{
  "id": "1512.05308",
  "version": "v1",
  "published": "2015-12-16T20:07:34.000Z",
  "updated": "2015-12-16T20:07:34.000Z",
  "title": "Confining classical particles with magnetic fields in 2 dimensions",
  "authors": [
    "Gabriel Martins"
  ],
  "comment": "8 pages, 4 figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the dynamics of a classical charged particle moving in a bounded planar domain $\\Omega$ under the influence of a purely magnetic field $\\mathbf{B}$ which blows up at the boundary of the domain. We prove that under appropriate blow-up conditions the particle will never reach the boundary. As a corollary we obtain completeness of the magnetic flow. Our blow-up condition is that $\\mathbf{B}$ should not be integrable along normal rays emanating from the boundary, while its tangential derivative should be integrable along the same rays.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-16T20:07:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "78A30",
      "70H07"
    ],
    "keywords": [
      "confining classical particles",
      "dimensions",
      "appropriate blow-up conditions",
      "magnetic flow",
      "bounded planar domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}