{
  "id": "2202.05203",
  "version": "v1",
  "published": "2022-02-10T18:04:19.000Z",
  "updated": "2022-02-10T18:04:19.000Z",
  "title": "Field theoretical approach to open quantum systems and the Lindblad equation",
  "authors": [
    "Hans C. Fogedby"
  ],
  "comment": "34 pages, 3 figures, latex document, submitted for publication",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We develop a field theoretical approach to open quantum systems based on condensed matter many body methods. The time evolution of the reduced density matrix for the open system is determined by a transmission matrix. Invoking Wick's theorem in connection with a Caldeira-Leggett quantum oscillator environment the transmission matrix satisfies a Dyson equation characterised by an irreducible kernel. The Dyson equation is equivalent to a general master equation for the reduced density matrix. We consider the Born approximation for the kernel. Applying a condensed matter \"quasi-particle-type\" approximation we obtain a Master equation of the Markov type. Imposing the rotating wave approximation we obtain a Markov master equation of the Lindblad form. As a standard example we discuss the case of a single qubit coupled to a thermal heat bath.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-10T18:04:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open quantum systems",
      "field theoretical approach",
      "lindblad equation",
      "reduced density matrix",
      "transmission matrix"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}