{
  "abstract": "We investigate time-dependent semiclassical measures associated with the magnetic Schr\\\"odinger flow on the flat two-dimensional torus in long-time regimes. Under a geometric nonvanishing assumption on an effective magnetic force, we identify two thresholds and prove a dynamical form of quantum unique ergodicity for such systems. If the time scale $\\tau_h \\gg h^{-1/2}$, then the configuration marginal is the normalized Lebesgue measure on $\\mathbb T^2$. In addition, if $\\tau_h \\gg h^{-1}$, then the momentum marginal is, conditionally on each regular level set, the normalized invariant measure on that curve.",
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  "arxiv": "2609.19224",
  "author_total": 1,
  "authors": [
    {
      "name": "Julien Lechaux"
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  "doi": "10.48550/arxiv.2609.19224",
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  "published": "2026-09-02",
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      "first_seen": "2026-10-30T12:17:34Z",
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      "native_id": "2609.19224",
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      "url": "https://arxiv.org/abs/2609.19224"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
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    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
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  "title": "Long-time dynamics for the magnetic Schrödinger equation on the torus",
  "title_text": "Long-time dynamics for the magnetic Schrödinger equation on the torus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/4pk99dtm6v2ak",
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