{"paper":{"title":"Floquet Isospectrality of the Zero Potential for Discrete Periodic Schr\\\"odinger Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.SP","authors_text":"Cindy Zhuang, Ethan Tran, Jenna Plute, Jonah Robinson, Matthew Faust, Rodrigo Matos, Wencai Liu, Yichen Tao","submitted_at":"2024-01-18T05:19:07Z","abstract_excerpt":"Let $\\Gamma=q_1\\mathbb{Z}\\oplus q_2 \\mathbb{Z}\\oplus\\cdots\\oplus q_d\\mathbb{Z}$, with $q_j\\in (\\mathbb{Z}^+)^d$ for each $j\\in \\{1,\\ldots,d\\}$, and denote by $\\Delta$ the discrete Laplacian on $\\ell^2\\left( \\mathbb{Z}^d\\right)$. Using Macaulay2, we first numerically find complex-valued $\\Gamma$-periodic potentials $V:\\mathbb{Z}^d\\to \\mathbb{C}$ such that the operators $\\Delta+V$ and $\\Delta$ are Floquet isospectral. We then use combinatorial methods to validate these numerical solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.09731","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.09731/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}