13,795 research outputs found
On the theory of vortex quantum tunnelling in the dense Bose superfluid helium II
The quantum tunnelling and nucleation theory of vortices in helium II is
reviewed. Arguments are given that the only reliable method to calculate
tunnelling probabilities in this highly correlated, strongly interacting
many-body system is the semiclassical, large scale approach for evaluation of
the tunnelling exponent, which does not make any assumptions about the unknown
dynamical behaviour of the fluid on microscopic scales. The geometric
implications of this semiclassical theory are represented in some detail and
its relevance for the interpretation of experimental data is discussed.Comment: 25 pages, 6 figures, revised version, to appear in Physica
Thin-disk models in an Integrable Weyl-Dirac theory
We construct a class of static, axially symmetric solutions representing
razor-thin disks of matter in an Integrable Weyl-Dirac theory proposed in
Found. Phys. 29, 1303 (1999). The main differences between these solutions and
the corresponding general relativistic one are analyzed, focusing on the
behavior of physical observables (rotation curves of test particles, density
and pressure profiles). We consider the case in which test particles move on
Weyl geodesics. The same rotation curve can be obtained from many different
solutions of the Weyl-Dirac theory, although some of these solutions present
strong qualitative differences with respect to the usual general relativistic
model (such as the appearance a ring-like density profile). In particular, for
typical galactic parameters all rotation curves of the Weyl-Dirac model present
Keplerian fall-off. As a consequence, we conclude that a more thorough analysis
of the problem requires the determination of the gauge function on
galactic scales, as well as restrictions on the test-particle behavior under
the action of the additional fields introduced by this theory.Comment: 18 pages, 3 figures; accepted in General Relativity and Gravitatio
Introduction to Quantum Mechanics and the Quantum-Classical transition
In this paper we present a survey of the use of differential geometric
formalisms to describe Quantum Mechanics. We analyze Schroedinger and
Heisenberg frameworks from this perspective and discuss how the momentum map
associated to the action of the unitary group on the Hilbert space allows to
relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics
and discuss the implications of bi-Hamiltonian structures at the quantum level.Comment: Survey paper based on the lectures delivered at the XV International
Workshop on Geometry and Physics Puerto de la Cruz, Tenerife, Canary Islands,
Spain September 11-16, 2006. To appear in Publ. de la RSM
Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information
In this paper we present a survey of the use of differential geometric
formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework
from this perspective and provide a description of the Weyl-Wigner
construction. Finally, after reviewing the basics of the geometric formulation
of quantum mechanics, we apply the methods presented to the most interesting
cases of finite dimensional Hilbert spaces: those of two, three and four level
systems (one qubit, one qutrit and two qubit systems). As a more practical
application, we discuss the advantages that the geometric formulation of
quantum mechanics can provide us with in the study of situations as the
functional independence of entanglement witnesses.Comment: AmsLaTeX, 37 pages, 8 figures. This paper is an expanded version of
some lectures delivered by one of us (G. M.) at the ``Advanced Winter School
on the Mathematical Foundation of Quantum Control and Quantum Information''
which took place at Castro Urdiales (Spain), February 11-15, 200
Photometry of supernovae in an image series : methods and application to the Supernova Legacy Survey (SNLS)
We present a technique to measure lightcurves of time-variable point sources
on a spatially structured background from imaging data. The technique was
developed to measure light curves of SNLS supernovae in order to infer their
distances. This photometry technique performs simultaneous PSF photometry at
the same sky position on an image series. We describe two implementations of
the method: one that resamples images before measuring fluxes, and one which
does not. In both instances, we sketch the key algorithms involved and present
the validation using semi-artificial sources introduced in real images in order
to assess the accuracy of the supernova flux measurements relative to that of
surrounding stars. We describe the methods required to anchor these PSF fluxes
to calibrated aperture catalogs, in order to derive SN magnitudes. We find a
marginally significant bias of 2 mmag of the after-resampling method, and no
bias at the mmag accuracy for the non-resampling method. Given surrounding star
magnitudes, we determine the systematic uncertainty of SN magnitudes to be less
than 1.5 mmag, which represents about one third of the current photometric
calibration uncertainty affecting SN measurements. The SN photometry delivers
several by-products: bright star PSF flux mea- surements which have a
repeatability of about 0.6%, as for aperture measurements; we measure relative
astrometric positions with a noise floor of 2.4 mas for a single-image bright
star measurement; we show that in all bands of the MegaCam instrument, stars
exhibit a profile linearly broadening with flux by about 0.5% over the whole
brightness range.Comment: Accepted for publication in A&A. 20 page
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