{
  "abstract": "We study the asymptotic behavior of the optimal stabilization prefactor for the free Schrödinger equation, optimized over all bounded stationary linear feedbacks. For a prescribed decay rate $δ>0$, let $\\widehat{C}_S(δ)$ denote this optimal prefactor. Assuming that the uncontrolled region contains a nonempty open set and that the observability cost satisfies $C(T)\\le C_0e^{C_0/T}$ for small $T>0$, we prove $$ e^{c\\sqrtδ}\\le \\widehat{C}_S(δ)\\le e^{C\\sqrtδ}, \\qquad δ\\gg1. $$ The lower bound is based on the uncontrolled open hole and a quantitative cutoff construction adapted to the Laplacian, while the upper bound combines an exponentially weighted Gramian with the small-time observability cost $C(T)\\lesssim e^{C/T}$. The results apply to controlled Schrödinger equations in three settings: flat tori, including a strip-control example beyond the geometric control condition; the whole space $\\mathbb{R}^n$ with exterior-ball control; and bounded smooth domains satisfying the geometric control condition for generalized geodesics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28055",
  "author_total": 3,
  "authors": [
    {
      "name": "Shanlin Huang"
    },
    {
      "name": "Changqin Quan"
    },
    {
      "name": "Gengsheng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1w5gtzt7jbvf1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28055",
  "fulltext_url": null,
  "id": "1w5gtzt7jbvf1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28055",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7214168605",
  "pdf_url": "https://arxiv.org/pdf/2609.28055",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1w5gtzt7jbvf1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28055",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28055"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Asymptotic Growth of Optimal Stabilization Prefactors for the Schrödinger Equations",
  "title_text": "Asymptotic Growth of Optimal Stabilization Prefactors for the Schrödinger Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1w5gtzt7jbvf1",
  "venue": "arXiv",
  "versions": []
}