277 research outputs found
Diffeomorphism-invariant properties for quasi-linear elliptic operators
For quasi-linear elliptic equations we detect relevant properties which
remain invariant under the action of a suitable class of diffeomorphisms. This
yields a connection between existence theories for equations with degenerate
and non-degenerate coerciveness.Comment: 16 page
Geometrical classification of Killing tensors on bidimensional flat manifolds
Valence two Killing tensors in the Euclidean and Minkowski planes are
classified under the action of the group which preserves the type of the
corresponding Killing web. The classification is based on an analysis of the
system of determining partial differential equations for the group invariants
and is entirely algebraic. The approach allows to classify both characteristic
and non characteristic Killing tensors.Comment: 27 pages, 20 figures, pictures format changed to .eps, typos
correcte
Generalizations of a method for constructing first integrals of a class of natural Hamiltonians and some remarks about quantization
In previous papers we determined necessary and sufficient conditions for the
existence of a class of natural Hamiltonians with non-trivial first integrals
of arbitrarily high degree in the momenta. Such Hamiltonians were characterized
as (n+1)-dimensional extensions of n-dimensional Hamiltonians on
constant-curvature (pseudo-)Riemannian manifolds Q. In this paper, we
generalize that approach in various directions, we obtain an explicit
expression for the first integrals, holding on the more general case of
Hamiltonians on Poisson manifolds, and show how the construction of above is
made possible by the existence on Q of particular conformal Killing tensors or,
equivalently, particular conformal master symmetries of the geodesic equations.
Finally, we consider the problem of Laplace-Beltrami quantization of these
first integrals when they are of second-degree.Comment: Presented at the conference Quantum Theory and Symmetries 7, Praha,
August 7-13 2011. In v2 some typos corrected, a comment added after eq. (4),
a comment about ref. [1] correcte
Tri-hamiltonian vector fields, spectral curves and separation coordinates
We show that for a class of dynamical systems, Hamiltonian with respect to
three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are
provided by the common roots of a set of bivariate polynomials. These
polynomials, which generalise those considered by E. Sklyanin in his
algebro-geometric approach, are obtained from the knowledge of: (i) a common
Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu
P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to
its symplectic leaves. The frameworks is applied to Lax equations with spectral
parameter, for which not only it unifies the separation techniques of Sklyanin
and of Magri, but also provides a more efficient ``inverse'' procedure not
involving the extraction of roots.Comment: 49 pages Section on reduction revisite
Experimental quantum cryptography scheme based on orthogonal states
Since, in general, non-orthogonal states cannot be cloned, any eavesdropping
attempt in a Quantum Communication scheme using non-orthogonal states as
carriers of information introduces some errors in the transmission, leading to
the possibility of detecting the spy. Usually, orthogonal states are not used
in Quantum Cryptography schemes since they can be faithfully cloned without
altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [\prl
75 (1995) 1239] proposed a protocol in which, even if the data exchange is
realized using two orthogonal states, any attempt to eavesdrop is detectable by
the legal users. In this scheme the orthogonal states are superpositions of two
localized wave packets travelling along separate channels. Here we present an
experiment realizing this scheme
Reply to Comment on "Quantum dense key distribution"
In this Reply we propose a modified security proof of the Quantum Dense Key
Distribution protocol detecting also the eavesdropping attack proposed by
Wojcik in his Comment.Comment: To appear on PRA with minor change
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