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.     

Infinite order differential operators in spaces of entire functions

Differential operators ?(Δ_θ,ω), where ? is an exponential type entire function of a single complex variable and Δ_θ,ω=(θ+ωz)D+zD², D=∂/∂z, , θ?0, , acting in the spaces of exponential type entire function are studied. It is shown that, for ω?0, such operators preserve the set of Laguerre entire functions provided the function ? also belongs to this set. The latter consists of the polynomials possessing real nonpositive zeros only and of their uniform limits on compact subsets of the complex plane . The operator exp(aΔ_θ,ω), a?0 is studied in more details. In particular, it is shown that it preserves the set of Laguerre entire functions for all . An integral representation of exp(aΔ_θ,ω), a>0 is obtained. These results are used to obtain the solutions to certain Cauchy problems employing Δ_θ,ω.     

Whitney's extension problem for multivariate -functions

We prove that the trace of the space to an arbitrary closed subset is characterized by the following ``finiteness' property. A function belongs to the trace space if and only if the restriction to an arbitrary subset consisting of at most can be extended to a function such that

The constant is sharp.

The proof is based on a Lipschitz selection result which is interesting in its own right.

     

Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals

A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N , correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough.     

Power losses in the international linear collider 20 mrad extraction line at 1 TeV

We have performed a detailed study of the power losses in the post-collision extraction line of a TeV e ⁺ e ⁻ collider with a crossing angle of 20 mrad at the interaction point. Five cases were considered: four luminosity configurations for ILC and one for CLIC. For all of them, the strong beam-beam effects at the interaction point lead to an emittance growth for the outgoing beam, as well as to the production of beamstrahlung photons and e ⁺ e ⁻ coherent pairs. The power losses along the extraction line, which are due to energy deposition by a fraction of the disrupted beam, of the beamstrahlung photons and of the coherent pairs, were estimated in the case of ideal collisions, as well as with a vertical position or angular offset at the interaction point.      

Self-collimation and beam splitting in low-index photonic crystals

We study self-collimation and beam splitting in low-refractive-index photonic crystals created within chalcogenide glass. We propose a beam splitter structure that allows direct experimental verification of photonic-crystal effects at optical wavelengths in a straightforward and definitive manner. The beam splitter provides angular separation of 90° using a highly compact spatial footprint, thus delivering direct application in highly integrated photonic devices.     

Efficient Olefin Epoxidation by Robust Re4 Cluster‐Supported MnIII Complexes with Peracids: Evidence of Simultaneous Operation of Multiple Active Oxidant Species,MnVO,MnIVO,and MnIII?OOC(O)R

Two new tetranuclear chalcocyanide cluster complexes, [{Mn(saloph)H₂O}₄Re₄Q₄(CN)₁₂]?4 CH₃OH? 8 H₂O (saloph=N,N′‐o‐phenylenebis(salicylidenaminato), Q=Se ( 1 ‐Se), Te ( 2 ‐Te)), have been synthesized by the diffusion of a methanolic solution of [PPh₄]₄[Re₄Q₄(CN)₁₂] into a methanolic solution of [Mn(saloph)]⁺. The structure of 2 ‐Te has been determined by X‐ray crystallography. These rhenium cluster‐supported [Mn^III(saloph)] complexes have been found to efficiently catalyze a wide range of olefin epoxidations under mild experimental conditions in the presence of meta‐chloroperbenzoic acid (mCPBA). Olefin epoxidation by these catalysts is proposed to involve the multiple active oxidants Mn^V?O, Mn^IV?O, and Mn^III? OOC(O)R. Evidence in support of this interpretation has been derived from reactivity and Hammett studies, H₂¹⁸O‐exchange experiments, and the use of peroxyphenylacetic acid as a mechanistic probe. Moreover, it has been observed that the participation of Mn^V?O, Mn^IV?O, and Mn^III? OOC(O)R can be controlled by changing the substrate concentration. This mechanism provides the greatest congruity with related oxidation reactions that employ certain Mn complexes as catalysts.     

Quantitative real-time measurements of DNA hybridization with alkylated nonoxidized silicon nanowires in electrolyte solution

The quantitative, real-time detection of single-stranded oligonucleotides with silicon nanowires (SiNWs) in physiologically relevant electrolyte solution is demonstrated. Debye screening of the hybridization event is circumvented by utilizing electrostatically adsorbed primary DNA on an amine-terminated NW surface. Two surface functionalization chemistries are compared: an amine-terminated siloxane monolayer on the native SiO2 surface of the SiNW, and an amine-terminated alkyl monolayer grown directly on a hydrogen-terminated SiNW surface. The SiNWs without the native oxide exhibit improved solution-gated field-effect transistor characteristics and a significantly enhanced sensitivity to single-stranded DNA detection, with an accompanying 2 orders of magnitude improvement in the dynamic range of sensing. A model for the detection of analyte by SiNW sensors is developed and utilized to extract DNA-binding kinetic parameters. Those values are directly compared with values obtained by the standard method of surface plasmon resonance (SPR) and demonstrated to be similar. The nanowires, however, are characterized by higher detection sensitivity. The implication is that SiNWs can be utilized to quantitate the solution-phase concentration of biomolecules at low concentrations. This work also demonstrates the importance of surface chemistry for optimizing biomolecular sensing with silicon nanowires.