{"paper":{"title":"Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alexander V. Sobolev","submitted_at":"2025-06-19T09:51:48Z","abstract_excerpt":"Consider a bound state (an eigenfunction) $\\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\\gamma$ and of the one-particle kinetic energy density matrix $\\tau$ associated with $\\psi$. The paper contains two results. First, we obtain the bounds $\\lambda_k(\\gamma)\\le C_1 k^{-8/3}$ and $\\lambda_k(\\tau)\\le C_2 k^{-2}$ with some positive constants $C_1, C_2$ that depend explicitly on the eigenfunction $\\psi$. The sharpness of these bounds is confirmed by the asymptotic results obtained by the author in earlier papers. The advantage of these bounds over "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16178","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/2506.16178/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"}