{"paper":{"title":"Anderson's Orthogonality Catastrophe for One-dimensional Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math.MP"],"primary_cat":"math-ph","authors_text":"Heinrich K\\\"uttler, Peter Otte, Wolfgang Spitzer","submitted_at":"2013-01-21T16:51:17Z","abstract_excerpt":"We derive rigorously the leading asymptotics of the so-called Anderson integral in the thermodynamic limit for one-dimensional, non-relativistic, spin-less Fermi systems. The coefficient, $\\gamma$, of the leading term is computed in terms of the S-matrix. This implies a lower and an upper bound on the exponent in Anderson's orthogonality catastrophe, $\\tilde CN^{-\\tilde\\gamma}\\leq \\mathcal{D}_N\\leq CN^{-\\gamma}$ pertaining to the overlap, $\\mathcal{D}_N$, of ground states of non-interacting fermions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4923","kind":"arxiv","version":2},"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"}