{"paper":{"title":"On the long-time asymptotics of quantum dynamical semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Guido A. Raggio, Pablo R. Zangara","submitted_at":"2014-02-28T15:46:59Z","abstract_excerpt":"We consider semigroups $\\{\\alpha_t: \\; t\\geq 0\\}$ of normal, unital, completely positive maps $\\alpha_t$ on a von Neumann algebra ${\\mathcal M}$. The (predual) semigroup $\\nu_t (\\rho):= \\rho \\circ \\alpha_t$ on normal states $\\rho$ of $\\mathcal M$ leaves invariant the face ${\\mathcal F}_p:= \\{\\rho : \\; \\rho (p)=1\\}$ supported by the projection $p\\in {\\mathcal M}$, if and only if $\\alpha_t(p)\\geq p$ (i.e., $p$ is sub-harmonic). We complete the arguments showing that the sub-harmonic projections form a complete lattice. We then consider $r_o$, the smallest projection which is larger than each sup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7287","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"}