{"paper":{"title":"Resonances and Spectral Shift Function Singularities for Magnetic Quantum Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"G. Raikov, J.-F. Bony, V. Bruneau","submitted_at":"2012-05-15T13:30:21Z","abstract_excerpt":"In this survey article we consider the operator pair $(H,H_0)$ where $H_0$ is the shifted 3D Schr\\\"odinger operator with constant magnetic field, $H : = H_0 + V$, and $V$ is a short-range electric potential of a fixed sign. We describe the asymptotic behavior of the Krein spectral shift function (SSF) $\\xi(E; H,H_0)$ as the energy $E$ approaches the Landau levels $2bq$, $q \\in {\\mathbb Z}_+$, which play the role of thresholds in the spectrum of $H_0$. The main asymptotic term of $\\xi(E; H,H_0)$ as $E \\to 2bq$ with a fixed $q \\in {\\mathbb Z}_+$ is written in the terms of appropriate compact Ber"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3362","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"}