Area-preserving diffeomorphisms and higher-spin algebras

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonicd=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphereS ² as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic spaceS ^1,1, and can be rewritten as . As an application of our results, we formulate a newd=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms ofS ^1,1.     

Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box

We analyze the quantum dynamics of a micromechanical resonator capacitively coupled to a Cooper-pair box. With appropriate quantum state control of the Cooper box, the resonator can be driven into a superposition of spatially separated states. The Cooper box can also be used to probe the decay of the resonator superposition state due to environmental decoherence.     

Synthesis of hyperbranched poly(aryl amine)s via a carbene insertion approach

A novel diazirine functionalised aniline derivative, 3-(3-aminophenyl)-3-methyldiazirine 1, was prepared and employed as an AB(2)-type monomer in the synthesis of hyperbranched polymers; thus providing the first instance in which polyamines have been prepared via carbene insertion polymerisation. Photolysis of the monomer 1 in bulk and in solution resulted in the formation of hyperbranched poly(aryl amine)s with degrees of polymerisation (DP) varying from 9 to 26 as determined by gel permeation chromatography (GPC). In solution, an increase in the initial monomer concentration was generally found to result in a decrease in the molecular weight characteristics of the resulting poly(aryl amine)s. Subsequent thermal treatment of the poly(aryl amine)s caused a further increase in the DP values up to a maximum of 31. Nuclear magnetic resonance (NMR) spectroscopic analysis revealed that the increase in molecular weight upon thermal treatment resulted from hydroamination of styrenic species formed in the initial photopolymerisation or activation of diazirine moieties.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.