{"paper":{"title":"Spectral Asymptotics for Waveguides with Perturbed Periodic Twisting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Raikov","submitted_at":"2014-07-03T01:20:19Z","abstract_excerpt":"We consider the twisted waveguide $\\Omega_\\theta$, i.e. the domain obtained by the rotation of the bounded cross section $\\omega \\subset {\\mathbb R}^{2}$ of the straight tube $\\Omega : = \\omega \\times {\\mathbb R}$ at angle $\\theta$ which depends on the variable along the axis of $\\Omega$. We study the spectral properties of the Dirichlet Laplacian in $\\Omega_\\theta$, unitarily equivalent under the diffeomorphism $\\Omega_\\theta \\to \\Omega$ to the operator $H_{\\theta'}$, self-adjoint in ${\\rm L}^2(\\Omega)$. We assume that $\\theta' = \\beta - \\epsilon$ where $\\beta$ is a $2\\pi$-periodic function, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0757","kind":"arxiv","version":4},"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"}