Elliptic fibrations associated with the Einstein spacetimes

Given a conformally nonflat Einstein spacetime we define a fibration $P$ over it. The fibres of this fibration are elliptic curves (2-dimensional tori) or their degenerate counterparts. Their topology depends on the algebraic type of the Weyl tensor of the Einstein metric. The fibration $P$ is a double branched cover of the bundle of null direction over the spacetime and is equipped with six linearly independent 1-forms which satisfy certain relatively simple system of equations.Comment: 15 pages, Late

Contribution to the myrmecofauna (Formicidae, Hymenoptera) of Mt. Kopaonik (Serbia)

The myrmecofauna of Serbia is still insufficiently investigated. In the past ants were not a challenge for the entomologists of Serbia, only a few of which paid attention to ants and registered some ant species among other insect species. Živojinović (1950) registered 18 species of ants in the forest region of Majdanpek (Serbia), although he considered some valid species (Lasius alienus, L. brunneus, Camponotus herculeanus, and Formica pratensis) as subspecies. Vogrin (1955) elaborated Hymenoptera Aculeata of Yugoslavia, and registered 16 species of ants in Serbia (Srem). Gradojević (1963) listed 11 species of ants of Deliblatska Peščara (Deliblato Sands) (Vojvodina, Serbia)

Two atoms in an anisotropic harmonic trap

We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional geometries. Finally, we discuss the application of an energy-dependent pseudopotential, which allows to extend the validity of our results to the case of tight traps and large scattering lengths.Comment: RevTeX 4 pages, 2 figure

Orbital and interlayer Skyrmions crystals in bilayer graphene

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where $\omega_{c}^{\ast}$ is the effective cyclotron frequency and $$ All Landau levels but N=0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N=0 has an extra degeneracy due to the fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of statesComment: 18 pages with 13 figure

On the algebraic classification of spacetimes

We briefly overview the Petrov classification in four dimensions and its generalization to higher dimensions.Comment: Submitted to Journal of Physics, conference series, proceedings of 4th meeting on constrained dynamics and quantum gravity, 12-16 September 2005, Sardinia, Ital