{
  "id": "1809.09377",
  "version": "v1",
  "published": "2018-09-25T09:29:40.000Z",
  "updated": "2018-09-25T09:29:40.000Z",
  "title": "Evolution operator for time-dependent non-Hermitian Hamiltonians",
  "authors": [
    "Bijan Bagchi"
  ],
  "comment": "9 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "The evolution operator U(t) for a time-independent parity-time-symmetric systems is well studied in the literature. However, for the non-Hermitian time-dependent systems, a closed form expression for the evolution operator is not available. In this paper, we make use of a procedure, originally developed by A.R.P. Rau [Phys.Rev.Lett, 81, 4785-4789 (1998)], in the context of deriving the solution of Liuville-Bloch equations in the product form of exponential operators when time-dependent external fields are present, for the evaluation of U(t) in the interaction picture wherein the corresponding Hamiltonian is time-dependent and in general non-Hermitian. This amounts to a transformation of the whole scheme in terms of addressing a nonlinear Riccati equation the existence of whose solutions depends on the fulfillment of a certain accompanying integrabilty condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-25T09:29:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "evolution operator",
      "time-dependent non-hermitian hamiltonians",
      "time-independent parity-time-symmetric systems",
      "non-hermitian time-dependent systems",
      "nonlinear riccati equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}