Gap Labels and Asymptotic Gap Opening for Full Shifts
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913616631955456 |
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| author | Damanik, David Emilsdóttir, Íris Fillman, Jake |
| author_facet | Damanik, David Emilsdóttir, Íris Fillman, Jake |
| contents | We discuss gap labelling for operators generated by the full shift over a compact subset of the real line. The set of Johnson--Schwartzman gap labels is the algebra generated by weights of clopen subsets of the support of the single-site distribution. Due to the presence of a dense set of periodic orbits, it is impossible to find a sampling function for which all gaps allowed by the gap labelling theorem open simultaneously. Nevertheless, for a suitable choice of the single-site distribution, we show that for generic sampling functions, every spectral gap opens in the large-coupling limit. Furthermore, we show that for other choices of weights there are gaps that cannot open for purely diagonal operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gap Labels and Asymptotic Gap Opening for Full Shifts Damanik, David Emilsdóttir, Íris Fillman, Jake Spectral Theory Mathematical Physics Dynamical Systems We discuss gap labelling for operators generated by the full shift over a compact subset of the real line. The set of Johnson--Schwartzman gap labels is the algebra generated by weights of clopen subsets of the support of the single-site distribution. Due to the presence of a dense set of periodic orbits, it is impossible to find a sampling function for which all gaps allowed by the gap labelling theorem open simultaneously. Nevertheless, for a suitable choice of the single-site distribution, we show that for generic sampling functions, every spectral gap opens in the large-coupling limit. Furthermore, we show that for other choices of weights there are gaps that cannot open for purely diagonal operators. |
| title | Gap Labels and Asymptotic Gap Opening for Full Shifts |
| topic | Spectral Theory Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2412.13391 |