{"paper":{"title":"The dynamics of the Schr\\\"odinger flow from the point of view of semiclassical measures","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 Macia, Nalini Anantharaman","submitted_at":"2011-02-04T16:57:14Z","abstract_excerpt":"On a compact Riemannian manifold, we study the various dynamical properties of the Schr\\\"odinger flow $(e^{it\\Delta/2})$, through the notion of semiclassical measures and the quantum-classical correspondence between the Schr\\\"odinger equation and the geodesic flow. More precisely, we are interested in its high-frequency behavior, as well as its regularizing and unique continuation-type properties. We survey a variety of results illustrating the difference between positive, negative and vanishing curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0970","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"}