Block-Transitive Designs in Affine Spaces

This paper deals with block-transitive $t$-$(v,k,\lambda)$ designs in affine spaces for large $t$, with a focus on the important index $\lambda=1$ case. We prove that there are no non-trivial 5-$(v,k,1)$ designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-$(v,k,1)$ designs, except possibly when the group is one-dimensional affine. Our approach involves a consideration of the finite 2-homogeneous affine permutation groups.Comment: 10 pages; to appear in: "Designs, Codes and Cryptography

Tetravalent Colloids by Nematic Wetting

In an elegant paper, D. Nelson suggested a method to produce tetravalent colloids based on a tetrahedral configuration created on the surface of a spherical particle. It emerges from a two-dimensional nematic liquid crystal placed on a sphere due to the presence of four 1/2 disclinations, i.e., topological defects in the orientational order. In this paper we show that such a tetrahedral configuration also occurs in the wetting layers which form around spheres dispersed in a liquid crystal above the nematic-isotropic phase transition. Nematic wetting therefore offers an alternative route towards tetravalent colloids.Comment: 7 pages, 4 figures, submitted to Europhys. Let

Combined potential of future long-baseline and reactor experiments

We investigate the determination of neutrino oscillation parameters by experiments within the next ten years. The potential of conventional beam experiments (MINOS, ICARUS, OPERA), superbeam experiments (T2K, NOvA), and reactor experiments (D-CHOOZ) to improve the precision on the ``atmospheric'' parameters $\Delta m^2_{31}$, $\theta_{23}$, as well as the sensitivity to $\theta_{13}$ are discussed. Further, we comment on the possibility to determine the leptonic CP-phase and the neutrino mass hierarchy if $\theta_{13}$ turns out to be large.Comment: 4 pages, 4 figures, Talk given by T.S. at the NOW2004 workshop, Conca Specchiulla (Otranto, Italy), 11--17 Sept. 200

Corner overgrowth: Bending a high mobility two-dimensional electron system by 90 degrees

Introducing an epitaxial growth technique called corner overgrowth, we fabricate a quantum confinement structure consisting of a high-mobility GaAs/AlGaAs heterojunction overgrown on top of an ex-situ cleaved substrate corner. The resulting corner-junction quantum-well heterostructure effectively bends a two-dimensional electron system (2DES) at an atomically sharp $90^{\rm o}$ angle. The high-mobility 2DES demonstrates fractional quantum Hall effect on both facets. Lossless edge-channel conduction over the corner confirms a continuum of 2D electrons across the junction, consistent with Schroedinger-Poisson calculations of the electron distribution. This growth technique differs distinctly from cleaved-edge overgrowth and enables a complementary class of new embedded quantum heterostructures.Comment: 3 pages, 4 figures, latest version accepted to AP

Quantum Hypergraph States

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalised stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.Comment: 9+5 pages, 5 figures, 1 table, published versio