“Model Hamiltonian for one- and two-dimensional superfluids”

A model Hamiltonian describing bosons in one and two space dimensions interacting via a repulsive interparticle potential is shown to give rise to the phenomenon of superfluidity. The model has macroscopic occupation of infinitely many single-particle quantum states and the energy spectrum of the elementary excitations exhibits both phonon and roton features. Relations are found between the roton parameters, the speed of first sound and the condensate fraction where any two of them can be taken as independent variables. It is also shown that the type of condensate considered is not excluded by any rigorous proof.     

Stereoselective Nickel‐Catalyzed [2+2] Cycloadditions of Ene‐Allenes

A stereoselective nickel‐catalyzed [2+2] cycloaddition of ene‐allenes is reported. This transformation encompasses a broad range of ene‐allene substrates, thus providing efficient access to fused cyclobutanes from easily accessed π‐components. A simple and inexpensive first‐row catalytic system comprised of [Ni(cod)₂] and dppf was used in this process, thus constituting an attractive approach to synthetically challenging cyclobutane frameworks under mild reaction conditions.     

Possibility of Self-Induced Transparency in Multi-Layer Semiconductor Heterostructure Placed in a Quantizing Magnetic Field

The possibility of self-induced transparency is discussed in a semiconductor structure with 3D-quantized electron spectrum. A model structure is proposed, for which a significant decrease of pulse duration and an increase of power is obtained.     

Inequalities among static and dynamic critical-point exponents

The mode-mode coupling theoretical expression for the decay rate of order-parameter fluctuations in simple fluids near the critical point is evaluated with the aid of the recently extended Ornstein-Zernike theory. This gives that ψ?ν for the critical-point exponent ψ which characterize the behavior of the thermal conductivity. Also, the results for sound-wave absorption and dispersion near the gas-liquid critical point need not depend on a single reduced frequency variable since scaling may be violated.     

Nonlinear Optical Processes in 3D-Quantized Spectrum of a Semiconductor

Two-photon and three-photon Raman scattering processes are considered. Analytical expressions are derived for the non-linear susceptibility, gain coefficient and generation threshold. It is shown that the resonant fluorescence accompanies the Raman scattering and the hot luminescence processes when the finite population of states is taken into account. Numerical evaluations show that the specification of the medium leads to low generation thresholds and high magnitudes of gain coefficients.     

Palladium-catalyzed ring-forming aminoacetoxylation of alkenes

A mild, palladium(II)-catalyzed ring-forming aminoacetoxylation of alkenes is described. Treatment of a range of nitrogen nucleophiles with catalytic palladium(II) in the presence of PhI(OAc)2 as oxidant resulted in alkene aminoacetoxylation, affording a variety of nitrogen-containing heterocycles. Our studies indicate the possibility for high levels of reaction regio- and stereocontrol. It appears that this is a stereoselective trans alkene difunctionalization and thus a useful alternative to related cis-selective, metal-catalyzed alkene aminohydroxylation processes.     

Mechanistic study of beta-hydrogen elimination from organoplatinum(II) enolate complexes

A detailed mechanistic investigation of the thermal reactions of a series of bisphosphine alkylplatinum(II) enolate complexes is reported. The reactions of methylplatinum enolate complexes in the presence of added phosphine form methane and either free or coordinated enone, depending on the steric properties of the enone. Kinetic studies were conducted to determine the relationship between the rates and mechanism of beta-hydrogen elimination from enolate complexes and the rates and mechanism of beta-hydrogen elimination from alkyl complexes. The rates of reactions of the enolate complexes were inversely dependent on the concentration of added phosphine, indicating that beta-hydrogen elimination from the enolate complexes occurs after reversible dissociation of a phosphine. A normal, primary kinetic isotope effect was measured, and this effect was consistent with rate-limiting beta-hydrogen elimination or C-H bond-forming reductive elimination to form methane. Reactions of substituted enolate complexes were also studied to determine the effect of the steric and electronic properties of the enolate complexes on the rates of beta-hydrogen elimination. These studies showed that reactions of the alkylplatinum enolate complexes were retarded by electron-withdrawing substituents on the enolate and that reactions of enolate complexes possessing alkyl substituents at the beta-position occurred at rates that were similar to those of complexes lacking alkyl substituents at this position. Despite the trend in electronic effects on the rates of reactions of enolate complexes and the substantial electronic differences between an enolate and an alkyl ligand, the rates of decomposition of the enolate complexes were similar to those of the analogous alkyl complexes. To the extent that the rates of reaction of the two types of complexes are different, those involving beta-hydrogen elimination from the enolate ligand were faster. A difference between the rate-determining steps for decomposition of the two classes of complexes and an effect of stereochemistry on the selectivity for beta-hydrogen elimination are possible origins of the observed phenomena.     

Generalized coherent state approach to star products and applications to the fuzzy sphere

We construct a star product associated with an arbitrary two-dimensional Poisson structure using generalized coherent states on the complex plane. From our approach one easily recovers the star product for the fuzzy torus, and also one for the fuzzy sphere. For the latter we need to define the ‘fuzzy’ stereographic projection to the plane and the fuzzy sphere integration measure, which in the commutative limit reduce to the usual formulae for the sphere.