{
  "abstract": "We study the observability of the Schrödinger equation on the $d$-dimensional torus $\\T^d=\\R^d/(2π\\Z)^d$, $d \\geq 1$, from an open subset $ω\\subset \\T^d$. Our main result establishes a quantitative observability estimate for the free Schrödinger equation in the regime of small times $T$ and small observation sets of the form $ω= \\prod_{j=1}^{d}(a_j,b_j)$. A central ingredient in the proof is a cluster decomposition method combined with an induction scheme introduced by Bourgain and further developed by Burq and Zhu.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.02480",
  "author_total": 2,
  "authors": [
    {
      "name": "Kévin Le Balc'h"
    },
    {
      "name": "Jiaqi Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16yy4yev684s0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.02480",
  "fulltext_url": null,
  "id": "16yy4yev684s0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.02480",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7160329053",
  "pdf_url": "https://arxiv.org/pdf/2605.02480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16yy4yev684s0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2605.02480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.02480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Quantitative observability of the Schrödinger equation in the torus from open sets",
  "title_text": "Quantitative observability of the Schrödinger equation in the torus from open sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/16yy4yev684s0",
  "venue": "arXiv",
  "versions": []
}