Log-dimensional spectral properties of one-dimensional quasicrystals

Damanik, David; Landrigan, Michael

doi:10.1090/S0002-9939-02-06747-3

Log-dimensional spectral properties of one-dimensional quasicrystals
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Proc. Amer. Math. Soc. 131 (2003), 2209-2216 Request permission

Abstract:

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.

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