{"paper":{"title":"Bounds on the spectral shift function and the density of states","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dirk Hundertmark, Ivan Veselic', Peter Stollmann, Rowan Killip, Shu Nakamura","submitted_at":"2004-12-21T22:41:15Z","abstract_excerpt":"We study spectra of Schr\\\"odinger operators on $\\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values $\\mu_n$ of the difference of the semigroups as $n\\to \\infty$ and deduce bounds on the spectral shift function of the pair of operators.\n  Thereafter we consider alloy type random Schr\\\"odinger operators. The single site potential $u$ is assumed to be non-negative and of compact support. The distributions of the random coupling constants are assumed to be H\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0412078","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":""},"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"}