{
  "id": "2212.01671",
  "version": "v1",
  "published": "2022-12-03T18:56:02.000Z",
  "updated": "2022-12-03T18:56:02.000Z",
  "title": "Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations",
  "authors": [
    "Fabio Bagarello"
  ],
  "comment": "In press in Mathematical Physics, Analysis and Geometry",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In some recent literature the role of non self-adjoint Hamiltonians, $H\\neq H^\\dagger$, is often considered in connection with gain-loss systems. The dynamics for these systems is, most of the times, given in terms of a Schr\\\"odinger equation. In this paper we rather focus on the Heisenberg-like picture of quantum mechanics, stressing the (few) similarities and the (many) differences with respected to the standard Heisenberg picture for systems driven by self-adjoint Hamiltonians. In particular, the role of the symmetries, *-derivations and integrals of motion is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-03T18:56:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non self-adjoint hamiltonians",
      "heisenberg dynamics",
      "symmetries",
      "derivations",
      "standard heisenberg picture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}