{
  "id": "1005.1604",
  "version": "v1",
  "published": "2010-05-10T16:34:17.000Z",
  "updated": "2010-05-10T16:34:17.000Z",
  "title": "Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system",
  "authors": [
    "Andrea Smirne",
    "Bassano Vacchini"
  ],
  "comment": "12 pages, no figures",
  "journal": "Phys. Rev. A 82, 022110 (2010)",
  "doi": "10.1103/PhysRevA.82.022110",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The considered system includes the damped and undamped Jaynes-Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and time-convolutionless generator as well as Nakajima-Zwanzig memory kernel. This non-perturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that depending on the state of the environment the operator structures of the two set of equations of motion can exhibit important differences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-10T16:34:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Yz",
      "03.65.Ta",
      "42.50.Lc"
    ],
    "keywords": [
      "two-level system",
      "non-markovian dynamics",
      "nakajima-zwanzig memory kernel",
      "time dependent function",
      "exact time-convolutionless master equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2010,
      "month": "Aug",
      "volume": 82,
      "number": 2,
      "pages": "022110"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvA..82b2110S"
    }
  }
}