{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2111","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"}