Evolution of a black hole-inhabited brane close to reconnection

Last moments of a mini black hole escaping from a brane are studied. It is argued that at the point of reconnection, where the piece of the brane attached to the black hole separates from the rest, the worldsheet of the brane becomes isotropic (light-like). The degenerate mode of evolution, with the worldsheet isotropic everywhere, is investigated. In particular, it is shown that the brane approaches the reconnection point from below if it reconnects within a certain limit distance, and from above if it reconnects beyond that distance. The rate of relaxation to the degenerate mode is established. If the dimension of the brane is $p$, the nondegeneracy, measured by the determinant of the relevant part of the induced metric tensor, falls down as (latitudinal angle)$^{2(p - 1)}$.Comment: 20 pages, 4 figure

Stability with respect to domain of the low Mach number limit of compressible viscous fluids

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter \ep \to 0 and the fluid is confined to an exterior spatial domain \Omega_\ep that may vary with \ep. As $\epsilon \rightarrow 0$, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.Comment: 32 page

Dissociative recombination measurements of HCl+ using an ion storage ring

We have measured dissociative recombination of HCl+ with electrons using a merged beams configuration at the heavy-ion storage ring TSR located at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. We present the measured absolute merged beams recombination rate coefficient for collision energies from 0 to 4.5 eV. We have also developed a new method for deriving the cross section from the measurements. Our approach does not suffer from approximations made by previously used methods. The cross section was transformed to a plasma rate coefficient for the electron temperature range from T=10 to 5000 K. We show that the previously used HCl+ DR data underestimate the plasma rate coefficient by a factor of 1.5 at T=10 K and overestimate it by a factor of 3.0 at T=300 K. We also find that the new data may partly explain existing discrepancies between observed abundances of chlorine-bearing molecules and their astrochemical models.Comment: Accepted for publication in ApJ (July 7, 2013

Multi-scale analysis of compressible viscous and rotating fluids

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter \ep. If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account

A quantization procedure based on completely positive maps and Markov operators

We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other. Motivated by these facts, we describe a quantization procedure based on CP maps which are induced by Markov (transfer) operators. Classical dynamics are described by an action over essentially bounded functions. A non-expansive linear map, which depends on a choice of a probability measure, is the centerpiece connecting phenomena over function and matrix spaces

Spectroscopy and dissociative recombination of the lowest rotational states of H3+

The dissociative recombination of the lowest rotational states of H3+ has been investigated at the storage ring TSR using a cryogenic 22-pole radiofrequency ion trap as injector. The H3+ was cooled with buffer gas at ~15 K to the lowest rotational levels, (J,G)=(1,0) and (1,1), which belong to the ortho and para proton-spin symmetry, respectively. The rate coefficients and dissociation dynamics of H3+(J,G) populations produced with normal- and para-H2 were measured and compared to the rate and dynamics of a hot H3+ beam from a Penning source. The production of cold H3+ rotational populations was separately studied by rovibrational laser spectroscopy using chemical probing with argon around 55 K. First results indicate a ~20% relative increase of the para contribution when using para-H2 as parent gas. The H3+ rate coefficient observed for the para-H2 source gas, however, is quite similar to the H3+ rate for the normal-H2 source gas. The recombination dynamics confirm that for both source gases, only small populations of rotationally excited levels are present. The distribution of 3-body fragmentation geometries displays a broad part of various triangular shapes with an enhancement of ~12% for events with symmetric near-linear configurations. No large dependences on internal state or collision energy are found.Comment: 10 pages, 9 figures, to be published in Journal of Physics: Conference Proceeding

Energy-sensitive imaging detector applied to the dissociative recombination of D2H+

We report on an energy-sensitive imaging detector for studying the fragmentation of polyatomic molecules in the dissociative recombination of fast molecular ions with electrons. The system is based on a large area (10 cm x 10 cm) position-sensitive, double-sided Si-strip detector with 128 horizontal and 128 vertical strips, whose pulse height information is read out individually. The setup allows to uniquely identify fragment masses and is thus capable of measuring branching ratios between different fragmentation channels, kinetic energy releases, as well as breakup geometries, as a function of the relative ion-electron energy. The properties of the detection system, which has been installed at the TSR storage ring facility of the Max-Planck Institute for Nuclear Physics in Heidelberg, is illustrated by an investigation of the dissociative recombination of the deuterated triatomic hydrogen cation D2H+. A huge isotope effect is observed when comparing the relative branching ratio between the D2+H and the HD+D channel; the ratio 2B(D2+H)/B(HD+D), which is measured to be 1.27 +/- 0.05 at relative electron-ion energies around 0 eV, is found to increase to 3.7 +/- 0.5 at ~5 eV.Comment: 11 pages, 12 figures, submitted to Physical Review

Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?

