Self-written waveguides in photopolymerizable resins

We study the optically induced growth and interaction of self-written waveguides in a photopolymerizable resin. We investigate experimentally how the interaction depends on the mutual coherence and the relative power of the input beams and suggest an improved analytical model that describes the growth of single waveguides and the main features of their interaction in photosensitive materials.     

Classical Limits of Euclidean Gibbs States for Quantum Lattice Models

Models of quantum and classical particles on a lattice ^d are considered. The classical model is obtained from the corresponding quantum model when the reduced mass of the particle m = / #x210F;² tends to infinity. For these models, the convergence of the Euclidean Gibbs states, when m + , is described in terms of the weak convergence of local Gibbs specifications, determined by conditional Gibbs measures. In fact, it is shown that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with pair interactions possessing the translation invariance, has also been shown.     

Pi-envelopes of Lie superalgebras

In this paper we find necessary and sufficient conditions on a finite-dimensional Lie superalgebra under which any associative PI-envelope of is finite-dimensional. We also extend M. Scheunert's result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.

     

Bounded harmonic functions on nonamenable covers of compact manifolds

We show that the space of bounded harmonic functions on a nonamenable cover of a compact Riemannian manifold is infinite dimensional. Supported by US-Israel Binational Science Foundation Grant No. 84-00028.     

A room-temperature protocol for the rhodium(I)-catalyzed addition of arylboron compounds to sulfinimines

[reaction: see text] The addition of organoboronic acids to chiral sulfinimines proceeds under mild conditions at room temperature, using Rh(I) catalysis in the absence of external phosphine ligands. Clean reaction only occurs in the presence of water as a cosolvent. The sulfinamide adducts are formed with high diastereoselectivities, providing a convenient route to the synthesis of enantiomerically enriched chiral benzylic amines.     

Giant lamb shift in photonic crystals

We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.     

Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.     

The structure of poly(ethylene oxide)8: NaBPh4 from a single crystal oligomer and polycrystalline polymer

We show that the structure of a polymer electrolyte may be solved by growing single crystals of an oligomeric (short chain) complex which provided an adequate starting model for refinement of the equivalent polymeric structure using powder diffraction: the efficacy of this method has been demonstrated by determining for the first time the structure of an 8 : 1 complex, poly(ethylene oxide)(8) : NaBPh(4).