{"paper":{"title":"A Correlational Bound for Eigenvalues of Fermionic 2-Body Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Martin Ravn Christiansen","submitted_at":"2025-05-27T13:21:51Z","abstract_excerpt":"We prove that the eigenvalues of a 2-body operator $\\gamma_{2}^{\\Psi}$ associated to a fermionic $N$-particle state $\\Psi$ are highly constrained by the structure of the corresponding eigenvectors: If $\\Phi=\\sum_{k=1}^{\\infty}\\lambda_{k}u_{k}\\wedge v_{k}$ is the canonical form of an eigenvector $\\Phi$ with eigenvalue $\\Lambda$, then $\\Lambda\\leq(1+\\frac{N-2}{2}\\sum_{k=1}^{\\infty}\\lambda_{k}^{4})^{-1}N$. We also prove a lower bound on $\\sup_{\\Vert \\Psi\\Vert =1}\\langle \\Phi,\\gamma_{2}^{\\Psi}\\Phi\\rangle$ for fixed $\\Phi$, and state a conjecture motivated by these results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21167","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/2505.21167/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"}