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 Ampullae of the Inner Ear in the Lizard Podarcis S. Sicula. Ultrastructural Aspects

The inner ear ampullae of the lizard Podarcis s. sicula were studied to determine better the ultrastructure of ampullar epithelial cells. Our study confirmed that the ampullae of the membranous labyrinth of this lizard are similar to those of other vertebrates in their ultrastructural aspect. Moreover, our observations revealed a special type of dark cells, restricted to a small area of the crista. They appeared similar to type II sensory cells and showed a dark, finely granular cytoplasm, containing numerous mitochondria and ribosomes, extensive Golgi apparatus and abundant glycogen. The morphology of these cells suggests that they may be special sensory cells, or different stages of sensory cells, probably implied in the crista cell turn-over described for some vertebrate groups

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

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