{"paper":{"title":"Long time semiclassical Egorov theorem for $\\hbar$-pseudodifferential systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Marouane Assal","submitted_at":"2016-02-22T16:58:11Z","abstract_excerpt":"In the Heisenberg picture, we study the semiclassical time evolution of a bounded quantum observable $Q^w(x,\\hbar D_x)$ associated to a $(m\\times m)$ matrix-valued symbol $Q$ generated by a semiclassical matrix-valued Hamiltonian $H\\sim H_0+\\hbar H_1$. Under a non-crossing assumption on the eigenvalues of the principal symbol $H_0$ that ensures the existence of almost invariant subspaces of $L^{2}(\\mathbb R^n)\\otimes \\mathbb C^m$, and for a class of observables that are semiclassically block-diagonal with respect to the projections onto these almost invariants subspaces, we establish a long ti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06856","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"}