On the Stability of Stochastic Parametrically Forced Equations with Rank One Forcing

We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the stochastic excitation is small, the stability of such systems was computed using a weighted sum of the extended power spectral density over the eigenvalues of the unperturbed operator. In this paper, we show how to convert this to a sum over the residues of the extended power spectral density. For systems where the parametric forcing term is a rank one matrix, this leads to an enormous simplification.Comment: 16 page

Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential

A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. To acomplish this, a similar path to the one used in the angular momentum case is employed; hence, the radial eigenfuntions calculated comprise non unitary representations of the algebra. One of the interesting properties of such non unitary representations is that they are not labeled by integer nor by half-integer numbers as happens in the usual angular momentum representation.Comment: 20 pages 1 eps figure in a single zipped file, submitted to J. Math. Phy

The soft X-ray excess AGN RE J2248-511

We model the spectral energy distribution of the ultrasoft broad-line AGN RE J2248-511 with Comptonised accretion disc models. These are able to reproduce the steep optical and ultrasoft X-ray slopes, and the derived black hole mass is consistent with independent mass estimates. This AGN displays properties of both broad and narrow line Seyfert 1 galaxies, but we conclude that it is intrinsically a `normal' Seyfert 1 viewed at high inclination angle.Comment: 4 pages, 1 figure. MG10 Proceeding

A retarded coupling approach to intermolecular interactions

A wide range of physical phenomena such as optical binding and resonance energy transfer involve electronic coupling between adjacent molecules. A quantum electrodynamical description of these intermolecular interactions reveals the presence of retardation effects. The clarity of the procedure associated with the construction of the quantum amplitudes and the precision of the ensuing results for observable energies and rates are widely acknowledged. However, the length and complexity of the derivations involved in such quantum electrodynamical descriptions increase rapidly with the order of the process under study. Whether through the use of time-ordering approaches, or the more expedient state-sequence method, time-consuming calculations cannot usually be bypassed. A simple and succinct method is now presented, which provides for a direct and still entirely rigorous determination of the quantum electrodynamical amplitudes for processes of arbitrarily high order. Using the approach, new results for optical binding in two- and three-particle systems are secured and discussed