Quantum Systems and Alternative Unitary Descriptions

Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We show how different invariant Hermitian scalar products give rise to different descriptions of a quantum system in the Ehrenfest and Heisenberg picture.Comment: 18 page

Alternative structures and bi-Hamiltonian systems on a Hilbert space

We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems.Comment: 11 page

Classical and Quantum Systems: Alternative Hamiltonian Descriptions

In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson structures.Comment: To appear on Theor. Math. Phy

The WINGS Survey: a progress report

A two-band (B and V) wide-field imaging survey of a complete, all-sky X-ray selected sample of 78 clusters in the redshift range z=0.04-0.07 is presented. The aim of this survey is to provide the astronomical community with a complete set of homogeneous, CCD-based surface photometry and morphological data of nearby cluster galaxies located within 1.5 Mpc from the cluster center. The data collection has been completed in seven observing runs at the INT and ESO-2.2m telescopes. For each cluster, photometric data of about 2500 galaxies (down to V~23) and detailed morphological information of about 600 galaxies (down to V~21) are obtained by using specially designed automatic tools. As a natural follow up of the photometric survey, we also illustrate a long term spectroscopic program we are carrying out with the WHT-WYFFOS and AAT-2dF multifiber spectrographs. Star formation rates and histories, as well as metallicity estimates will be derived for about 350 galaxies per cluster from the line indices and equivalent widths measurements, allowing us to explore the link between the spectral properties and the morphological evolution in high- to low-density environments, and across a wide range in cluster X-ray luminosities and optical properties.Comment: 12 pages, 10 eps figures, Proceedings of the SAIt Conference 200

Towards a definition of quantum integrability

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarily isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.Comment: 37 pages, AmsLatex, 1 figur

A symplectic realization of the Volterra lattice

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page

[domestic Violence Against Children (first Part)].

The authors interviewed 76.2% of the pediatricians from the Pediatric Department-School of Medical Sciences-Campinas University-UNICAMP, to analyse the difficulties of this professional group in the evaluation of the domestic violence against children. From the group of professionals, 86.7% had already attended a situation involving child abuse; the therapeutic aspects were referred in 44.4% as most important, and in 46%, the difficulties in the diagnostic aspects were referred. They conclude that, despite the experiences with the theme, a lot more could be done and studied.71313-

The Geometry of Integrable and Superintegrable Systems

The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical structure like symplectic, Poisson, etc. Such geometrical structure provides a generalized toroidal bundle on the carrier space of the system. Non--canonical diffeomorphisms of such structure generate alternative Hamiltonian structures for complete integrable Hamiltonian systems. The energy-period theorem provides the first non--trivial obstruction for the equivalence of integrable systems