{"paper":{"title":"The spectrum of the scattering matrix near resonant energies in the semiclassical limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Shu Nakamura","submitted_at":"2012-02-21T17:06:11Z","abstract_excerpt":"The object of study in this paper is the on-shell scattering matrix $S(E)$ of the Schr\\\"odinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of $S(E)$ in the semiclassical limit when the energy parameter $E$ varies from $E_\\text{res}-\\varepsilon$ to $E_\\text{res}+\\varepsilon$, where $E_\\text{res}$ is a real part of a resonance, and $\\varepsilon$ is sufficiently small. The main result of our work describes the spectral flow of the scattering matrix through a given point on the unit circle. This result is closely related to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4702","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"}