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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 $-\\Delta\\_{{\\bf \\Omega}}$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.07202","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-03-23T14:35:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ef3b8a3da13c57b45e1d87aa2d51d7a40e6bbf77fb8f51f275087430f1948552","abstract_canon_sha256":"15f5b32e1860770065bc79ba50cae759002dcd25614ed6784ffe31d6f36ee8ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:40.431428Z","signature_b64":"tKWYOV3jkDO3p/7TwMO+XjaBfaFKTVJlDMt4BXGU/7LXHuyVo/gTBRm/qTXwR138NSGHmKh9klRtqfi043QxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2db4559bf528d5fecd68e3f998a6033106b8a4b093176f8c793a4727f13d626f","last_reissued_at":"2026-05-18T00:54:40.430829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:40.430829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $-\\Delta\\_{{\\bf \\Omega}}$. 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