Log-dimensional spectral properties of one-dimensional quasicrystals

Details Log-dimensional spectral properties of one-dimensional quasicrystals Log-dimensional spectral properties of one-dimensional quasicrystals

2002-01-03

arxiv.org/abs/math-ph/0201009v1

Physics

Mathematical Physics

7 pages

Scientific paper

We consider discrete one-dimensional Schr\"odinger 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.

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