We study the commutation relations within the Pauli groups built on all decompositions of a given Hilbert space dimension $q$, containing a square, into its factors. Illustrative low dimensional examples are the quartit ($q=4$) and two-qubit ($q=2^2$) systems, the octit ($q=8$), qubit/quartit ($q=2\times 4$) and three-qubit ($q=2^3$) systems, and so on. In the single qudit case, e.g. $q=4,8,12,...$, one defines a bijection between the $\sigma (q)$ maximal commuting sets [with $\sigma[q)$ the sum of divisors of $q$] of Pauli observables and the maximal submodules of the modular ring $\mathbb{Z}_q^2$, that arrange into the projective line $P_1(\mathbb{Z}_q)$ and a independent set of size $\sigma (q)-\psi(q)$ [with $\psi(q)$ the Dedekind psi function]. In the multiple qudit case, e.g. $q=2^2, 2^3, 3^2,...$, the Pauli graphs rely on symplectic polar spaces such as the generalized quadrangles GQ(2,2) (if $q=2^2$) and GQ(3,3) (if $q=3^2$). More precisely, in dimension $p^n$ ($p$ a prime) of the Hilbert space, the observables of the Pauli group (modulo the center) are seen as the elements of the $2n$-dimensional vector space over the field $\mathbb{F}_p$. In this space, one makes use of the commutator to define a symplectic polar space $W_{2n-1}(p)$ of cardinality $\sigma(p^{2n-1})$, that encodes the maximal commuting sets of the Pauli group by its totally isotropic subspaces. Building blocks of $W_{2n-1}(p)$ are punctured polar spaces (i.e. a observable and all maximum cliques passing to it are removed) of size given by the Dedekind psi function $\psi(p^{2n-1})$. For multiple qudit mixtures (e.g. qubit/quartit, qubit/octit and so on), one finds multiple copies of polar spaces, ponctured polar spaces, hypercube geometries and other intricate structures. Such structures play a role in the science of quantum information.Comment: 18 pages, version submiited to J. Phys. A: Math. Theo

Perfect-fluid cylinders and walls - sources for the Levi-Civita space-time

The diagonal metric tensor whose components are functions of one spatial coordinate is considered. Einstein's field equations for a perfect-fluid source are reduced to quadratures once a generating function, equal to the product of two of the metric components, is chosen. The solutions are either static fluid cylinders or walls depending on whether or not one of the spatial coordinates is periodic. Cylinder and wall sources are generated and matched to the vacuum (Levi--Civita) space--time. A match to a cylinder source is achieved for -\frac{1}{2}<\si<\frac{1}{2}, where \si is the mass per unit length in the Newtonian limit \si\to 0, and a match to a wall source is possible for |\si|>\frac{1}{2}, this case being without a Newtonian limit; the positive (negative) values of \si correspond to a positive (negative) fluid density. The range of \si for which a source has previously been matched to the Levi--Civita metric is 0\leq\si<\frac{1}{2} for a cylinder source.Comment: 22 pages, LaTeX, one included figure. Revised version: three (non-perfect-fluid) interior solutions are added, one of which falsifies the original conjecture in Sec. 4, and the circular geodesics of the Levi-Civita space-time are discussed in a footnot

Two-Dimensional Black Holes and Planar General Relativity

The Einstein-Hilbert action with a cosmological term is used to derive a new action in 1+1 spacetime dimensions. It is shown that the two-dimensional theory is equivalent to planar symmetry in General Relativity. The two-dimensional theory admits black holes and free dilatons, and has a structure similar to two-dimensional string theories. Since by construction these solutions also solve Einstein's equations, such a theory can bring two-dimensional results into the four-dimensional real world. In particular the two-dimensional black hole is also a black hole in General Relativity.Comment: 11 pages, plainte