Generating ultralow-emittance ion beams in a storage ring

Laser cooling of heavy-ion beams in a storage ring is systematically studied with a multiparticle simulation code where not only exact lattice characteristics and space-charge forces but also realistic laser-ion interactions can be incorporated. The resonant coupling method is applied in order to extend the powerful longitudinal photon pressure to the transverse degrees of freedom. It is shown that, in spite of a space-charge-induced tune shift, the synchrobetatron resonance mechanism required for fast damping of transverse oscillations operates throughout the cooling process. Extremely efficient three-dimensional cooling of stored ion beams is thus feasible. It is demonstrated that, at low line density, normalized root-mean-squared emittances of the order of 10(-12) m.rad can be reached in all three directions by employing only existing technologies.     

On the Arithmetic of Del Pezzo Surfaces of Degree 2

We study the arithmetic of certain del Pezzo surfaces of degree2. We produce examples of Brauer-Manin obstruction to the Hasseprinciple, coming from 2- and 4-torsion elements in the Brauergroup. 2000 Mathematics Subject Classification 14G05 (primary),12G05 (secondary).     

On a Theorem of Høegh-Krohn

A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products , where \mathfraka _t , t are time automorphisms and F _j are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F _j taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator.     

Potentiometric and theoretical studies of the carbonate sensors based on 3-bromo-4-hexyl-5-nitrotrifluoroacetophenone

Novel carbonate ionophore, trifluoroacetophenone derivative (TFA) substituted by two acceptor substituents in the phenyl ring (3-bromo-4-hexyl-5-nitrotrifluoroacetophenone), was synthesized. Solvent polymeric membrane sensors based on this ionophore exhibited heightened selectivity to carbonate ions in the presence of the most important interfering anions. A wide range of potentiometric properties were studied and compared with those of sensors based on mono-substituted ionophores. Special attention was paid to pH dependence of sensor responses and to elaboration of appropriate conditions for carbonate analysis. A segmented-sandwich membrane method was applied for determination of the stoichiometry of ionophore-carbonate complexes, which was determined to be 1:3, and apparent complex formation constants which were 14.4 and 13.6 for DOS- and NPOE-plasticized membranes, respectively. Theoretical studies on TFA derivatives by semi-empirical (AM1 and PM3) and ab initio(6-31+G*) methods were performed, considering different types of possible ionophore-ion interactions. The formation of hydrogen bonds between carbonate and hydrated TFA was proved to be much more favourable in terms of energy compared to tetrahedral nucleophilic adducts that earlier were postulated to being formed in the membrane phase. The final conclusion on the mechanism of carbonate sensing by TFA-based solvent polymeric membrane sensors was made on the basis of computational data and detailed analysis of the literature.     

Using micelles for a new approach to fluorescent sensors for metal cations

A new approach based on self-assembly inside micelles has been individuated to prepare a system behaving as a water-operating selective fluorescent sensor for Cu2+ and Ni2+.     

Generation and stability of discrete gap solitons

We analyze stability and generation of discrete gap solitons in weakly coupled optical waveguides. We demonstrate how both stable and unstable solitons can be observed experimentally in the engineered binary waveguide arrays and also reveal a connection between the gap-soliton instabilities and limitations on the mutual beam focusing in periodic photonic structures.     

Spatial optical solitons supported by mutual focusing

We study composite spatial optical solitons supported by two-wave mutual focusing induced by cross-phase modulation in Kerr-like nonlinear media. We find the families of both single- and two-hump solitons and discuss their properties and stability. We also reveal remarkable similarities between recently predicted holographic solitons in photorefractive media and parametric solitons in quadratic nonlinear crystals.     

Matter-wave gap solitons in atomic band-gap structures

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons.     

Multigap discrete vector solitons

We analyze nonlinear collective effects in periodic systems with multigap transmission spectra such as light in waveguide arrays or Bose-Einstein condensates in optical lattices. We reveal that the interband interactions in nonlinear periodic structures can be efficiently managed by controlling their geometry. We predict novel types of discrete vector solitons supported by nonlinear coupling between different band gaps and study their stability.