Gravitational instabilities in Kerr space-times

In this paper we consider the possible existence of unstable axisymmetric modes in Kerr space times, resulting from exponentially growing solutions of the Teukolsky equation. We describe a transformation that casts the radial equation that results upon separation of variables in the Teukolsky equation, in the form of a Schr\"odinger equation, and combine the properties of the solutions of this equations with some recent results on the asymptotic behaviour of spin weighted spheroidal harmonics to prove the existence of an infinite family of unstable modes. Thus we prove that the stationary region beyond a Kerr black hole inner horizon is unstable under gravitational linear perturbations. We also prove that Kerr space-time with angular momentum larger than its square mass, which has a naked singularity, is unstable.Comment: 9 pages, 4 figures, comments, references and calculation details added, asymptotic expansion typos fixe

Classical and quantum three-dimensional integrable systems with axial symmetry

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of a kinetic part plus a potential dependent on the position only, the $z$-component of the angular momentum, $L$, and a Hamiltonian-like constant, $\widetilde H$, for which the kinetic part is quadratic in the momenta. We find the explicit form of these potentials compatible with complete integrability. The classical equations of motion, written in terms of two arbitrary potential functions, is separated in oblate spheroidal coordinates. The quantization of such systems leads to a set of two differential equations that can be presented in the form of spheroidal wave equations.Comment: 17 pages, 3 figure

Westbrook's Molecular Gun: Discovery of Near-IR Micro-Structures in AFGL 618

We present high-sensitivity near-IR images of a carbon-rich proto-planetary nebula, AFGL 618, obtained with the Subaru Telescope. These images have revealed ``bullets'' and ``horns'' extending farther out from the edges of the previously known bipolar lobes. The spatial coincidence between these near-IR micro-structures and the optical collimated outflow structure, together with the detection of shock-excited, forbidden IR lines of atomic species, strongly suggests that these bullets and horns represent the locations from which [\ion{Fe}{2}] IR lines arise. We have also discovered CO clumps moving at $> 200$ km s$^{-1}$ at the positions of the near-IR bullets by re-analyzing the existing $^{12}$CO $J=1-0$ interferometry data. These findings indicate that the near-IR micro-structures represent the positions of shocked surfaces at which fast-moving molecular clumps interface with the ambient circumstellar shell.Comment: 2 figures. To appear in the ApJ Letter

Polarized Spectroscopy Studies of Single Molecules of Porphycenes

Using ambient atmosphere instead of pure nitrogen environment enabled efficient recording of room temperature fluorescence from single molecules of porphycenes, chromophores with a high triplet formation efficiency. Double hydrogen transfer between two chemically identical trans tautomers has been demonstrated for parent porphycene and three alkyl derivatives by the analysis of spatial patterns of the emission obtained after raster scanning the sample excited with an appropriately polarized laser beam. Because of tautomerization, fluorescence in porphycenes is due to two nearly orthogonal transition dipole moments. This property allows the spatial orientation of the single molecule chromophores to be determined using radially and azimuthally polarized laser beams as excitation sources

Scalable register initialization for quantum computing in an optical lattice

The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation.Comment: 5 pages, 2 figure