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91.
We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets. 相似文献
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96.
Marí a J. Martí n Dragan Vukotic 《Proceedings of the American Mathematical Society》2006,134(6):1701-1705
We show that every composition operator which is an isometry of the Dirichlet space is induced by a univalent full map of the disk into itself that fixes the origin. This is an analogue of the Hardy space result for inner functions due to Nordgren. The proof relies on the Stone-Weierstrass theorem and the Riesz representation theorem.
97.
98.
This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in
classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual
relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways
and the non-commutative analogue of the factorization theorem is obtained. As an application we discuss exponential families.
Our factorization theorem also implies two further important results, previously known only in finite Hilbert space dimension,
but proved here in generality: the Koashi-Imoto theorem on maps leaving a family of states invariant, and the characterization
of the general form of states in the equality case of strong subadditivity.
Supported by the EU Research Training Network Quantum Probability with Applications to Physics, Information Theory and Biology
and Center of Excellence SAS Physics of Information I/2/2005.
Supported by the Hungarian grant OTKA T032662 相似文献
99.
Clément Gallo 《Comptes Rendus Mathematique》2006,342(5):319-323
We give an upper bound on the growth rate of the Schrödinger group on Zhidkov spaces. In dimension 1, we prove that this bound is sharp. To cite this article: C. Gallo, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
100.
(S)-2-[2-(p-Tolylsulfinyl)phenyl]acetaldehyde reacts with different O-silylated ketenethioacetals in the presence of Yb(OTf)3 yielding β-hydroxythioesters in high yields and diastereoselectivities. The obtained compounds were readily transformed into β-hydroxyacids and their corresponding diols. These Mukaiyama aldol reactions are a direct evidence of the ability of the sulfinyl group to control 1,5- and 1,6-asymmetric induction processes. 相似文献