Measurements of αs\alpha_s from event shapes and the four-jet rate

New results from measurements of the strong coupling constant $\alpha_s(M_Z)$ at LEP are presented. In particular, a new LEP combination of results based on event-shape variables has become available, where a new method for the estimation of the theoretical uncertainty has been implemented. Furthermore, two other analyses are quoted, based on power corrections and the four-jet rate.Comment: Talk presented at the 31st International Conference on High Energy Physics, Amsterdam, 24-31 July 200

Systems of symplectic forms on four-manifolds

We study almost Hermitian 4-manifolds with holonomy algebra, for the canonical Hermitian connection, of dimension at most one. We show how Riemannian 4-manifolds admitting five orthonormal symplectic forms fit therein and classify them. In this set-up we also fully describe almost Kaehler 4-manifolds.Comment: Final version, to appear in Annali di SNS.added thm. 5.

Complex homothetic foliations on K\"ahler manifolds

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.Comment: Final version, up to typos. To appear in BLM

The Dicke model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity

We show that the motion of a laser-driven Bose-Einstein condensate in a high-finesse optical cavity realizes the spin-boson Dicke-model. The quantum phase transition of the Dicke-model from the normal to the superradiant phase corresponds to the self-organization of atoms from the homogeneous into a periodically patterned distribution above a critical driving strength. The fragility of the ground state due to photon measurement induced back action is calculated.Comment: 5 pages, 2 figure

Photonic tuning of quasi-particle decay in a superfluid

We show that the damping rate of elementary excitations of hybrid systems close to a phase transition can undergo a remarkable resonance like enhancement before mode softening takes place. In particular, we consider the friction of a collective density wave in a homogeneous superfluid of weakly interacting bosonic atoms coupled to the electromagnetic field of a single mode optical resonator. Here the Beliaev damping can thus be controlled by an external laser drive and be enhanced by several orders of magnitude