind at each site. We also show that solitons colocalize with the intermolecular binding sites thereby strengthening the binding effect and investigate the conformational statistics of the resulting bimolecular aggregates.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Experimental versus numerical eigenvalues of a Bunimovich stadium billiard: a comparison

We compare the statistical properties of eigenvalue sequences for a gamma=1 Bunimovich stadium billiard. The eigenvalues have been obtained in two ways: one set results from a measurement of the eigenfrequencies of a superconducting microwave resonator (real system), and the other set is calculated numerically (ideal system). We show influence of mechanical imperfections of the real system in the analysis of the spectral fluctuations and in the length spectra compared to the exact data of the ideal system. We also discuss the influence of a family of marginally stable orbits, the bouncing ball orbits, in two microwave stadium billiards with different geometrical dimensions.