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Dry Ten Martini Problem in the non-critical case
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abstract
We solve the Dry Ten Martini Problem in the non-critical case, i.e., all possible spectral gaps are open for almost Mathieu operators with $\lambda\ne \pm 1$.
Forward citations
Cited by 3 Pith papers
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Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
For subcritical almost Mathieu operators with Diophantine frequency, each exceptional lower-scaling-index level set has Hausdorff dimension 0 but log-Hausdorff dimension 1.
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Cantor spectrum for multidimensional quasi-periodic Schr\"odinger operators
A dense, positive-Hausdorff-dimension set of frequencies gives the multidimensional almost Mathieu operator a zero-measure Cantor spectrum, and critical almost Mathieu spectra can have arbitrarily small positive box d...
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Fibonacci number systems and the localization criterion in the many-body Aubry-Andr\'e model
The paper introduces a fractional Fibonacci number system and argues that densities with finite base-phi expansions are always localized in the many-body Aubry-André model.
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