{"paper":{"title":"Tunneling resonances in systems without a classical trapping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. Golovina, D. Borisov, P. Exner","submitted_at":"2012-10-01T15:55:15Z","abstract_excerpt":"In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths $\\ell_\\pm$ separated by a window of length 2a. It is known that if the barriers are semiinfinite, i.e. we have two adjacent waveguides coupled laterally through the boundary window, the system has for any a>0 a finite number of eigenvalues below the essential spectrum threshold. Here we demonstrate that for large but finite $\\ell_\\pm$ the system has resonances which converge to the said eigenvalues as $\\ell_\\pm\\to\\infty$, and derive the leading term in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0449","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"}