The Dry Ten Martini Problem for Sturmian Hamiltonians
The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schr\"odinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the solution is a representation of the spectrum a...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively
solved. Concretely, we prove that all spectral gaps are open for Schr\"odinger
operators with Sturmian potentials and non-vanishing coupling constant. A key
approach towards the solution is a representation of the spectrum as the
boundary of an infinite tree. This tree is constructed via particular periodic
approximations and it encodes substantial spectral characteristics. |
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| DOI: | 10.48550/arxiv.2402.16703 |