{ "id": "1201.6221", "version": "v1", "published": "2011-12-05T19:21:23.000Z", "updated": "2011-12-05T19:21:23.000Z", "title": "On convergence to equilibrium distribution for Dirac equation", "authors": [ "Alexander Komech", "Elena Kopylova" ], "comment": "15 pages, 0 figures", "categories": [ "math-ph", "math.MP" ], "abstract": "We consider the Dirac equation in $\\R^3$ with a potential, and study the distribution $\\mu_t$ of the random solution at time $t\\in\\R$. The initial measure $\\mu_0$ has zero mean, a translation-invariant covariance, and a finite mean charge density. We also assume that $\\mu_0$ satisfies a mixing condition of Rosenblatt- or Ibragimov-Linnik-type. The main result is the long time convergence of projection of $\\mu_t$ onto the continuous spectral space. The limiting measure is Gaussian.", "revisions": [ { "version": "v1", "updated": "2011-12-05T19:21:23.000Z" } ], "analyses": { "subjects": [ "35Q41", "47A40", "60F05" ], "keywords": [ "dirac equation", "equilibrium distribution", "finite mean charge density", "long time convergence", "initial measure" ], "note": { "typesetting": "TeX", "pages": 15, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2012arXiv1201.6221K" } } }