{"paper":{"title":"Eigenvalue asymptotics for the one-particle density matrix and one-particle kinetic energy density operator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Alexander V. Sobolev, S{\\o}ren Fournais","submitted_at":"2026-08-10T13:07:18Z","abstract_excerpt":"Let $\\psi({\\mathbf x})$, ${\\mathbf x} \\in{\\mathbb R}^{3N}$, be an eigenfunction of the $N$-particle atomic Schr\\\"odinger operator. We consider the one-particle density matrix $\\gamma(x, y)$ and one-particle kinetic energy density $\\varkappa(x, y)$, $x, y\\in {\\mathbb R}^3$, associated with the eigenfunction $\\psi$. Both functions play a central role in quantum chemistry computations of atomic and molecular bound states: the knowledge of the eigenvalue behaviour of the integral operators ${\\sf{\\Gamma}}$ and ${\\sf{K}}$ with kernels $\\gamma(x, y)$ and $\\varkappa(x, y)$ serves to estimate the error"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09570","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/2608.09570/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"}