Gravity in non-commutative geometry

We study general relativity in the framework of non-commutative differential geometry. As a prerequisite we develop the basic notions of non-commutative Riemannian geometry, including analogues of Riemannian metric, curvature and scalar curvature. This enables us to introduce a generalized Einstein-Hilbert action for non-commutative Riemannian spaces. As an example we study a space-time which is the product of a four dimensional manifold by a two-point space, using the tools of non-commutative Riemannian geometry, and derive its generalized Einstein-Hilbert action. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gravity. This field is geometrically interpreted as describing the distance between the two points in the internal space.Dedicated to H. ArakiSupported in part by the Swiss National Foundation (SNF)     

Einfluss der Partikelgeometrie auf die optischen Eigenschaften stark absorbierender Farbstoffteilchen

The extinction coefficients of spherical and ellipsoidal modelparticles of complex index of refraction have been measured. In the case of spherical particles the results are in good agreement with the predictions of the MIE theory. An empirical relationship has been worked out which relates the optical behaviour of needle-shaped ellipsoidal particles of defined eccentricity and size to an equivalent MIE diameter. The measurements have been performed in the range of size 0,2 < D₀ < 1,3 μ and eccentricity 1 ? p < 10.     

Induced Absorption of C60 and a Water-Soluble C60-Derivative in SiO2 Sol-Gel Matrices

Porous sol-gel glasses, either impregnated with pure C₆₀ or doped with a methanofullerene derivative, have been studied and induced absorption or reverse saturable absorption (RSA) has been observed in both types of solid materials. The samples impregnated by pure C₆₀ mainly contain well-dispersed fullerene molecules. Unlike crystalline films of C₆₀, their absorption dynamics can be well described by a 5-level model, developed for non-interacting C₆₀-molecules in solutions. Methanofullerene samples, on the other hand, show signs of micellar aggregation and therefore RSA dynamics that are influenced by solid state effects. We observe an important decrease of transmission at high fluences for both kinds of samples, a shortened singlet-state lifetime to that observed in solution, but nonetheless, a triplet yield, that cannot be considered as negligible. In the case of pure C₆₀ in a sol-gel matrix, we can explain the faster de-excitation dynamics, relative to behavior in solution, mainly by the absence of stabilizing aromatic solvents and also by the interaction of the amorphous environment with the molecules. Concerning the methanofullerene samples, the acceleration of the de-excitation dynamics can be principally attributed to solid-state effects due to the micellar aggregation.     

A liquid crystalline supramolecular complex of C60 with a cyclotriveratrylene derivative

Cyclotriveratrylene (CTV) derivatives substituted with 9 (1) or 18 (2) long alkyl chains have been prepared. Whereas no liquid crystalline behavior has been observed for 1, the CTV derivative 2 has mesomorphic properties. Indeed, at room temperature compound 2 exhibits a nematic phase characterized by cybotactic groups with a local lamello-columnar order. Both CTV derivatives 1 and 2 are able to form supramolecular complexes with C60 in the solid state. In both cases, the 2:1 host-guest species have been obtained as brown compounds. No liquid crystalline behavior was observed for the supramolecular complex [C60 is included in (1)2]. In contrast, observation of the brown product obtained from C60 and the CTV derivative 2 directly after preparation by polarized optical microscopy revealed a fluid birefringent phase at room temperature. When the sample is heated above 70 degrees C, the birefringence of the texture under the microscope disappears and the X-ray diffraction pattern is transformed into a pattern characteristic of a cubic phase. For the first time in thermotropic liquid crystals, the space group of this cubic phase can be assigned as I4(1)32.     

Investigations of Thin Films with Amphiphilic Dendrimers Bearing Peripheral Fullerene Subunits

In spite of a molecular mass of 7704.6 g mol(-1), third-generation compound G3 (shown schematically; Z=C(8)H(17)) is able to form stable Langmuir films. In a systematic study, the amphiphilic properties of the corresponding dendrimers of first (G1) and second generation (G2), with one and two peripheral fullerene units, respectively, were investigated and a model could be proposed for the multilayer films obtained from G1.     

Generalized hypergeometric functions on the torus and the adjoint representation ofU q (sl 2)

We study the homology groups with coefficient in local systems arising in the free field representation of minimal models of conformal field theory on an elliptic curve with punctures. We define an action of the quantum enveloping algebraU _q (sl ₂) on a space of relative cycles, extending results obtained previously for the sphere. Absolute cycles are identified with singular vectors. In the case of one puncture, we find that the resulting topological representation is essentially the adjoint representation.     

Final state interactions in deuteron breakup by protons at 585 and 800 MeV

Neutron-proton final state interactions (FSI) were observed in the deuteron breakup reaction ²H(p, 2p)n-via a kinematically complete experiment at incident proton energies of 585 and 800 MeV. Kinematic conditions were chosen which allowed the final state proton and neutron to have small relative energies; data were taken at four proton c.m. scattering angles at 800 MeV, ranging from 71° to 119° and at 94° and 106° at 585 MeV. The data are analyzed in terms of the Goldberger-Watson formalism for final state interactions, and the individual contributions of the ¹S₀ and ³S₁ np states are determined. The ${}^3\text{S}{}_1{}^1\text{S}{}_0$ ratio is large, as expected from some reaction models. The ratio of ³S₁ (almost elastic) to pd elastic cross sections is in good agreement with FSI analysis.