{"paper":{"title":"A Phase Space Electronic Structure View of The Solid State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Joseph Subotnik, Nadine Bradbury","submitted_at":"2026-08-06T16:51:54Z","abstract_excerpt":"We develop a phase space electronic structure view of the solid state, where electronic bands are parameterized by both nuclear position $\\mathbf{Q}$ and nuclear momentum $\\mathbf{\\Pi}$ (rather than the standard practice of only $\\mathbf{Q}$). Within this phase space, non-Born-Oppenheimer electronic structure context, we prove a nuclear wavevector ($\\mathbf{q}$)-dependent version of Nafie's equality relating the change in electronic momentum as a function of nuclear momentum, $\\partial \\langle\\mathbf{p}\\rangle/\\partial \\mathbf{\\Pi}_q$, to the change in electronic position as a function of nucl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06260","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/2608.06260/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"}