{"paper":{"title":"Recovering hidden Bloch character: Unfolding Electrons, Phonons, and Slabs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"D. A. Casavant, J. M. Soler, P. B. Allen, T. Berlijn","submitted_at":"2012-12-22T15:54:10Z","abstract_excerpt":"For a quantum state, or classical harmonic normal mode, of a system of spatial periodicity \"R\", Bloch character is encoded in a wavevector \"K\". One can ask whether this state has partial Bloch character \"k\" corresponding to a finer scale of periodicity \"r\". Answering this is called \"unfolding.\" A theorem is proven that yields a mathematically clear prescription for unfolding, by examining translational properties of the state, requiring no \"reference states\" or basis functions with the finer periodicity (r,k). A question then arises, how should one assign partial Bloch character to a state of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5702","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":""},"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"}