462 research outputs found
From the Equations of Motion to the Canonical Commutation Relations
The problem of whether or not the equations of motion of a quantum system
determine the commutation relations was posed by E.P.Wigner in 1950. A similar
problem (known as "The Inverse Problem in the Calculus of Variations") was
posed in a classical setting as back as in 1887 by H.Helmoltz and has received
great attention also in recent times. The aim of this paper is to discuss how
these two apparently unrelated problems can actually be discussed in a somewhat
unified framework. After reviewing briefly the Inverse Problem and the
existence of alternative structures for classical systems, we discuss the
geometric structures that are intrinsically present in Quantum Mechanics,
starting from finite-level systems and then moving to a more general setting by
using the Weyl-Wigner approach, showing how this approach can accomodate in an
almost natural way the existence of alternative structures in Quantum Mechanics
as well.Comment: 199 pages; to be published in "La Rivista del Nuovo Cimento"
(www.sif.it/SIF/en/portal/journals
A look to the inside of haloes: a characterisation of the halo shape as a function of overdensity in the Planck cosmology
In this paper we study the triaxial properties of dark matter haloes of a
wide range of masses extracted from a set of cosmological N-body simulations.
We measure the shape at different distances from the halo centre (characterised
by different overdensity thresholds), both in three and in two dimensions. We
discuss how halo triaxiality increases with mass, redshift and distance from
the halo centre. We also examine how the orientation of the different
ellipsoids are aligned with each other and what is the gradient in internal
shapes for halos with different virial configurations. Our findings highlight
that the internal part of the halo retains memory of the violent formation
process keeping the major axis oriented toward the preferential direction of
the in-falling material while the outer part becomes rounder due to continuous
isotropic merging events. This effect is clearly evident in high mass haloes -
which formed more recently - while it is more blurred in low mass haloes. We
present simple distributions that may be used as priors for various mass
reconstruction algorithms, operating in different wavelengths, in order to
recover a more complex and realistic dark matter distribution of isolated and
relaxed systems.Comment: accepted for publication by MNRAS (15 pag. and 14 fig.
Covariant Jacobi Brackets for Test Particles
We show that the space of observables of test particles carries a natural
Jacobi structure which is manifestly invariant under the action of the
Poincar\'{e} group. Poisson algebras may be obtained by imposing further
requirements. A generalization of Peierls procedure is used to extend this
Jacobi bracket on the space of time-like geodesics on Minkowski space-time.Comment: 13 pages Submitted to MPL
Reduction and unfolding: the Kepler problem
In this paper we show, in a systematic way, how to relate the Kepler problem
to the isotropic harmonic oscillator. Unlike previous approaches, our
constructions are carried over in the Lagrangian formalism dealing with second
order vector fields. We therefore provide a tangent bundle version of the
Kustaahneimo-Stiefel map.Comment: latex2e, 28 pages; misprints correcte
Symmetries, group actions, and entanglement
We address several problems concerning the geometry of the space of Hermitian
operators on a finite-dimensional Hilbert space, in particular the geometry of
the space of density states and canonical group actions on it. For quantum
composite systems we discuss and give examples of measures of entanglement.Comment: 21 page
Hamilton-Jacobi approach to Potential Functions in Information Geometry
The search for a potential function allowing to reconstruct a given
metric tensor and a given symmetric covariant tensor on a manifold
is formulated as the Hamilton-Jacobi problem associated with a
canonically defined Lagrangian on . The connection between this
problem, the geometric structure of the space of pure states of quantum
mechanics, and the theory of contrast functions of classical information
geometry is outlined.Comment: 16 pages. A discussion on the Kullback-Leibler divergence has been
added. To appear in Journal of Mathematical Physic
Topological aspects of generalized Harper operators
A generalized version of the TKNN-equations computing Hall conductances for
generalized Dirac-like Harper operators is derived. Geometrically these
equations relate Chern numbers of suitable (dual) bundles naturally associated
to spectral projections of the operators.Comment: 8 pages; needs aipproc.cls and corresponding style files. To appear
in: "The Eight International Conference on Progress in Theoretical Physics",
Mentouri University, Constantine, Algeria, October 2011; Conference
proceedings of the AIP, edited by N. Mebarki and J. Mimoun
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