{"paper":{"title":"On the distribution of perturbations of propagated Schr\\\"odinger eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Dmitry Jakobson, John Toth, Yaiza Canzani","submitted_at":"2012-10-16T17:15:17Z","abstract_excerpt":"Let $(M,g_0)$ be a compact Riemmanian manifold of dimension $n$. Let $P_0 (\\h) := -\\h^2\\Delta_{g}+V$ be the semiclassical Schr\\\"{o}dinger operator for $\\h \\in (0,\\h_0]$, and let $E$ be a regular value of its principal symbol $p_0(x,\\xi)=|\\xi|^2_{g_0(x)} +V(x)$. Write $\\varphi_\\h$ for an $L^2$-normalized eigenfunction of $P(\\h)$, $P_0(\\h)\\varphi_\\h =E(\\h)\\varphi_\\h$ and $E(\\h) \\in [E-o(1),E+ o(1)]$. Consider a smooth family of perturbations $g_u$ of $g_0$ with $u$ in the ball $\\mathcal B^k(\\varepsilon) \\subset \\mathbb R^k$ of radius $\\varepsilon>0$. For $P_{u}(\\h) := -\\h^2 \\Delta_{g_u} +V$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4499","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"}