{"paper":{"title":"Dynamical Amrein-Berthier Uncertainty for Fractional Schr\\\"odinger Flows","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Diego Fiorletta, Piero D'Ancona","submitted_at":"2026-06-09T10:41:11Z","abstract_excerpt":"We prove dynamical Amrein-Berthier uncertainty principles for fractional Schr\\\"odinger flows. For the free Hamiltonian $H=(-\\Delta)^\\alpha$ on $L^2(\\mathbb{R}^n)$, with $\\alpha>\\frac{1}{2}$, we show that two--time localization on finite measure sets $E,F$ forces the quantitative estimate \\begin{equation*} \\|u(t)\\|_{L^{2}}\\lesssim_{E,F,T,n,\\alpha} \\|u(0)\\|_{L^{2}(E^{c})} + \\|u(T)\\|_{L^{2}(F^{c})}, \\qquad T\\neq0,\\ t\\in \\mathbb{R} \\end{equation*} for $u(t)=e^{-itH}u(0)$ at every time. The threshold $\\alpha>\\frac{1}{2}$ is tied to the stationary phase structure of the fractional kernel. If $\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10685","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/2606.10685/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"}