Eine notwendige und hinreichende Bedingung für Doppelreihen

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Über einen Lückensatz für Dirichletsche Reihen

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Über das Wachstum analytischer Funktionen in Halbstreifen und ähnlichen Gebieten

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Ensemble modeling of very small ZnO nanoparticles

The detailed structural characterization of nanoparticles is a very important issue since it enables a precise understanding of their electronic, optical and magnetic properties. Here we introduce a new method for modeling the structure of very small particles by means of powder X-ray diffraction. Using thioglycerol-capped ZnO nanoparticles with a diameter of less than 3 nm as an example we demonstrate that our ensemble modeling method is superior to standard XRD methods like, e.g., Rietveld refinement. Besides fundamental properties (size, anisotropic shape and atomic structure) more sophisticated properties like imperfections in the lattice, a size distribution as well as strain and relaxation effects in the particles and-in particular-at their surface (surface relaxation effects) can be obtained. Ensemble properties, i.e., distributions of the particle size and other properties, can also be investigated which makes this method superior to imaging techniques like (high resolution) transmission electron microscopy or atomic force microscopy, in particular for very small nanoparticles. For the particles under study an excellent agreement of calculated and experimental X-ray diffraction patterns could be obtained with an ensemble of anisotropic polyhedral particles of three dominant sizes, wurtzite structure and a significant relaxation of Zn atoms close to the surface.     

Behavior of electronic interferometers in the nonlinear regime

We investigate theoretically the behavior of the current oscillations in an electronic Mach-Zehnder interferometer (MZI) as a function of its source bias. Recently, the MZI visibility data showed an unexplained lobe pattern with a peculiar phase rigidity. Moreover, the effect did not depend on the MZI path length difference. We argue that these effects may be a new many-body manifestation of particle-wave duality in quantum mechanics. When biasing the interferometer sources so much that multiple electrons are on each arm at any instant in time, quantum shot noise (a particle phenomena) must affect the interference pattern of the electrons that create it. A solution to the interaction Hamiltonian presented here shows that the interference visibility has a lobe pattern with applied bias that has a period proportional to the average path length and independent of the path length difference, together with a phase rigidity.     

Ein Satz über die absolute Konvergenz der Fourier-Reihe

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