{
  "id": "cond-mat/0011175",
  "version": "v1",
  "published": "2000-11-10T05:29:08.000Z",
  "updated": "2000-11-10T05:29:08.000Z",
  "title": "Stochastic Dynamics of a Vortex Loop. Thermal Equilibrium",
  "authors": [
    "Sergey K. Nemirovskii",
    "Luiza P. Kondaurova",
    "Makoto Tsubota"
  ],
  "comment": "latex, 7 pages, uses subeqnar.sty, sprmindx.sty, cropmark.sty, physprbb.sty, svmult.cls, to be published in \"Quantized vortex dynamics and superfluid turbulence\", Ed. C. Barenghi (Springer Verlag, Berlin, 2001)",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We study stochastic behavior of a single vortex loop appeared in imperfect Bose gas. Dynamics of Bose-condensate is supposed to obey Gross-Pitaevskii equation with additional noise satisfying fluctuation-dissipation relation. The corresponding Fokker-Planck equation for probability functional has a solution $\\mathcal{P}(\\{{\\psi}(\\mathbf{r})\\})=\\mathcal{N}\\exp (-H{\\psi}(\\mathbf{r)} /T),$ where $H\\psi(\\mathbf{r})$ is a Ginzburg-Landau free energy. Considering a vortex filaments as a topological defects of the field ${\\psi}(\\mathbf{r})$ we derive a Langevin-type equation of motion of the line with correspondingly transformed stirring force. The respective Fokker-Planck equation for probability functional $\\mathcal{P}(\\{\\mathbf{s}(\\xi)\\})$ in vortex loop configuration space is shown to have a solution of the form $\\mathcal{P}(\\{\\mathbf{s}(\\xi)\\})=\\mathcal{N}\\exp (-H{\\mathbf{s}} /T),$ where $\\mathcal{N}$ is a normalizing factor and $H{\\mathbf{s}}$ is energy of vortex line configurations. In other words a thermal equilibrium of Bose-condensate results in a thermal equilibrium of vortex loops appeared in Bose-condensate. Some consequences of that fact and possible violations are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-11-10T05:29:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermal equilibrium",
      "stochastic dynamics",
      "probability functional",
      "additional noise satisfying fluctuation-dissipation relation",
      "vortex loop configuration space"
    ],
    "publication": {
      "journal": "Quantized Vortex Dynamics and Superfluid Turbulence",
      "year": 2001,
      "volume": 571,
      "pages": 212
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001LNP...571..212N"
    }
  }
}