All-coupling frequency independence of Sturmian spectral dimensions
All-coupling frequency independence of Sturmian spectral dimensions
Let and let be an irrational frequency. Denote by the phase-independent spectrum of the corresponding Sturmian Schrödinger operator. The paper proves that the Hausdorff and upper box-counting dimensions are almost everywhere constant in when . Large-coupling conjecture. The assumption can be dropped in the theorem, so the same almost-everywhere constancy holds for every . A proof is described as currently well out of reach because the methods rely essentially on large coupling.
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Primary source
David Damanik and Anton Gorodetski, “Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians”, arXiv:1406.4810 (2014).
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