SPECTRAL and DYNAMICAL PROPERTIES of SPARSE ONE-DIMENSIONAL CONTINUOUS SCHRODINGER and DIRAC OPERATORS

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2013-10-01
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Carvalho, Silas L. [UNIFESP]
Oliveira, Cesar R. de
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Spectral and dynamical properties of some one-dimensional continuous Schrodinger and Dirac operators with a class of sparse potentials (which take non-zero values only at some sparse and suitably randomly distributed positions) are studied. By adapting and extending to the continuous setting some of the techniques developed for the corresponding discrete operator cases, the Hausdorff dimension of their spectral measures and lower dynamical bounds for transport exponents are determined. Furthermore, it is found that the condition for the spectral Hausdorff dimension to be positive is the same for the existence of a singular continuous spectrum.
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Proceedings of the Edinburgh Mathematical Society. New York: Cambridge Univ Press, v. 56, n. 3, p. 667-700, 2013.