On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type

We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations. Hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions, particularly that of having exponentially small remainders when truncated, and, as a consequence, provide a useful computational tool for evaluating special functions. The methods we discuss can be applied to linear differential equations of hypergeometric type and may have wider applicability

Optimal quantum repeaters for qubits and qudits

A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e. involve a single additional probe qubit, and optimal, i.e. provide the maximum information adding the minimum amount of noise. Information gain and state disturbance are quantified by fidelities which, for our schemes, saturate the ultimate bound imposed by quantum mechanics for randomly distributed signals. Special classes of signals are also investigated, in order to improve the information-disturbance trade-off. Extension to higher dimensional signals (qudits) is straightforward.Comment: Revised version. To appear in PR

A multi-epoch spectroscopic study of the BAL quasar APM 08279+5255: I. C IV absorption variability

Broad Absorption Lines indicate gas outflows with velocities from thousands km/s to about 0.2 the speed of light, which may be present in all quasars and may play a major role in the evolution of the host galaxy. The variability of absorption patterns can provide informations on changes of the density and velocity distributions of the absorbing gas and its ionization status. We collected 23 photometrical and spectro-photometrical observations at the 1.82m Telescope of the Asiago Observatory since 2003, plus other 5 spectra from the literature. We analysed the evolution in time of the equivalent width of the broad absorption feature and two narrow absorption systems, the correlation among them and with the R band magnitude. We performed a structure function analysis of the equivalent width variations. We present an unprecedented monitoring of a broad absorption line quasar based on 28 epochs in 14 years. The shape of broad absorption feature shows a relative stability, while its equivalent width slowly declines until it sharply increases during 2011. In the same time the R magnitude stays almost constant until it sharply increases during 2011. The equivalent width of the narrow absorption redwards of the systemic redshift only shows a decline. The broad absorption behaviour suggests changes of the ionisation status as the main cause of variability. We show for the first time a correlation of this variability with the R band flux. The different behaviour of the narrow absorption system might be due to recombination time delay. The structure function of the absorption variability has a slope comparable with typical optical variability of quasars. This is consistent with variations of the 200 A ionising flux originating in the inner part of the accretion disk.Comment: 10 pages, 8 figures, to appear on Astronomy & Astrophysic

Superspace formulation of general massive gauge theories and geometric interpretation of mass-dependent BRST symmetries

A superspace formulation is proposed for the osp(1,2)-covariant Lagrangian quantization of general massive gauge theories. The superalgebra os0(1,2) is considered as subalgebra of sl(1,2); the latter may be considered as the algebra of generators of the conformal group in a superspace with two anticommuting coordinates. The mass-dependent (anti)BRST symmetries of proper solutions of the quantum master equations in the osp(1,2)-covariant formalism are realized in that superspace as invariance under translations combined with mass-dependent special conformal transformations. The Sp(2) symmetry - in particular the ghost number conservation - and the "new ghost number" conservation are realized as invariance under symplectic rotations and dilatations, respectively. The transformations of the gauge fields - and of the full set of necessarily required (anti)ghost and auxiliary fields - under the superalgebra sl(1,2) are determined both for irreducible and first-stage reducible theories with closed gauge algebra.Comment: 35 pages, AMSTEX, precision of reference

Marginal states of the resistive tearing mode with flow in cylindrical geometry

The linear stability of tearing modes in a cylindrical plasma subject to a sub-Alfvénic equilibrium shear flow along the equilibrium magnetic field is considered. The equations in the resistive boundary layer at the rational surface are solved numerically using a Fourier transform combined with a finite-element approach. The behaviour of the growth rate as a function of the flow and the various parameters (including a perpendicular fluid viscosity) is obtained. Marginal stability curves showing the dependence of the familiar matching parameter Δ' with flow and shear are also given

Characterization of qubit chains by Feynman probes

We address the characterization of qubit chains and assess the performances of local measurements compared to those provided by Feynman probes, i.e. nonlocal measurements realized by coupling a single qubit regis- ter to the chain. We show that local measurements are suitable to estimate small values of the coupling and that a Bayesian strategy may be successfully exploited to achieve optimal precision. For larger values of the coupling Bayesian local strategies do not lead to a consistent estimate. In this regime, Feynman probes may be exploited to build a consistent Bayesian estimator that saturates the Cram\'er-Rao bound, thus providing an effective characterization of the chain. Finally, we show that ultimate bounds to precision, i.e. saturation of the quantum Cram\'er-Rao bound, may be achieved by a two-step scheme employing Feynman probes followed by local measurements.Comment: 8 pages, 5 figure