{
  "id": "2002.05499",
  "version": "v1",
  "published": "2020-02-13T14:04:04.000Z",
  "updated": "2020-02-13T14:04:04.000Z",
  "title": "Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase",
  "authors": [
    "Tommy Ohlsson",
    "Shun Zhou"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "quant-ph",
    "hep-ph",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the transition probabilities for the \"flavor\" eigenstates in the two-level quantum system, which is described by a non-Hermitian Hamiltonian with the parity and time-reversal (PT) symmetry. Particularly, we concentrate on the so-called PT-broken phase, where two eigenvalues of the non-Hermitian Hamiltonian turn out to be a complex conjugate pair. In this case, we find that the transition probabilities will be unbounded in the limit of infinite time $t \\to +\\infty$. After making a connection between the PT-broken phase and the neutral-meson system in particle physics, we observe that the infinite-time behavior of the transition probabilities can be attributed to the negative decay width of one eigenstate of the non-Hermitian Hamiltonian. We also present some brief remarks on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-13T14:04:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transition probabilities",
      "pt-broken phase",
      "flavor eigenstates",
      "two-level quantum system",
      "non-hermitian hamiltonian turn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}