Continuum Fibonacci Schrödinger Operators in the Strongly Coupled Regime
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918408410365952 |
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| author | Damanik, David Embree, Mark Fillman, Jake Gorodetski, Anton Mei, May |
| author_facet | Damanik, David Embree, Mark Fillman, Jake Gorodetski, Anton Mei, May |
| contents | We study Schrödinger operators on the real line whose potentials are generated by the Fibonacci substitution sequence and a rule that replaces symbols by compactly supported potential pieces. We consider the case in which one of those pieces is identically zero, and study the dimension of the spectrum in the large-coupling regime. Our results include a generalization of theorems regarding explicit examples that were studied previously and a counterexample that shows that the naïve generalization of previously established statements is false. In particular, in the aperiodic case, the local Hausdorff dimension of the spectrum does not necessarily converge to zero uniformly on compact subsets as the coupling constant is sent to infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuum Fibonacci Schrödinger Operators in the Strongly Coupled Regime Damanik, David Embree, Mark Fillman, Jake Gorodetski, Anton Mei, May Spectral Theory Mathematical Physics Dynamical Systems 35J10 We study Schrödinger operators on the real line whose potentials are generated by the Fibonacci substitution sequence and a rule that replaces symbols by compactly supported potential pieces. We consider the case in which one of those pieces is identically zero, and study the dimension of the spectrum in the large-coupling regime. Our results include a generalization of theorems regarding explicit examples that were studied previously and a counterexample that shows that the naïve generalization of previously established statements is false. In particular, in the aperiodic case, the local Hausdorff dimension of the spectrum does not necessarily converge to zero uniformly on compact subsets as the coupling constant is sent to infinity. |
| title | Continuum Fibonacci Schrödinger Operators in the Strongly Coupled Regime |
| topic | Spectral Theory Mathematical Physics Dynamical Systems 35J10 |
| url | https://arxiv.org/abs/2603.24462 |