Quasi-exact solvability beyond the SL(2) algebraization

We present evidence to suggest that the study of one dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual \sla(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the \sla(2) Lie algebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is done via another algebraization in which the algebraic hamiltonian cannot be expressed as a polynomial in the generators of \sla(2). We then show an example of a new quasi-exactly solvable potential which cannot be obtained within the Lie-algebraic approach.Comment: Submitted to the proceedings of the 2005 Dubna workshop on superintegrabilit

First clear evidence of quantum chaos in the bound states of an atomic nucleus

We study the spectral fluctuations of the $^{208}$Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of $6.20$ MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter $\omega$, which takes the value $\omega=0$ for regular systems and $\omega \simeq 1$ for chaotic systems. We obtain $\omega=0.85 \pm 0.02$ which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in $^{208}$Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.Comment: 9 pages, 1 figur

Electric polarizability of nuclei from a longitudinal sum rule

The nuclear electric polarizability is theoretically analyzed using a sum rule derived from the longitudinal part of the forward Compton amplitude. Beyond the leading dipole contribution, this approach leads to the presence of potential-dependent terms that do not show up in previous analyses. The significance of these new contributions is illustrated by performing an explicit calculation for a proton-neutron system interacting via a separable potential.Comment: 9 pages, revtex. Minor changes, two references added. To appear in Nucl. Phys.

Large Scale Morphological Segregation in Optically Selected Galaxy Redshift Catalogs

We present the results of an exhaustive analysis of the morphological segregation of galaxies in the CfA and SSRS catalogs through the scaling formalism. Morphological segregation between ellipticals and spirals has been detected at scales up to 15-20 h$^{-1}$ Mpc in the CfA catalog, and up to 20-30 h$^{-1}$ Mpc in the SSRS catalog. Moreover, it is present not only in the densest areas of the galaxy distribution, but also in zones of moderate density.Comment: 9 pages, (1 figure included), uuencode compressed Postscript, (accepted for publication in ApJ Letters), FTUAM-93-2

Enriching Ontologies with Multilingual Information

Multilinguality in ontologies has become an impending need for institutions worldwide that have to deal with data and linguistic resources in different natural languages. Since most ontologies are developed in one language, obtaining multilingual ontologies implies to localize or adapt them to a concrete language and culture community. As the adaptation of the ontology conceptualization demands considerable efforts, we propose to modify the ontology terminological layer by associating an external repository of linguistic data to the ontology. With this aim we provide a model called Linguistic Information Repository (LIR) that associated to the ontology meta-model allows terminological layer localization

The Inverse Amplitude Method and Adler Zeros

The Inverse Amplitude Method is a powerful unitarization technique to enlarge the energy applicability region of Effective Lagrangians. It has been widely used to describe resonances from Chiral Perturbation Theory as well as for the Strongly Interacting Symmetry Breaking Sector. In this work we show how it can be slightly modified to account also for the sub-threshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.Comment: 17 pages, 4 figure