1,065 research outputs found
SU(2) nonstandard bases: the case of mutually unbiased bases
This paper deals with bases in a finite-dimensional Hilbert space. Such a
space can be realized as a subspace of the representation space of SU(2)
corresponding to an irreducible representation of SU(2). The representation
theory of SU(2) is reconsidered via the use of two truncated deformed
oscillators. This leads to replace the familiar scheme {j^2, j_z} by a scheme
{j^2, v(ra)}, where the two-parameter operator v(ra) is defined in the
enveloping algebra of the Lie algebra su(2). The eigenvectors of the commuting
set of operators {j^2, v(ra)} are adapted to a tower of chains SO(3) > C(2j+1),
2j integer, where C(2j+1) is the cyclic group of order 2j+1. In the case where
2j+1 is prime, the corresponding eigenvectors generate a complete set of
mutually unbiased bases. Some useful relations on generalized quadratic Gauss
sums are exposed in three appendices.Comment: 33 pages; version2: rescaling of generalized Hadamard matrices,
acknowledgment and references added, misprints corrected; version 3:
published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA/ (22 pages
On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere
Producción CientÃficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space
to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context
A unified approach to SIC-POVMs and MUBs
15 pagesA unified approach to (symmetric informationally complete) positive operator valued measures and mutually unbiased bases is developed in this article. The approach is based on the use of operator equivalents expanded in the enveloping algebra of SU(2). Emphasis is put on similarities and differences between SIC-POVMs and MUBs
Precise location of unsurveyed seamounts in the Austral archipelago area using SEASAT data
SEASAT altimetric geoid data are used to detect uncharted seamounts in the Austral archipelago area. The various physical parameters which affect the geoid signature of a seamount are inspected to analyse their influence on the precision of the location. If the correct elastic thickness is assumed, the precision on the location is order 15 km. Ten previously unsurveyed seamounts have been located in the Austral archipelago. It appears that they are emplaced along two well-defined azimuths and that two parallel distinct volcanic chains form the Austral archipelag
L'agencement des chaînes (panafricaines et hercynienne) sur la bordure occidentale du craton Ouest Africain
Interprétation gravimétrique de la Sierra-Leone : mise en évidence d'une suture de collision dans la chaîne panafricaine des Rockelides
Mechanical behaviour of the lithosphere beneath the Adamawa uplift (Cameroon, West Africa) based on gravity data
Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
We examine in detail the relative equilibria in the four-vortex problem where
two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and
\Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is
that for m > 0, the convex configurations all contain a line of symmetry,
forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for
all m but the isosceles trapezoid case exists only when m is positive. In fact,
there exist asymmetric convex configurations when m < 0. In contrast to the
Newtonian four-body problem with two equal pairs of masses, where the symmetry
of all convex central configurations is unproven, the equations in the vortex
case are easier to handle, allowing for a complete classification of all
solutions. Precise counts on the number and type of solutions (equivalence
classes) for different values of m, as well as a description of some of the
bifurcations that occur, are provided. Our techniques involve a combination of
analysis and modern and computational algebraic geometry
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