{"paper":{"title":"Solutions of random-phase approximation equation for positive-semidefinite stability matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"H. Nakada","submitted_at":"2016-06-10T03:16:40Z","abstract_excerpt":"It is mathematically proven that, if the stability matrix $\\mathsf{S}$ is positive-semidefinite, solutions of the random-phase approximation (RPA) equation are all physical or belong to Nambu-Goldstone (NG) modes, and the NG-mode solutions may form Jordan blocks of $\\mathsf{N\\,S}$ ($\\mathsf{N}$ is the norm matrix) but their dimension is not more than two. This guarantees that the NG modes in the RPA can be separated out via canonically conjugate variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03167","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"}