On the spectrum of magnetic Laplacian on the Lieb lattice
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914646978461696 |
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| author | Solis, Moises Gomez Spedale, Dylan Yang, Fan |
| author_facet | Solis, Moises Gomez Spedale, Dylan Yang, Fan |
| contents | We study the magnetic Laplacian on the Lieb lattice, and prove Cantor spectrum for arbitrary irrational magnetic flux. We also provide a complete spectral analysis for the reduced one-dimensional Hamiltonian, proving Cantor spectra for all irrational frequencies, and sharp arithmetic phase transitions. Part of our analysis reveals a novel coexistence phenomenon of point spectrum and absolutely/singular continuous spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the spectrum of magnetic Laplacian on the Lieb lattice Solis, Moises Gomez Spedale, Dylan Yang, Fan Mathematical Physics Mesoscale and Nanoscale Physics Spectral Theory We study the magnetic Laplacian on the Lieb lattice, and prove Cantor spectrum for arbitrary irrational magnetic flux. We also provide a complete spectral analysis for the reduced one-dimensional Hamiltonian, proving Cantor spectra for all irrational frequencies, and sharp arithmetic phase transitions. Part of our analysis reveals a novel coexistence phenomenon of point spectrum and absolutely/singular continuous spectrum. |
| title | On the spectrum of magnetic Laplacian on the Lieb lattice |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Spectral Theory |
| url | https://arxiv.org/abs/2401.11405 |