Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions

We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.     

33S solid state NMR of sulphur speciation in silicate glasses

³³S solid-state NMR is reported from some model crystalline sulphides, sulphates, sulphites and thiosulphates. This is the first report of ³³S NMR signals of the latter two species from a solid. Good quality spectra, which have distinct, well separated shift ranges can be identified for all these groupings, except for sulphites and hydrogen sulphites whose resonances are very broad. Nonetheless the presence of sulphites and hydrogen sulphites can be confirmed from their characteristic sharp, intense time domain echoes. ³³S MAS NMR is also applied to a range of dry and hydrous silicate glasses with 1wt% 99 at% ³³S-enriched sulphur. It is clear that in all these glasses sulphate is present, and in mixed cation systems there is some evidence of preferential association of sulphate with a specific cation. In a dry potassium silicate glass sample two resolved ³³S resonances are observed, a sulphate, and the second from thiosulphate. Hence solid state ³³S NMR is shown to be a feasible probe that can be applied to this problem that can readily distinguish different sulphur species.     

Resonator-enhanced optical dipole trap for fermionic lithium atoms

We demonstrate a novel optical dipole trap that is based on enhancement of the optical power density of a Nd:YAG laser beam in a resonator. The trap is particularly suited for experiments with ultracold gases, as it combines a potential depth of the order of 1 mK with storage times of several tens of seconds. We study the interactions in a gas of fermionic lithium atoms in our trap and observe the influence of spin-changing collisions and off-resonant photon scattering. A key element in reaching long storage times is the use of an ultralow-noise laser. The dependence of storage time on laser noise is investigated.     

Determination of the magnetic symmetry of hexagonal manganites by second harmonic generation

Optical second harmonic spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic x-ray diffraction experiments are overcome. High spatial resolution leads to additional information about magnetically ordered matter. As an example, the noncollinear magnetic structure of the hexagonal manganites RMnO3 ( R = Sc, Y, Ho, Er, Tm, Yb, Lu) is analyzed. The results show that some earlier conclusions on their magnetic symmetry and properties should be revised.     

Nonlinear robust optimization via sequential convex bilevel programming

In this paper, we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min–max problems which arise in the context of semi-infinite programming. Here, our main motivation are nonlinear inequality constrained robust optimization problems. In the first part of the paper, we propose a conservative approximation strategy for such nonlinear and non-convex robust optimization problems: under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given, we show how to formulate a lower-level concave min–max problem which approximates the robust counterpart in a conservative way. This approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties. In the second part of the paper, we review existing theory on optimality conditions for nonlinear lower-level concave min–max problems which arise in the context of semi-infinite programming. Regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem, we end up with a structured mathematical program with complementarity constraints (MPCC). The special hierarchical structure of this MPCC can be exploited in a novel sequential convex bilevel programming algorithm. We discuss the surprisingly strong global and locally quadratic convergence properties of this method, which can in this form neither be obtained with existing SQP methods nor with interior point relaxation techniques for general MPCCs. Finally, we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example.     

Ueber die cubischen Raumcurven,welche die Tangentenfläche einer gegebenen cubischen Raumcurve in vier,fünf oder sechs Punkten berühren

Ohne Zusammenfassung     

Über Derivate des Diacetonalkamins

Ohne Zusammenfassung