{
  "id": "1706.06653",
  "version": "v1",
  "published": "2017-06-20T20:13:08.000Z",
  "updated": "2017-06-20T20:13:08.000Z",
  "title": "Asymptotics of free fermions in a quadratic well at finite temperature and the Moshe-Neuberger-Shapiro random matrix model",
  "authors": [
    "Karl Liechty",
    "Dong Wang"
  ],
  "comment": "46 pages, 2 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We derive the local statistics of the canonical ensemble of free fermions in a quadratic potential well at finite temperature, as the particle number approaches infinity. This free fermion model is equivalent to a random matrix model proposed by Moshe, Neuberger and Shapiro. Limiting behaviors obtained before for the grand canonical ensemble are observed in the canonical ensemble: We have at the edge the phase transition from the Tracy--Widom distribution to the Gumbel distribution via the Kardar-Parisi-Zhang (KPZ) crossover distribution, and in the bulk the phase transition from the sine point process to the Poisson point process. A similarity between this model and a class of models in the KPZ universality class is explained. We also derive the multi-time correlation functions and the multi-time gap probability formulas for the free fermions along the imaginary time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-20T20:13:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "82B10",
      "82B23"
    ],
    "keywords": [
      "moshe-neuberger-shapiro random matrix model",
      "finite temperature",
      "particle number approaches infinity",
      "asymptotics",
      "multi-time gap probability formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}