{"paper":{"title":"Stark resonances in a quantum waveguide with analytic curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Mounira Gharsalli, Philippe Briet (CPT)","submitted_at":"2016-03-23T14:35:27Z","abstract_excerpt":"We investigate the influence of an electric field on trapped modes arising in a two-dimensional curved quantum waveguide ${\\bf \\Omega}$ i.e. bound states of the corresponding Laplace operator $-\\Delta\\_{{\\bf \\Omega}}$. Here the curvature of the guide is supposed to satisfy some assumptions of analyticity, and decays as $O(|s|^{-\\varepsilon}), \\varepsilon > 3$ at infinity. We show that under conditions on the electric field $ \\bf F$, ${\\bf H}(F):= -\\Delta\\_{{\\bf \\Omega}} + {\\bf F}. {\\bf x} $ has resonances near the discrete eigenvalues of $-\\Delta\\_{{\\bf \\Omega}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07202","kind":"arxiv","version":3},"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"}