{"paper":{"title":"Economised path integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"physics.chem-ph","authors_text":"David E. Manolopoulos, Zezhu Zeng","submitted_at":"2026-07-07T15:45:10Z","abstract_excerpt":"The Hessian of the ring polymer spring potential in the standard Trotter path integral is a $P\\times P$ symmetric circulant matrix with a centroid eigenvalue of zero. All such matrices commute and are diagonalised by the same bead to normal mode transformation matrix, and their eigenvalues contain $\\lceil P/2\\rceil-1$ degenerate pairs by symmetry. However, this still leaves some freedom to improve on the Trotter approximation: one can optimise the remaining $\\lfloor P/2\\rfloor$ independent non-zero normal mode frequencies to fit the exact quantum mechanical radii of gyration of harmonic ring p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06414","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/2607.06414/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"}