{"paper":{"title":"Generalised Quantum Waveguides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jonas Lampart, Stefan Haag, Stefan Teufel","submitted_at":"2014-02-05T15:09:10Z","abstract_excerpt":"We study general quantum waveguides and establish explicit effective Hamiltonians for the Laplacian on these spaces. A conventional quantum waveguide is an $\\varepsilon$-tubular neighbourhood of a curve in $\\mathbb{R}^3$ and the object of interest is the Dirichlet Laplacian on this tube in the asymptotic limit $\\varepsilon\\to0$. We generalise this by considering fibre bundles $M$ over a $d$-dimensional submanifold $B\\subset\\mathbb{R}^{d+k}$ with fibres diffeomorphic to $F\\subset\\mathbb{R}^k$, whose total space is embedded into an $\\varepsilon$-neighbourhood of $B$. From this point of view $B$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1067","kind":"arxiv","version":1},"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"}