{
  "id": "2003.05876",
  "version": "v1",
  "published": "2020-03-12T16:12:46.000Z",
  "updated": "2020-03-12T16:12:46.000Z",
  "title": "Passage through exceptional point: Case study",
  "authors": [
    "Miloslav Znojil"
  ],
  "comment": "19 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is conjectured that the exceptional-point (EP) singularity of a one-parametric quasi-Hermitian $N$ by $N$ matrix Hamiltonian $H(t)$ can play the role of a quantum phase-transition interface connecting different dynamical regimes of a unitary quantum system. Six realizations of the EP-mediated quantum phase transitions \"of the third kind\" are described in detail. Fairly realistic Bose-Hubbard (BH) and discrete anharmonic oscillator (AO) models of any matrix dimension $N$ are considered in the initial, intermediate, or final phase. In such a linear algebraic illustration of the changes of phase, all ingredients (and, first of all, all transition matrices) are constructed in closed, algebraic, non-numerical form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-12T16:12:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional point",
      "case study",
      "linear algebraic illustration",
      "discrete anharmonic oscillator",
      "ep-mediated quantum phase transitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}