{
  "id": "1706.03134",
  "version": "v1",
  "published": "2017-06-09T21:34:30.000Z",
  "updated": "2017-06-09T21:34:30.000Z",
  "title": "Symmetry breaking and restoration in the Ginzburg-Landau model of nematic liquid crystals",
  "authors": [
    "Marcel Clerc",
    "Michał Kowalczyk",
    "Panayotis Smyrnelis"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study qualitative properties of global minimizers of the Ginzburg-Landau energy which describes light-matter interaction in the theory of nematic liquid crystals near the Friedrichs transition. This model is depends on two parameters: $\\epsilon>0$ which is small and represents the coherence scale of the system and $a\\geq 0$ which represents the intensity of the applied laser light. In particular we are interested in the phenomenon of symmetry breaking as $a$ and $\\epsilon$ vary. We show that when $a=0$ the global minimizer is radially symmetric and unique and that its symmetry is instantly broken as $a>0$ and then restored for sufficiently large values of $a$. Symmetry breaking is associated with the presence of a new type of topological defect which we named the shadow vortex. The symmetry breaking scenario is a rigorous confirmation of experimental and numerical results obtained in our earlier work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-09T21:34:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nematic liquid crystals",
      "symmetry breaking",
      "ginzburg-landau model",
      "restoration",
      "global minimizer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}