{
  "id": "1302.4074",
  "version": "v2",
  "published": "2013-02-17T14:49:30.000Z",
  "updated": "2013-07-03T03:06:26.000Z",
  "title": "Trace asymptotics formula for the Schrödinger operators with constant magnetic fields",
  "authors": [
    "Mouez Dimassi",
    "Anh Tuan Duong"
  ],
  "comment": "21 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "In this paper, we consider the 2D- Schr\\\"odinger operator with constant magnetic field $H(V)=(D_x-By)^2+D_y^2+V_h(x,y)$, where $V$ tends to zero at infinity and $h$ is a small positive parameter. We will be concerned with two cases: the semi-classical limit regime $V_h(x,y)=V(h x,h y)$, and the large coupling constant limit case $V_h(x,y)=h^{-\\delta} V(x,y)$. We obtain a complete asymptotic expansion in powers of $h^2$ of ${\\rm tr}(\\Phi(H(V),h))$, where $\\Phi(\\cdot,h)\\in C^\\infty_0(\\mathbb R;\\mathbb R)$. We also give a Weyl type asymptotics formula with optimal remainder estimate of the counting function of eigenvalues of $H(V)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-03T03:06:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "35J10",
      "35P20",
      "35C20",
      "47F05"
    ],
    "keywords": [
      "constant magnetic field",
      "trace asymptotics formula",
      "schrödinger operators",
      "large coupling constant limit case",
      "weyl type asymptotics formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4074D"
    }
  }
}