{"paper":{"title":"Concentration and non-concentration for the Schr\\\"odinger evolution on Zoll manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Fabricio Maci\\`a, Gabriel Rivi\\`ere","submitted_at":"2015-05-19T10:28:50Z","abstract_excerpt":"We study the long time dynamics of the Schr\\\"odinger equation on Zoll manifolds. We establish criteria under which the solutions of the Schr\\\"odinger equation can or cannot concentrate on a given closed geodesic. As an application, we derive some results on the set of semiclassical measures for eigenfunctions of Schr\\\"odinger operators: we prove that adding a potential to the Laplacian on the sphere results on the existence of geodesics $\\gamma$ such that $\\delta_\\gamma$ cannot be obtained as a semiclassical measure for some sequence of eigenfunctions. We also show that the same phenomenon occ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04945","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"}