{"ID":2864392,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23965","arxiv_id":"2509.23965","title":"Observability of Schrödinger propagators on tori in rough settings","abstract":"On tori of arbitrary dimensions, Schrödinger propagators with bounded potentials are conjectured to be observable from space-time domains of positive Lebesgue measure. We reduce this conjecture to certain integrability bounds for free Schrödinger waves, thereby proving the conjecture on the one-dimensional torus and producing new examples of observation domains. These bounds are far weaker than Bourgain's conjectured periodic Strichartz estimates, yet remain highly nontrivial.","short_abstract":"On tori of arbitrary dimensions, Schrödinger propagators with bounded potentials are conjectured to be observable from space-time domains of positive Lebesgue measure. We reduce this conjecture to certain integrability bounds for free Schrödinger waves, thereby proving the conjecture on the one-dimensional torus and pr...","url_abs":"https://arxiv.org/abs/2509.23965","url_pdf":"https://arxiv.org/pdf/2509.23965v2","authors":"[\"Nicolas Burq\",\"Hui Zhu\"]","published":"2025-09-28T16:42:27Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math-ph\",\"math.FA\",\"math.OC\"]","methods":"[]","has_code":false}