60,515 research outputs found
The ordered K-theory of a full extension
Let A be a C*-algebra with real rank zero which has the stable weak
cancellation property. Let I be an ideal of A such that I is stable and
satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a
full extension if and only if the extension is stenotic and K-lexicographic. As
an immediate application, we extend the classification result for graph
C*-algebras obtained by Tomforde and the first named author to the general
non-unital case. In combination with recent results by Katsura, Tomforde, West
and the first author, our result may also be used to give a purely
K-theoretical description of when an essential extension of two simple and
stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9
is not correct as stated. See arXiv:1505.05951 for more details. Since
Theorem 4.9 is an application to the main results of the paper, the main
results of this paper are not affected by the error. Version III comments:
Some typos and errors corrected. Some references adde
Relative entropy of entanglement for certain multipartite mixed states
We prove conjectures on the relative entropy of entanglement (REE) for two
families of multipartite qubit states. Thus, analytic expressions of REE for
these families of states can be given. The first family of states are composed
of mixture of some permutation-invariant multi-qubit states. The results
generalized to multi-qudit states are also shown to hold. The second family of
states contain D\"ur's bound entangled states. Along the way, we have discussed
the relation of REE to two other measures: robustness of entanglement and
geometric measure of entanglement, slightly extending previous results.Comment: Single column, 22 pages, 9 figures, comments welcom
Saturation of Spin-Polarized Current in Nanometer Scale Aluminum Grains
We describe measurements of spin-polarized tunnelling via discrete energy
levels of single Aluminum grains. In high resistance samples (),
the spin-polarized tunnelling current rapidly saturates as a function of the
bias voltage. This indicates that spin-polarized current is carried only via
the ground state and the few lowest in energy excited states of the grain. At
the saturation voltage, the spin-relaxation rate of the highest
excited states is comparable to the electron tunnelling rate: and in two samples. The ratio of
to the electron-phonon relaxation rate is in agreement with the Elliot-Yafet
scaling, an evidence that spin-relaxation in Al grains is governed by the
spin-orbit interaction.Comment: 5 pages, 4 figure
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