{
  "abstract": "We study the time-of-arrival (TOA) distribution of a Gaussian wave packet in the semiclassical regime for a general one-dimensional quadratic Hamiltonian, namely a forced harmonic oscillator with time-dependent frequency. Expanding the Gaussian probability density as a series in derivatives of the Dirac delta and using the standard rules for the composition of distributions with the classical trajectory, we obtain compact closed-form expressions for the leading semiclassical mean arrival time and its standard deviation. The mean acquires a quantum shift of order $σ^2$ set by the classical velocity and acceleration and by the time derivative of the Ermakov width, while the spread reduces to the simple form $Δ\\mathcal{T}_x\\simeqσ(t_x)/v_x$. The latter implies a time--position uncertainty relation that depends only on the fundamental solutions of the classical equation of motion. We apply the framework to free fall and to two models of a time-dependent opening trap under gravity, and we validate every expression against exact numerical integration of the TOA distribution. These results extend earlier free-fall predictions to realistic settings in which the trapping potential cannot be neglected.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19027",
  "author_total": 3,
  "authors": [
    {
      "name": "Mathieu Beau"
    },
    {
      "name": "Maximilien Barbier"
    },
    {
      "name": "Vincent Bucourt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5j36ge1k6yvps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19027",
  "fulltext_url": null,
  "id": "5j36ge1k6yvps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19027",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7213529002",
  "pdf_url": "https://arxiv.org/pdf/2609.19027",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5j36ge1k6yvps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.19027",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19027"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Time of arrival in the semiclassical regime for Gaussian wave packets",
  "title_text": "Time of arrival in the semiclassical regime for Gaussian wave packets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/5j36ge1k6yvps",
  "venue": "arXiv",
  "versions": []
}