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.     

Michael reaction. IV. NaNH2 catalyzed one stage reaction between phenylacetic acid dialkylamides and cinnamic acid methyl ester or dialkylamides. Influence of reaction conditions on the stereochemistry

The NaNH₂ catalyzed one stage reaction between phenylacetic acid dialkylamides and cinnamic acid methyl ester or dialkylamides was studied under various conditions. Conditions were found for easy preparation of each of the both possible diastereomeric derivatives of 2,3-diphenylglutaric acid. It was proved that catalytic amounts of NaNH₂ take part in the reaction. It is assumed that the observederythro/threo equilibrium ratios are determined by an isomerization via two different carbanions (at C₂ and C₄) of the reaction products.Part III:J. Stefanovsky andL. Viteva, Comun. Dept. Chem. Bulg. Acad. Sci.4, 159 (1971).     

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.     

Complete band gaps in one-dimensional left-handed periodic structures

Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic band gap. It is believed that modulation of the refractive index in all three spatial dimensions is required to open a complete band gap and prevent the propagation of electromagnetic waves in all directions. Here we reveal that, in sharp contrast to what was known before and contrary to the accepted physical intuition, a one-dimensional periodic structure containing the layers of transparent left-handed (or negative-index) metamaterial can trap light in three-dimensional space due to the existence of a complete band gap.     

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.