305 research outputs found
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
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