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We investigate the nature of the essential spectrum of the Dirichlet Laplacian H_\\theta, self-adjoint in L^2 (\\Omega_\\theta), and consider related scattering problems. First, we show that if the derivative of the difference \\theta_1 - \\theta_2 decays fast enough as |x_3| goes to infinity, then the wave operators for the operator"},"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":"1109.2111","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-09T19:56:00Z","cross_cats_sorted":[],"title_canon_sha256":"4b0c39cb7ded11d68e74d9b4d6c8e769a7aaf3b6cb90d682946c68e67c86609e","abstract_canon_sha256":"730839d563a6ca6ea4518a580aead150d96e3329f1f8dd8eaaedf18247614aea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:00.633211Z","signature_b64":"GNaEx/Gbj4ygBA1Sb3GKhPyTfMXz5dLxSJIb2HNG03LWhI3FIzpK+Q+NYUApYtptbKIbUMvZYkeYTil06Ws6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f18d85726f0eb3207b99fa15196d1fac6a07386d295036efbd6492c5235a4c1a","last_reissued_at":"2026-05-18T03:10:00.632793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:00.632793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering in twisted waveguides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Georgi Raikov, Hynek Kovarik, Philippe Briet","submitted_at":"2011-09-09T19:56:00Z","abstract_excerpt":"We consider a twisted quantum waveguide i.e. a domain of the form \\Omega_{\\theta} : = r_\\theta \\omega \\times R, where \\omega \\subset R^2 is a bounded domain, and r_\\theta = r_\\theta(x_3) is a rotation by the angle \\theta(x_3) depending on the longitudinal variable x_3. 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