{"paper":{"title":"Typical Macroscopic Long-Time Behavior for Random Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Cornelia Vogel, Roderich Tumulka, Stefan Teufel","submitted_at":"2023-03-23T13:18:28Z","abstract_excerpt":"We consider a closed macroscopic quantum system in a pure state $\\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\\mathcal{H}_\\nu$ (macro spaces) of Hilbert space, each of which has large dimension. We extend previous work on the question what the evolution of $\\psi_t$ looks like macroscopically, specifically on how much of $\\psi_t$ lies in each $\\mathcal{H}_\\nu$. Previous bounds concerned the \\emph{absolute} error for typical $\\psi_0$ and/or $t$ and are valid for arbitrary Hamiltonians $H$; now, we provide bounds on the \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.13242","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.13242/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}