{
  "id": "2311.16010",
  "version": "v1",
  "published": "2023-11-27T17:09:27.000Z",
  "updated": "2023-11-27T17:09:27.000Z",
  "title": "Long-term behaviour in an exactly solvable model of pure decoherence and the problem of Markovian embedding",
  "authors": [
    "Anton Trushechkin"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a well-known exactly solvable model of an open quantum system with pure decoherence. The aim of this paper is twofold. Firstly, decoherence is a property of open quantum systems important for both quantum technologies and the fundamental question of quantum-classical transition. It is worthwhile to study how the long-term rate of decoherence depends on the spectral density characterizing the system-bath interaction in this exactly solvable model. Secondly, we address a more general problem of the Markovian embedding of a non-Markovian open system dynamics. It is often assumed that a non-Markovian open quantum system can be embedded into a larger Markovian system. However, we show that such embedding is possible only for the Ohmic spectral densities (for the case of a positive bath temperature) and is impossible for both the sub- and super-Ohmic spectral densities. From the other side, for the Ohmic spectral densities, an asymptotic large-time Markovianity (in terms of the quantum regression formula) takes place.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-27T17:09:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exactly solvable model",
      "pure decoherence",
      "markovian embedding",
      "long-term behaviour",
      "spectral density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}