Approximationseigenschaft,Lifting und Kohomologie bei lokalkonvexen Produktgarben

Motivated by examples like spaces of solutions of hypoelliptic operators, we treat product sheaves, prove density theorems in connection with the approximation property and use them for results on liftings and the vanishing of cohomology groups. Theorems of this type (2.4,2.9,3.3) are derived on regular subsets (2.3) of a product for product sheaves, where one factor has essentially a partition of unity. In the case of the compact open topology, we obtain the approximation property on arbitrary open subsets by a localization principle (4.5,4.9). The nuclearity of a sheaf in the co-topology turns out to imply strong nuclearity (1.11); the same is shown for the sheaf of holomorphic functions on the dual of a strongly nuclear (F)-space (1.12).

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Herrn Professor Gottfried Köthe zum 70. Geburtstag gewidmet     

Die Zusammenhangskomponenten der Lösungen analytischer Plateauprobleme

Ohne Zusammenfassung     

Photoconductance of two-dimensional ballistic microstructures

We calculate the photoconductance of two-dimensional ballistic microstructures subject to a high-frequency electromagnetic field. First, we study a simple quantum point contact. Absorption of photons is due to electronic transitions between different modes. A transition between a propagating and a nonpropagating mode results effectively in a backscattering process, and gives a negative or positive contribution to the current, depending on the gate voltage; the total quantized conductance acquires an additional, quite pronounced step-structure. Then, we demonstrate a new effect where the electron-photon interaction in a structure of slightly more complex geometry plays the same role as impurity scattering does in a “dirty” system. All relevant photons of the external electromagnetic field are coherent and spatial interference effects in electron-photon scattering become possible in spite of the inelastic nature of the collisions. These interference effects can be controlled by the gate voltage or the frequency of the electromagnetic field. As an illustration we calculate the photoconductance of a double point-contact geometry.     

Geometric doppler effect: spin-split dispersion of thermal radiation

A geometric Doppler effect manifested by a spin-split dispersion relation of thermal radiation is observed. A spin-dependent dispersion splitting was obtained in a structure consisting of a coupled thermal antenna array. The effect is due to a spin-orbit interaction resulting from the dynamics of the surface waves propagating along the structure whose local anisotropy axis is rotated in space. The observation of the spin-symmetry breaking in thermal radiation may be utilized for manipulation of spontaneous or stimulated emission.     

Paracyclophanes as model compounds for strongly interacting π-systems. Part 2: mono-hydroxy[2.2]paracyclophane

The structure of the electronic ground- and first excited state of mono-hydroxy [2.2]paracyclophane (MHPC) and the S(1)← S(0) electronic transition have been investigated by resonance-enhanced multiphoton ionisation (REMPI) and by quantum chemical spin-component-scaled-approximate coupled cluster second order (SCS-CC2) computations. The origin of the S(1)← S(0) transition was located at 30,772 cm(-1) (3.815 eV) in the REMPI spectrum. The value has to be compared with a computed excitation energy of 3.79 eV. The vibrational structure of the spectrum confirms a significant geometry change upon excitation along the coordinates corresponding to twist- and shift-motions in the molecule. It gives rise to an experimentally observed progression with a fundamental of +30 cm(-1) and an inverse anharmonicity. From the experimental data a shallow potential along the twist coordinate was derived for the S(1) state. For the shift vibration a wavenumber of +91 cm(-1) was observed, while +85 cm(-1) was computed. The ionisation energy of MHPC was determined to be 7.63 ± 0.05 eV using synchrotron radiation. When compared to earlier results on the parent compound [2.2]paracyclophane and pseudo-ortho-dihydroxy[2.2]paracyclophane it can be seen that already small variations in the substitution pattern have a significant impact on the shapes of the involved potential energy surfaces leading to strong variations in ground and excited state geometries and opto-electronic properties governing the exciton transfer processes.     

Observation of the spin-based plasmonic effect in nanoscale structures

Observation of surface-plasmon phenomena that are dependent upon the handedness of the circularly polarized incident light (spin) is presented. The polarization-dependent near-field intensity distribution obtained in our experiment is attributed to the presence of a geometric phase arising from the interaction of light with an anisotropic and inhomogeneous nanoscale structure. A near-field vortex surface mode with a spin-dependent topological charge was obtained in a plasmonic microcavity. The remarkable phenomenon of polarization-sensitive focusing in a plasmonic structure was also demonstrated.