{
  "annotation_id": "b39d175f-52f2-492d-a043-4e6ba6330c3a",
  "date_created": "2026-03-02T18:02:34.604000Z",
  "date_modified": "2026-03-02T18:02:34.604000Z",
  "file_hash": "338c5aea13a0aa9ea9cdafbc0edde99976428507feb2ac7f496ae9c47fc995e9",
  "private": false,
  "record": {
    "abstract": "In this paper we derive an exact master equation for two coupled quantum\nharmonic oscillators interacting via bilinear coupling with a common\nenvironment at arbitrary temperature made up of many harmonic oscillators with\na general spectral density function. We first show a simple derivation based on\nthe observation that the two-harmonic oscillator model can be effectively\nmapped into that of a single harmonic oscillator in a general environment plus\na free harmonic oscillator. Since the exact one harmonic oscillator master\nequation is available [Hu, Paz and Zhang, Phys. Rev. D \\textbf{45}, 2843\n(1992)], the exact master equation with all its coefficients for this two\nharmonic oscillator model can be easily deduced from the known results of the\nsingle harmonic oscillator case. In the second part we give an influence\nfunctional treatment of this model and provide explicit expressions for the\nevolutionary operator of the reduced density matrix which are useful for the\nstudy of decoherence and disentanglement issues. We show three applications of\nthis master equation: on the decoherence and disentanglement of two harmonic\noscillators due to their interaction with a common environment under Markovian\napproximation, and a derivation of the uncertainty principle at finite\ntemperature for a composite object, modeled by two interacting harmonic\noscillators. The exact master equation for two, and its generalization to $N$,\nharmonic oscillators interacting with a general environment are expected to be\nuseful for the analysis of quantum coherence, entanglement, fluctuations and\ndissipation of mesoscopic objects towards the construction of a theoretical\nframework for macroscopic quantum phenomena.",
    "arxiv_id": "quant-ph/0703088",
    "authors": [
      "Chung-Hsien Chou",
      "Ting Yu",
      "B. L. Hu"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech",
      "gr-qc"
    ],
    "doi": "10.1103/PhysRevE.77.011112",
    "journal_ref": "Phys.Rev.E77:011112,2008",
    "title": "Exact Master Equation and Quantum Decoherence of Two Coupled Harmonic   Oscillators in a General Environment",
    "url": "https://arxiv.org/abs/quant-ph/0703088"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dd88b0ad-b6ef-4625-802d-ca1af3cdeb9a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}