{"paper":{"title":"On orbital stability of ground states for finite crystals in fermionic Schr\\\"odinger--Poisson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Komech, Elena Kopylova","submitted_at":"2017-11-08T13:34:29Z","abstract_excerpt":"We consider the Schr\\\"odinger--Poisson--Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electron field is described by the $N$-particle Schr\\\"odinger equation with antisymmetric wave function.\n  Our main results are i) the global dynamics with moving ions, and ii) the orbital stability of periodic ground state under a novel Jellium and Wiener-type conditions on the ion charge density. Under Jellium condition both ionic and electronic charge densities of the ground state are uniform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02938","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"}