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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.11183 |
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| _version_ | 1866910049607090176 |
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| author | Brysiewicz, Taylor Faust, Matthew Liu, Wencai |
| author_facet | Brysiewicz, Taylor Faust, Matthew Liu, Wencai |
| contents | Using numerical certification, we prove the existence of a nontrivial real-valued two dimensional periodic potential whose associated discrete Schrödinger operator is Fermi isospectral to the zero potential. This provides a negative answer to a question posed by the third author concerning the rigidity of Fermi isospectrality in dimension two. This example also disproves a conjecture of Gieseker, Knörrer, and Trubowitz in the 1990s stating that for any nontrivial real-valued periodic potential in dimension two, the Fermi variety is irreducible at all energy levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11183 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A counterexample to Fermi isospectral rigidity for two dimensional discrete periodic Schrödinger operators Brysiewicz, Taylor Faust, Matthew Liu, Wencai Spectral Theory Mathematical Physics Algebraic Geometry 39A12 (primary), 14P05, 65H14, 65G20 (secondary) Using numerical certification, we prove the existence of a nontrivial real-valued two dimensional periodic potential whose associated discrete Schrödinger operator is Fermi isospectral to the zero potential. This provides a negative answer to a question posed by the third author concerning the rigidity of Fermi isospectrality in dimension two. This example also disproves a conjecture of Gieseker, Knörrer, and Trubowitz in the 1990s stating that for any nontrivial real-valued periodic potential in dimension two, the Fermi variety is irreducible at all energy levels. |
| title | A counterexample to Fermi isospectral rigidity for two dimensional discrete periodic Schrödinger operators |
| topic | Spectral Theory Mathematical Physics Algebraic Geometry 39A12 (primary), 14P05, 65H14, 65G20 (secondary) |
| url | https://arxiv.org/abs/2603.11183 |