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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.19072 |
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| _version_ | 1866914052349886464 |
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| author | Davis, Nyah Emilsdóttir, íris Li, Long Liang, Hangqi |
| author_facet | Davis, Nyah Emilsdóttir, íris Li, Long Liang, Hangqi |
| contents | We prove a dichotomy of almost periodicity for reflectionless one-dimensional Dirac operators whose spectra satisfy certain geometric conditions, extending work of Volberg--Yuditskii. We also construct a weakly mixing Dirac operator with a non-constant continuous potential whose spectrum is purely absolutely continuous, adapting Avila's argument for continuous Schrödinger operators. In particular, we disprove the Kotani--Last conjecture in the setting of one-dimensional Dirac operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Kotani-Last Conjecture for the Dirac Operator Davis, Nyah Emilsdóttir, íris Li, Long Liang, Hangqi Spectral Theory Dynamical Systems 47A10, 81Q10 We prove a dichotomy of almost periodicity for reflectionless one-dimensional Dirac operators whose spectra satisfy certain geometric conditions, extending work of Volberg--Yuditskii. We also construct a weakly mixing Dirac operator with a non-constant continuous potential whose spectrum is purely absolutely continuous, adapting Avila's argument for continuous Schrödinger operators. In particular, we disprove the Kotani--Last conjecture in the setting of one-dimensional Dirac operators. |
| title | On the Kotani-Last Conjecture for the Dirac Operator |
| topic | Spectral Theory Dynamical Systems 47A10, 81Q10 |
| url | https://arxiv.org/abs/2509.19072 |