{
  "id": "1210.5344",
  "version": "v2",
  "published": "2012-10-19T08:45:26.000Z",
  "updated": "2013-11-01T05:49:16.000Z",
  "title": "Time Dependent $\\mathcal{PT}$-Symmetric Quantum Mechanics",
  "authors": [
    "Jiangbin Gong",
    "Qing-hai Wang"
  ],
  "comment": "22 pages, 2 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The parity-time-reversal- ($\\mathcal{PT}$) symmetric quantum mechanics (PTQM) has developed into a noteworthy area of research. However, to date most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian operators. In this work, we propose an axiom in PTQM in order to study general time-dependent problems in PTQM, e.g., those with a time-dependent $\\mathcal{PT}$-symmetric Hamiltonian and with a time-dependent metric. We illuminate our proposal by examining a proper mapping from a time-dependent Schr\\\"odinger-like equation of motion for PTQM to the familiar time-dependent Schr\\\"odinger equation in conventional quantum mechanics. The rich structure of the proper mapping hints that time-dependent PTQM can be a fruitful extension of conventional quantum mechanics. Under our proposed framework, we further study in detail the Berry phase generation in a class of $\\mathcal{PT}$-symmetric two-level systems. It is found that a closed path in the parameter space of PTQM is often associated with an open path in a properly mapped problem in conventional quantum mechanics. In one interesting case we further interpret the Berry phase as the flux of a continuously tunable fictitious magnetic monopole, thus highlighting the difference between PTQM and conventional quantum mechanics despite the existence of a proper mapping between them.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-01T05:49:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric quantum mechanics",
      "time dependent",
      "tunable fictitious magnetic monopole",
      "berry phase",
      "conventional quantum mechanics despite"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/46/48/485302",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2013,
      "month": "Dec",
      "volume": 46,
      "number": 48,
      "pages": 485302
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JPhA...46V5302G"
    }
  }
}