{
  "id": "1911.08989",
  "version": "v1",
  "published": "2019-11-20T15:57:43.000Z",
  "updated": "2019-11-20T15:57:43.000Z",
  "title": "Perturbations of the Landau Hamiltonian: Asymptotics of eigenvalue clusters",
  "authors": [
    "G. Hernandez-Duenas",
    "S. Pérez-Esteva",
    "A. Uribe",
    "C. Villegas-Blas"
  ],
  "comment": "24 pages, 1 figure",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the asymptotic behavior of the spectrum of the Landau Hamiltonian plus a rapidly decaying potential, as the magnetic field strength, $B$, tends to infinity. After a suitable rescaling, this becomes a semiclassical problem where the role of Planck's constant is played by $1/B$. The spectrum of the operator forms eigenvalue clusters. We obtain a Szeg\\H{o} limit theorem for the eigenvalues in the clusters as a suitable cluster index and $B$ tend to infinity with a fixed ratio $\\calE$. The answer involves the averages of the potential over circles of radius $\\sqrt{\\calE/2}$ (circular Radon transform). We also discuss related inverse spectral results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-20T15:57:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic",
      "perturbations",
      "operator forms eigenvalue clusters",
      "circular radon transform",
      "magnetic field strength"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}