{
  "annotation_id": "726a4b9c-1d58-4df3-aeaf-6b5dd0e1d0b2",
  "date_created": "2026-03-02T18:01:48.880000Z",
  "date_modified": "2026-03-02T18:01:48.880000Z",
  "file_hash": "c4342f9904a7ffe9667d3af61603bb2a51a898998e35e4012ccc6de1bcc185b3",
  "private": false,
  "record": {
    "abstract": "In this paper we introduce a generalization to the algebraic Bender-Wu\nrecursion relation for the eigenvalues and the eigenfunctions of the anharmonic\noscillator. We extend this well known formalism to the time-dependent quantum\nstatistical Schroedinger equation, thus obtaining the imaginary-time evolution\namplitude by solving a recursive set of ordinary differential equations. This\napproach enables us to evaluate global and local quantum statistical quantities\nof the anharmonic oscillator to much higher orders than by evaluating Feynman\ndiagrams. We probe our perturbative results by deriving a perturbative\nexpression for the free energy which is then subject to variational\nperturbation theory as developed by Kleinert, yielding convergent results for\nthe free energy for all values of the coupling strength.",
    "arxiv_id": "quant-ph/0203014",
    "authors": [
      "Florian Weissbach",
      "Axel Pelster",
      "Bodo Hamprecht"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevE.66.036129",
    "journal_ref": "Phys. Rev. E 66, 036129 (2002)",
    "title": "High-Order Variational Perturbation Theory for the Free Energy",
    "url": "https://arxiv.org/abs/quant-ph/0203014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8e71f897-4f4b-4768-bc40-633060ec808c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}