Critical points of discrete periodic operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910318010040320 |
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| author | Faust, Matthew Sottile, Frank |
| author_facet | Faust, Matthew Sottile, Frank |
| contents | We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the Bloch variety, together with an effective criterion for when this bound is attained. We show that this criterion holds for Z^2- and Z^3-periodic graphs with sufficiently many edges and use our results to establish the spectral edges conjecture for some Z^2-periodic graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13649 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Critical points of discrete periodic operators Faust, Matthew Sottile, Frank Mathematical Physics Algebraic Geometry Spectral Theory 81U30, 81Q10, 14M25 We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the Bloch variety, together with an effective criterion for when this bound is attained. We show that this criterion holds for Z^2- and Z^3-periodic graphs with sufficiently many edges and use our results to establish the spectral edges conjecture for some Z^2-periodic graphs. |
| title | Critical points of discrete periodic operators |
| topic | Mathematical Physics Algebraic Geometry Spectral Theory 81U30, 81Q10, 14M25 |
| url | https://arxiv.org/abs/2206.13649 |