Log-dimensional Spectral Properties of One-dimensional Quasicrystals
نویسنده
چکیده
We consider discrete one-dimensional Schrödinger operators on the whole line and establish a criterion for continuity of spectral measures with respect to log-Hausdorff measures. We apply this result to operators with Sturmian potentials and thereby prove logarithmic quantum dynamical lower bounds for all coupling constants and almost all rotation numbers, uniformly in the phase.
منابع مشابه
Uniform spectral properties of one-dimensional quasicrystals, I. Absence of eigenvalues
We consider discrete one-dimensional Schrödinger operators with Sturmian potentials. For a fullmeasure set of rotation numbers including the Fibonacci case we prove absence of eigenvalues for all elements in the hull.
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تاریخ انتشار 2001