Percolation in strongly correlated systems: The massless Gaussian field

We derive a number of new results for correlated nearest neighbor site percolation onZ ^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS _x h percolate if and only ifh _c . with0 _c < . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.     

Étude de l'adsorption électrochimique de l'oxygène sur des lames minces d'or par la mesure de leur résistance électrique

The electrical resistance changes of thin gold film electrodes of preferential orientation [111] with film thickness and potential have been studied. The applicability of the Fuchs-Sondheimer (FS) relation to the decrease of resistance observed at the first negative polarization and the first few potential sweeps for different thicknesses have shown that this phenomenon is due to a surface process, interpreted as a cleaning of the electrodes. The resistance changes observed during the electrochemical adsorption and desorption of oxygen also obey the FS relation. The analysis of the resistance variation with the charge exchanged during these reactions has allowed us to show that the electrochemical adsorption of oxygen, on these gold films occurs by a two-dimensional island mechanism with formation of different structures of the surface layer. The values of the resistivity change caused by the adsorption of 1% oxygen atoms (with respect to the total number of metal atoms in the films) at low coverage have been compared with those observed in other systems (metal-gas, metal-metal).     

Spectral properties of a tight binding Hamiltonian with period doubling potential

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength.     

The traveling salesman problem in graphs with some excluded minors

Given a graph and a length function defined on its edge-set, the Traveling Salesman Problem can be described as the problem of finding a family of edges (an edge may be chosen several times) which forms a spanning Eulerian subgraph of minimum length. In this paper we characterize those graphs for which the convex hull of all solutions is given by the nonnegativity constraints and the classical cut constraints. This characterization is given in terms of excluded minors. A constructive characterization is also given which uses a small number of basic graphs.     

Distinctive field dependence of the longitudinal muon polarization for Mu* in polycrystalline silicon

A distinctive longitudinal magnetic field dependence of the muon polarization for anomalous muonium in polycrystalline semiconductor targets has been predicted. The polarization exhibits a cusp,i.e., a discontinuous jump in the slope from negative to positive. Measurements of the longitudinal polarization for polycrystalline silicon in fields up to 0.5 T, and temperatures 53 and 200 K have been made at LAMPF. A cusp in the field dependence indeed occurs at 0.345 T, in excellent agreement with the prediction. No cusp is observed at 200 K because Mu^* has been thermally ionized.