{"paper":{"title":"Semiclassical approximation and noncommutative geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thierry Paul (CMLS-EcolePolytechnique)","submitted_at":"2011-08-28T06:26:33Z","abstract_excerpt":"We consider the long time semiclassical evolution for the linear Schr\\\"odinger equation. We show that, in the case of chaotic underlying classical dynamics and for times up to $\\hbar^{-2+\\epsilon},\\ \\epsilon>0$, the symbol of a propagated observable by the corresponding von Neumann-Heisenberg equation is, in a sense made precise below, precisely obtained by the push-forward of the symbol of the observable at time $t=0$. The corresponding definition of the symbol calls upon a kind of Toeplitz quantization framework, and the symbol itself is an element of the noncommutative algebra of the (stron"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5495","kind":"arxiv","version":3},"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"}