A Deformation-Theoretical Approach to Weyl Quantization on Riemannian Manifolds

By using a sheaf-theoretical language, we introduce a notion of deformation quantization allowing not only for formal deformation parameters but also for real or complex ones as well. As a model for this approach to deformation quantization, we construct a quantization scheme for cotangent bundles of Riemannian manifolds. Here, we essentially use a complete symbol calculus for pseudodifferential operators on a Riemannian manifold. Depending on a scaling parameter, our quantization scheme corresponds to normally ordered, Weyl or antinormally ordered quantization. Finally, it is shown that our quantization scheme induces a family of pairwise isomorphic strongly closed star products on a cotangent bundle.     

An algebraic index theorem for orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem.     

The localized longitudinal index theorem for Lie groupoids and the van Est map

We define the “localized index” of longitudinal elliptic operators on Lie groupoids associated with Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of the localized index, is an action of the Hopf algebroid of jets around the unit space, and the characteristic map it induces on Lie algebroid cohomology. This map can be globalized to differentiable groupoid cohomology, giving a definition of the “global index”, that can be computed by localization. This correspondence between the “global” and “localized” index is given by the van Est map for Lie groupoids.     

Observation of doubly charged lead clusters below the critical size limit for Coulomb explosion of sphere configurations

Doubly charged lead clusters Pb₇²⁺, Pb₉²⁺, Pb₁₁²⁺ and Pb₁₃²⁺, far below the critical size for Coulomb explosion of par ticles with sphere like configurations (Pb₃₀) have been detected in time of flight mass spectra. Their existence can be explained by chain-like clusters.     

The effect of oxygen exposure on pentacene electronic structure

We use ultraviolet photoelectron spectroscopy to investigate the effect of oxygen and air exposure on the electronic structure of pentacene single crystals and thin films. It is found that O₂ and water do not react noticeably with pentacene, whereas singlet oxygen/ozone readily oxidize the organic compound. Also, we obtain no evidence for considerable p-type doping of pentacene by O₂ at low pressure. However, oxygen exposure lowers the hole injection barrier at the interface between Au and pentacene by 0.25 eV, presumably due to a modification of the Au surface properties.     

Reducing of birefringence of [111]-cut crystal rod using side-pumping and suitable crystal rotation

The beam quality and output power of high power solid-state lasers is influenced by birefringence. Inhomogeneous distribution of the thermal field inside the laser crystal rod occurs due to non-uniform absorption of the pump light inside the crystal and a heat sink only at boundaries. Due to the photoelastic effect, this distribution leads to inhomogeneous thermal strains and birefringence inside the rod. Plane stress and plane strain assumptions for an axially symmetric pumped crystal have been used formerly for analytical models for calculating the birefringence. This model leads in case of an [111]-cut crystal to an axially symmetric birefringence pattern. However, the shear strains in the axial-radial plane are neglected in this former models using plane stress and plane strain assumptions. This shear strains are taken into account by full 3D numerical calculations. A threefold symmetry pattern due to the anisotropic behaviour of the photoelastic tensor, which is contradictory to the ideal use of a radial or azimuthal polarized beam, is shown by results of the birefringence simulation. A laser rod pumped at three sides with threefold symmetry is analysed in order to reduce the effect of birefringence. In this case the absorption is not axially symmetric anymore. Within the crystal in regions where pumping is stronger, the pump light absorption and consequently the temperature, the strains and birefringence are higher. The degree of three-fold symmetry of birefringence will be reduced, if the region having a low birefringence due to the photoelastic effect is more strongly pumped than the rest of domain. This means the birefringence is affected by the rotation of crystal around its [111]-axis. By an optimal rotation with respect to the edges of the crystal, smallest birefringence can be obtained. For generating radial or azimuthal polarizations, the output beam of this laser device is therefore more suitable. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Algebraic Index for Riemannian Étale Groupoids

In this paper, we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a Riemannian étale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for Riemannian étale groupoids. We discuss solutions to that index problem when the groupoid is proper or defined by a constant Dirac structure on a 3-dimensional torus.     

Triphenylene silanes for direct surface anchoring in binary mixed self-assembled monolayers

New triphenylene-based silanes 2-(ω-(chlorodimethylsilyl)-n-alkyl)-3,6,7,10,11-penta-m-alkoxytriphenylene 4 (Tm-Cn) with n = 8 or 9 and m = 7, 8, 9, 10, or 11 were synthesized, and their self-assembly behavior in the liquid state and at glass and silicon oxide surfaces was investigated. The mesomorphic properties of triphenylene silanes 4 (Tm-Cn) and their precursors 3 (Tm-Cn) were determined by differential scanning calorimetry (DSC), polarizing optical microscopy (POM), and X-ray diffraction. From the small-angle X-ray scattering (SAXS) regime, a preferential discotic lamellar mesophase can be deduced, and wide-angle X-ray scattering (WAXS) highlights the liquid-like characteristics of the alkyl side chains. To transfer these bulk structural properties to thin films, self-assembled monolayers (SAMs) were obtained by adsorption from solution and characterized by water contact angle measurements, null ellipsometry, and atomic force microscopy (AFM). Employing the concentration as an additional degree of freedom, binary SAMs of 2-(ω-(chlorodimethylsilyl)-undecyl)-3,6,7,10,11-penta-decyloxytriphenylene 4 (T10-C11) were coassembled with chlorodecyldimethylsilane or chlorodimethyloctadecylsilane, and their capability as model systems for organic templating was evaluated. The structure of the resulting binary mixed SAMs was analyzed by water contact angle measurements, null ellipsometry, and X-ray reflectivity (XRR) in combination with theoretical modeling by a multidimensional Parratt algorithm and AFM. The composition dependence of film thickness and roughness can be explained by a microscopic model including the steric hindrance of the respective molecular constituents.