Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation

The sine-Gordon equation is considered in the hamiltonian framework provided by the Adler-Kostant-Symes theorem. The phase space, a finite dimensional coadjoint orbit in the dual space \grg^* of a loop algebra \grg, is parametrized by a finite dimensional symplectic vector space $W$ embedded into \grg^* by a moment map. Real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.Comment: 12 pg

Matrix Nonlinear Schr\"odinger Equations and Moment Maps into Loop Algebras†{}^\dag

It is shown how Darboux coordinates on a reduced symplectic vector space may be used to parametrize the phase space on which the finite gap solutions of matrix nonlinear Schr\"odinger equations are realized as isospectral Hamiltonian flows. The parametrization follows from a moment map embedding of the symplectic vector space, reduced by suitable group actions, into the dual \tilde\grg^{+*} of the algebra \tilde\grg^+ of positive frequency loops in a Lie algebra \grg. The resulting phase space is identified with a Poisson subspace of \tilde\grg^{+*} consisting of elements that are rational in the loop parameter. Reduced coordinates associated to the various Hermitian symmetric Lie algebras (\grg,\grk) corresponding to the classical Lie algebras are obtained.Comment: 17 pgs, plus 4 Tables Preprint CRM-183

IGR J14488-4008: an X-ray peculiar giant radio galaxy discovered by INTEGRAL

In this paper we report the discovery and detailed radio/X-ray analysis of a peculiar giant radio galaxy (GRG) detected by INTEGRAL, IGR J14488-4008. The source has been recently classified as a Seyfert 1.2 galaxy at redshift 0.123; the radio data denote the source to be a type II Fanaroff-Riley radio galaxy, with a linear projected size exceeding 1.5 Mpc, clearly assigning IGR J14488-4008 to the class of GRG. In the X-rays, the source shows a remarkable spectrum, characterised by absorption by ionised elements, a characteristic so far found in only other four broad line radio galaxies.Comment: 7 pages, 3 tables, 5 figures. Accepted for publication on MNRA

Gravity from self-interaction redux

I correct some recent misunderstandings about, and amplify some details of, an old explicit non-geometrical derivation of GR.Comment: Final, amplified, published version; GRG (2009

Gutzwiller Renormalization Group

We develop a variational scheme called "Gutzwiller renormalization group" (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method can exploit the low-entanglement property of the ground state in combination with the framework of the Gutzwiller wavefunction, and suggests that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and indicate that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.Comment: 5 pages, 3 figure

Localized Sensor Self-Deployment with Coverage Guarantee in Complex Environment

International audienceIn focused coverage problem, sensors are required to be deployed around a given point of interest (POI) with respect to a priority requirement: an area close to POI has higher priority to be covered than a distant one. A localized sensor self-deployment algorithm, named Greedy-Rotation-Greedy (GRG) [10], has recently been proposed for constructing optimal focused coverage. This previous work assumed obstacle-free environment and focused on theoretical aspects. Here in this paper, we remove this strong assumption, and extend GRG to practical settings. We equip GRG with a novel obstacle penetration technique and give it the important obstacle avoidance capability. The new version of GRG is referred to as GRG/OP. Through simulation, we evaluate its performance in comparison with plain GRG

The energetics of giant radio galaxy lobes from inverse Compton scattering observations

Giant radio galaxy (GRG) lobes are excellent laboratories to study the evolution of the particle and B-field energetics. However, these results are based on assumptions of the shape and extension of the GRG lobe electron spectrum. We re-examine the energetics of GRG lobes as derived by inverse Compton scattering of CMB photons (ICS-CMB) by relativistic electrons in RG lobes to assess the physical conditions of RG lobes, their energetics and their radiation regime. We consider the GRG DA 240 recently observed by Suzaku as a reference case and we also discuss other RG lobes observed with Chandra and XMM. We model the spectral energy distribution of the DA 240 East lobe to get constraint on the shape and the extension of the electron spectrum in the lobe by using multi-frequency information from radio to gamma-rays. We use radio and X-ray data to constrain the shape and normalization of the electron spectrum and we then calculate the SZ effect expected in GRG lobes that is sensitive to the total electron energy density. We show that the electron energy density U_e derived form X-ray observations yields only a rough lower limit to its actual value and that most of the estimates of U_e based on X-ray measurements have to be increased even by a large factor by considering realistic estimates of the lower electron momentum p_1. This brings RG lobes away from the equipartition condition towards a particle-dominated and Compton power dominance regime. We use the distribution of RG lobes in the U_e/U_B vs. U_e/U_CMB plane as a further divide between different physical regimes of particle and field dominance, and radiation mechanism dominance in RG lobes. We conclude that the SZ effect produced by ICS-CMB mechanism observable in RG lobes provides reliable estimate of p_1 and U_e and is the best tool to determine the total energy density of RG lobes and to assess their physical regime.Comment: 9 pages, 6 figures, A&A in pres