Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

A sharp $L^p$ spectral multiplier theorem of Mihlin--H\"ormander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation

Komparative Untersuchung der EU-REIT-Regime

In der EU ist seit dem Jahre 2003 eine deutliche Zunahme von Real Estate Investment Trust Regimen (REIT-Regimen) zu verzeichnen. Von einem EU-weiten Standardprodukt oder einem EU-REIT-Markt kann allerdings nicht gesprochen werden. Durch unterschiedliches nationalstaatliches Recht, die steuerliche Souveränität der EU-Staaten und allgemein divergierende Interessenlagen bestehen erhebliche Disparitäten zwischen den Regimen. Somit stellt sich einerseits die Frage nach den Unterschieden in der gesetzlichen Ausgestaltung im Detail und andererseits nach den resultierenden Implikationen für die verschiedenen Marktteilnehmer. Ausgehend von dieser Fragestellung wurden in einem Forschungsprojekt des Lehrstuhls Immobilienwirtschaft und Baubetriebswirtschaftslehre die gesetzlichen Bestimmungen der verschiedenen REIT-Varianten im Detail untersucht, anhand einer einheitlichen Struktur gegenübergestellt und verglichen. Darauf aufbauend wurde eine Beurteilung der Vor- und Nachteile aus Perspektive unterschiedlicher Marktteilnehmer vorgenommen (Immobilien-Aktiengesellschaften mit Konversionsabsichten, Industrieunternehmen, die betriebliche Immobilien in einen REIT ausgliedern wollen, sowie potenzielle REIT-Investoren). Das vorliegende Arbeitspapier fasst die wesentlichen Ergebnisse des Forschungsprojektes zusammen und bietet sowohl einen Einblick in die verschiedenen REIT-Gesetzgebungen der EU als auch eine Orientierung für die angesprochenen Interessengruppen. Projektleiter ist Michael G. Müller.

Adsorption studies of DNA origami on silicon dioxide

Self-assembled DNA nanostructures promise low-cost ways to create nanoscale shapes. DNA nanostructures can also be used to position particles with nanometer precision. Yet, reliable and low-cost ways of integrating the structures with MEMS technology still have to be developed and innovations are of great interest to the field. We have examined in detail the adherence of DNA origami tiles on silicon oxide surfaces of wafers in dependence on pH-value and magnesium ion concentration. The results of this work will help to pursue new strategies of positioning DNA nanostruc-tures on SiO2. Precise control over the strength of structure-surface adhesion is a prerequisite of relia-ble processes

Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model

The fidelity metric has recently been proposed as a useful and elegant approach to identify and characterize both quantum and classical phase transitions. We study this metric on the manifold of thermal states for the Lipkin-Meshkov-Glick (LMG) model. For the isotropic LMG model, we find that the metric reduces to a Fisher-Rao metric, reflecting an underlying classical probability distribution. Furthermore, this metric can be expressed in terms of derivatives of the free energy, indicating a relation to Ruppeiner geometry. This allows us to obtain exact expressions for the (suitably rescaled) metric in the thermodynamic limit. The phase transition of the isotropic LMG model is signalled by a degeneracy of this (improper) metric in the paramagnetic phase. Due to the integrability of the isotropic LMG model, ground state level crossings occur, leading to an ill-defined fidelity metric at zero temperature.Comment: 18 pages, 3 figure

Thermodynamics of ideal quantum gas with fractional statistics in D dimensions

We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D>=1 and with fractional exclusion statistics 0<=g<=1 connecting bosons (g=0) and fermions (g=1). In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between boson-like and fermion-like features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. The full isochoric heat capacity and the leading low-T term of the isobaric expansivity in D=2 are independent of g. The onset of Bose-Einstein condensation along the isobar occurs at a nonzero transition temperature in all dimensions. The T-dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.Comment: 15 pages, 31 figure

Interface-mediated interactions: Entropic forces of curved membranes

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.