The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces

Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c₀ and ?_p for 1?p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E?(⊕?₂ⁿ)_c0, that is, E is the c₀-direct sum of the finite-dimensional Hilbert spaces ?₂¹,?₂²,…,?₂ⁿ,… .     

Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source

A coherent anti-Stokes Raman scattering microscope based on a Ti:sapphire femtosecond oscillator and a photonic crystal fiber is demonstrated. The nonlinear response of the fiber is used to generate the additional wavelength needed in the Raman process. The applicability of the setup is demonstrated by imaging of micrometer-sized polystyrene beads.     

Ferroelectricity and structure of BaTiO3 grown on YBa 2Cu3O_{7 - \delta } thin films

We have investigated the crystal structure and the ferroelectric properties of BaTiO₃ thin films with YBa₂Cu₃O as the bottom and Au as the top electrode. Epitaxial heterostructures of YBa₂Cu₃O and BaTiO₃ were prepared by dc and rf sputtering, respectively. The crystal structure of the films was characterised by X-ray diffraction. The ferroelectric behaviour of the BaTiO₃ films was confirmed by hysteresis loop measurements using a Sawyer Tower circuit. We obtain a coercive field of 30 kV/cm and a remanent polarisation of 1.25 μC/cm². At sub-switching fields the capacitance of the films obeys a relation analogous to the Rayleigh law. This behaviour indicates an interaction of domain walls with randomly distributed pinning centres. At a field of 5 MV/m we calculate a 3% contribution of the irreversible domain wall motion to the total dielectric constant. Received 24 June 1999 and Received in final form 27 August 1999     

Oxidative degradation of nitrogen-containing organic compounds: vaccum-ultraviolet (VUV) photolysis of aqueous solutions of 3-amino 5-methylisoxazole

The oxidative degradation of 3-amino 5-methyl isoxazole initiated by the VUV photolysis of water at 172 nm has been studied. Mineralization of CO₂, H₂O, NO ₃ ^– and NH ₄ ⁺ is more efficient when reductive conditions (argon saturated solutions) are favoured. Formation of compounds which cannot be completely oxidised to CO₂ is observed. Experiments performed under strictly oxidative conditions show higher yields of these inert compounds and, hence, incomplete mineralization. Cyanide was formed in concentrations lower than 5×10^–5 mol/l. In alkaline aqueous solutions, cyanide is completely transformed into CO ₃ ^2– , NH ₄ ⁺ and NO ₃ ^– during the irradiation time needed to mineralize the isoxazole. Therefore, cyanide does not present a potential risk for the use of the VUV photolysis for isoxazole degradation. Similarly, organic nitrogen is converted into both, NO ₃ ^– and NH ₄ ⁺ . The relative concentrations of the two ions depend on total irradiation time, oxygen saturation and reactor geometry. A sequence of reactions is proposed and discussed.Dedicated to Professor Dr. Dieter Klockow on the occasion of his 60th birthday     

Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions

The ground state energy of an atom of nuclear charge Ze in a magnetic field B is evaluated exactly to leading order as Z → ∞. In this and a companion work (see [28]) we show that there are five regions as Z → ∞: B < Z^4/3, B ～ Z^4/3, Z^4/3 < B < Z³, B ～ Z³, B > Z³. Regions 1, 2, 3, and 4 (and conceivably 5) are relevant for neutron stars. Different regions have different physics and different asymptotic theories. Regions 1, 2, and 3 are described by a simple density functional theory of the semiclassical Thomas-Fermi form. Here we concentrate mainly on regions 4 and 5 which cannot be so described, although 3, 4, and 5 have the common feature (as shown here) that essentially all electrons are in the lowest Landau band. Region 5 does have, however, a simple non-classical density functional theory (which can be solved exactly). Region 4 does not, but, surprisingly, it can be described by a novel density matrix functional theory. © 1994 John Wiley & Sons, Inc.     

Partially Commutative Moment Problems

Partially commutative tensor algebras occur naturally in the algebraic formulation of Wightman field theory. A state on an algebra of this type leads via GNS-construction to a partially commutative family of hermitean operators on Hilbert space. We discuss the question when these operators can be extended to self adjoint operators preserving the commutation properties and state a necessary and sufficient condition for the existence of such an extension in terms of a positivity property of the state.     

Bose-Einstein condensate coupled to a nanomechanical resonator on an atom chip

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.     

Material Discrimination in Nanoparticle Hetero-Aggregates by Analysis of Scanning Transmission Electron Microscopy Images

Hetero-contacts are interfaces between different materials at the nanoscale leading to novel functional properties. In hetero-aggregates, primary particles of at least two different materials are mixed at primary particle or cluster level. Double flame spray pyrolysis (DFSP) is a versatile technique for the controlled synthesis of such materials. Characterization of hetero-aggregates by scanning transmission electron microscopy (STEM) requires acquisition and evaluation of many aggregate images in order to derive statistically significant results. Usually, STEM energy dispersive X-ray spectroscopy (EDXS) is used to acquire elemental maps providing the material distribution of the primary particles within hetero-aggregates. However, the acquisition of a single EDXS map takes up to several minutes. For this reason, determination of material types of primary particles from the intensity in high-angle annular dark field STEM images alone is desirable. These images can be acquired within a couple of seconds. In the present work, a method is suggested which allows for achieving this objective. It can be applied to distinguish materials with a significant difference in their atomic number and hence sufficient material contrast in the STEM images.