{
  "annotation_id": "ba178359-4765-41d2-842d-3e5bcb8c56eb",
  "date_created": "2026-03-02T18:02:44.971000Z",
  "date_modified": "2026-03-02T18:02:44.971000Z",
  "file_hash": "4b9709b3fad1a3948f21a2eccf69694d53d5687bf9924055936f7b15736a0228",
  "private": false,
  "record": {
    "abstract": "A precise calculation of the ground-state energy of the complex PT-symmetric\nHamiltonian $H=p^2+{1/4}x^2+i \\lambda x^3$, is performed using high-order\nRayleigh-Schr\\\"odinger perturbation theory. The energy spectrum of this\nHamiltonian has recently been shown to be real using numerical methods. The\nRayleigh-Schr\\\"odinger perturbation series is Borel summable, and Pad\\\u0027e\nsummation provides excellent agreement with the real energy spectrum. Pad\\\u0027e\nanalysis provides strong numerical evidence that the once-subtracted\nground-state energy considered as a function of $\\lambda^2$ is a Stieltjes\nfunction. The analyticity properties of this Stieltjes function lead to a\ndispersion relation that can be used to compute the imaginary part of the\nenergy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\\epsilon\nx^3$.",
    "arxiv_id": "quant-ph/9812039",
    "authors": [
      "Carl M. Bender",
      "Gerald V. Dunne"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "hep-th"
    ],
    "doi": "10.1063/1.532991",
    "journal_ref": "J.Math.Phys. 40 (1999) 4616-4621",
    "title": "Large-order Perturbation Theory for a Non-Hermitian PT-symmetric   Hamiltonian",
    "url": "https://arxiv.org/abs/quant-ph/9812039"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "85aa6f85-7233-4a96-92e7-2f667cce70f9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}