175 research outputs found
On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras
We establish an improved upper estimate on dimension of any solvable algebra
s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we
consider Levi decomposable algebras with a given nilradical n and investigate
restrictions on possible Levi factors originating from the structure of
characteristic ideals of n. We present a new perspective on Turkowski's
classification of Levi decomposable algebras up to dimension 9.Comment: 21 pages; major revision - one section added, another erased;
author's version of the published pape
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
We construct all solvable Lie algebras with a specific n-dimensional
nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional
maximal Abelian ideal). We find that for given n such a solvable algebra is
unique up to isomorphisms. Using the method of moving frames we construct a
basis for the Casimir invariants of the nilradical n_(n,2). We also construct a
basis for the generalized Casimir invariants of its solvable extension s_(n+1)
consisting entirely of rational functions of the chosen invariants of the
nilradical.Comment: 19 pages; added references, changes mainly in introduction and
conclusions, typos corrected; submitted to J. Phys. A, version to be
publishe
Edades radiométricas de los edificios miocenos de Fuerteventura (Islas Canarias).
Se han realizado once nuevas dataciones K-Ar de las coladas bĂĄsicas (basaltos, nefelinitas) y sĂĄlicas (traquitas) de los tres edificios principales subaĂ©reos (Tetir o Norte, Gran Tarajal o Central y JandĂa o Sur) que constituyen la Fase miocena de la isla. Se precisa algo mĂĄs la cronoestratigrafĂa relativa entre ellos, asĂ como la correspondiente a los tramos que los integran
Invariants of solvable rigid Lie algebras up to dimension 8
The invariants of all complex solvable rigid Lie algebras up to dimension
eight are computed. Moreover we show, for rank one solvable algebras, some
criteria to deduce to non-existence of non-trivial invariants or the existence
of fundamental sets of invariants formed by rational functions of the Casimir
invariants of the associated nilradical.Comment: 16 pages, 7 table
Rocas volcånicas submarinas en la base de la Formación Cañadas. Macizo de Tigaiga (N. de Tenerife)
A volcanic submarine formation crops out in the north coast of Tenerife, east of San Juan de la
Rambla. This unit is formed by massive and pil/owed lavas, pillow-breccias, hyaloc/astites and palagonitic
tuffs and is interpreted as consisUng of subaerial lavas that flowed into shal/ow marine
waters. The lavas are amphibolic trachybasalts. An unaltered sample coming fram the most massive
zone has yielded a whole rack 2.60±0.17 Ma K-Ar age. These submarine lavas are underlying
the oldest formations of the Las Cañadas Series dated at 1.24 Ma in that same area. The submarine
lavas correspond to a time period for which very scarce information was yet available in Tenerife
Bell-inequalities for Pairs from -Resonance Decays
We analyze the premises of recent propositions to test local realism via
Bell-inequalities using neutral kaons from -resonance decays as entangled
EPR-pairs. We pay special attention to the derivation of Bell-inequalities, or
related expressions, for unstable and oscillating kaon `quasi-spin' states and
to the possibility of the actual identification of these states through their
associated decay modes. We discuss an indirect method to extract probabilities
to find these states by combining experimental information with theoretical
input. However, we still find inconsistencies in previous derivations of
Bell-inequalities. We show that the identification of the quasi-spin states via
their associated decay mode does not allow the free choice to perform different
tests on them, a property which is crucial to establish the validity of any
Bell-inequality in the context of local realism. In view of this we propose a
different kind of Bell-inequality in which the free choice or adjustability of
the experimental set-up is guaranteed. We also show that the proposed
inequalities are violated by quantum mechanics.Comment: 22 pages. Late
Decoherence of entangled kaons and its connection to entanglement measures
We study the time evolution of the entangled kaon system by considering the
Liouville - von Neumann equation with an additional term which allows for
decoherence. We choose as generators of decoherence the projectors to the
2-particle eigenstates of the Hamiltonian. Then we compare this model with the
data of the CPLEAR experiment and find in this way an upper bound on the
strength of the decoherence. We also relate to an effective
decoherence parameter considered previously in literature. Finally we
discuss our model in the light of different measures of entanglement, i.e. the
von Neumann entropy , the entanglement of formation and the concurrence
, and we relate the decoherence parameter to the loss of
entanglement: .Comment: comments and references added, 18 pages, 1 figur
Bell inequalities for entangled kaons and their unitary time evolution
We investigate Bell inequalities for neutral kaon systems from Phi resonance
decay to test local realism versus quantum mechanics. We emphasize the unitary
time evolution of the states, that means we also include all decay product
states, in contrast to other authors. Only this guarantees the use of the
complete Hilbert space. We develop a general formalism for Bell inequalities
including both arbitrary "quasi spin" states and different times; finally we
analyze Wigner-type inequalities. They contain an additional term, a correction
function h, as compared to the spin 1/2 or photon case, which changes
considerably the possibility of quantum mechanics to violate the Bell
inequality. Examples for special "quasi spin" states are given, especially
those which are sensitive to the CP parameters epsilon and epsilon'.Comment: REVTeX, 22 page
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