Irreducibility of the Dispersion Polynomial for Periodic Graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910690611036160 |
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| author | Faust, Matthew Garcia, Jordy Lopez |
| author_facet | Faust, Matthew Garcia, Jordy Lopez |
| contents | We use methods from algebra and discrete geometry to study the irreducibility of the dispersion polynomial of a discrete periodic operator associated to a periodic graph after changing the period lattice. We provide numerous applications of these results to discrete periodic operators associated to families of graphs which include dense periodic graphs, and a family containing the hexagonal and diamond lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11534 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Irreducibility of the Dispersion Polynomial for Periodic Graphs Faust, Matthew Garcia, Jordy Lopez Algebraic Geometry Mathematical Physics Spectral Theory 47A75 (Primary) 14M25, 52B20 (Secondary) We use methods from algebra and discrete geometry to study the irreducibility of the dispersion polynomial of a discrete periodic operator associated to a periodic graph after changing the period lattice. We provide numerous applications of these results to discrete periodic operators associated to families of graphs which include dense periodic graphs, and a family containing the hexagonal and diamond lattices. |
| title | Irreducibility of the Dispersion Polynomial for Periodic Graphs |
| topic | Algebraic Geometry Mathematical Physics Spectral Theory 47A75 (Primary) 14M25, 52B20 (Secondary) |
| url | https://arxiv.org/abs/2302.11534 |