{
  "annotation_id": "777b80b1-1d78-4556-b965-737b4cfc7f1c",
  "date_created": "2026-03-02T18:02:24.085000Z",
  "date_modified": "2026-03-02T18:02:24.085000Z",
  "file_hash": "6638e9136b3e6a74562ddf226d91d5afa2d4f8dde922d9c41bcea566b4a28c29",
  "private": false,
  "record": {
    "abstract": "In the framework of the Lindblad theory for open quantum systems the damping\nof the harmonic oscillator is studied. A generalization of the fundamental\nconstraints on quantum mechanical diffusion coefficients which appear in the\nmaster equation for the damped quantum oscillator is presented; the\nSchr\\\"odinger and Heisenberg representations of the Lindblad equation are given\nexplicitly. On the basis of these representations it is shown that various\nmaster equations for the damped quantum oscillator used in the literature are\nparticular cases of the Lindblad equation and that the majority of these\nequations are not satisfying the constraints on quantum mechanical diffusion\ncoefficients. Analytical expressions for the first two moments of coordinate\nand momentum are also obtained by using the characteristic function of the\nLindblad master equation. The master equation is transformed into Fokker-Planck\nequations for quasiprobability distributions. A comparative study is made for\nthe Glauber $P$ representation, the antinormal ordering $Q$ representation and\nthe Wigner $W$ representation. It is proven that the variances for the damped\nharmonic oscillator found with these representations are the same. By solving\nthe Fokker-Planck equations in the steady state, it is shown that the\nquasiprobability distributions are two-dimensional Gaussians with widths\ndetermined by the diffusion coefficients. The density matrix is represented via\na generating function, which is obtained by solving a time-dependent linear\npartial differential equation derived from the master equation. Illustrative\nexamples for specific initial conditions of the density matrix are provided.",
    "arxiv_id": "quant-ph/0602149",
    "authors": [
      "A. Isar",
      "A. Sandulescu"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Romanian J. Phys., Vol. 37, No. 7 (1992), p. 643",
    "title": "Damped quantum harmonic oscillator",
    "url": "https://arxiv.org/abs/quant-ph/0602149"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7e316105-f7e2-4037-a086-1cdeb1a51c75",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}