{"paper":{"title":"An Egorov Theorem for Wasserstein Distances","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"quant-ph","authors_text":"Felipe Hern\\'andez, Jordan Cotler","submitted_at":"2025-09-08T20:03:38Z","abstract_excerpt":"We prove a new version of Egorov's theorem formulated in the Schr\\\"{o}dinger picture of quantum mechanics, using the $p$-Wasserstein metric applied to the Husimi functions of quantum states. The special case $p=1$ corresponds to a \"low-regularity\" Egorov theorem, while larger values $p>1$ yield progressively stronger estimates. As a byproduct of our analysis, we prove an optimal transport inequality analogous to a result of Golse and Paul in the context of mean-field many-body quantum mechanics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07185","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.07185/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"}