{
  "id": "0905.2879",
  "version": "v2",
  "published": "2009-05-18T16:32:45.000Z",
  "updated": "2009-12-17T21:49:01.000Z",
  "title": "Quantum and Classical Statistical Mechanics of a Class of non-Hermitian Hamiltonians",
  "authors": [
    "H. F. Jones",
    "E. S. Moreira Jr"
  ],
  "comment": "Title changed, to more accurately reflect content. Introduction expanded. References added",
  "journal": "J. Phys. A: Math. Theor. 43 (2010) 055307",
  "categories": [
    "quant-ph",
    "hep-th"
  ],
  "abstract": "This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very accurate even for small quantum numbers, and used to generate the quantum partition function. Graphs showing the thermal behavior of the entropy and the specific heat, at all regimes of temperature, are given. To obtain the corresponding classical partition function it turns out to be necessary in general to integrate over a complex \"phase space\". For the wrong-sign quartic, whose equivalent Hermitian Hamiltonian is known exactly, it is demonstrated explicitly how this formulation arises, starting from the Hermitian case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-17T21:49:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.30.-d",
      "03.65.Ge",
      "05.20.-y"
    ],
    "keywords": [
      "classical statistical mechanics",
      "non-hermitian hamiltonians",
      "equivalent hermitian hamiltonian",
      "second-order wkb approximation",
      "small quantum numbers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/43/5/055307",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Feb",
      "volume": 43,
      "number": 5,
      "pages": "055307"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 823501,
      "adsabs": "2010JPhA...43e5307J"
    }
  }
}