{"paper":{"title":"The adiabatic limit of Schr\\\"odinger operators on fibre bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Jonas Lampart, Stefan Teufel","submitted_at":"2014-02-03T13:54:17Z","abstract_excerpt":"We consider Schr\\\"odinger operators $H=-\\Delta_{g_\\varepsilon} + V$ on a fibre bundle $M\\stackrel{\\pi}{\\to}B$ with compact fibres and a metric $g_\\varepsilon$ that blows up directions perpendicular to the fibres by a factor ${\\varepsilon^{-1}\\gg 1}$. We show that for an eigenvalue $\\lambda$ of the fibre-wise part of $H$, satisfying a local gap condition, and every $N\\in \\mathbb{N}$ there exists a subspace of $L^2(M)$ that is invariant under $H$ up to errors of order $\\varepsilon^{N+1}$. The dynamical and spectral features of $H$ on this subspace can be described by an effective operator on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0382","kind":"arxiv","version":2},"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"}