{
  "id": "1211.2343",
  "version": "v2",
  "published": "2012-11-10T18:27:30.000Z",
  "updated": "2016-02-21T19:09:34.000Z",
  "title": "A quantum waveguide with Aharonov Bohm magnetic field",
  "authors": [
    "H. Najar",
    "M. Raissi"
  ],
  "comment": "24 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1011.3133, arXiv:0902.3731",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In a previous study \\cite{n} we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$. We impose the Neumann boundary condition on a disc window of radius $a$ and Dirichlet boundary conditions on the remained part of the boundary of the strip. We proved that such system exhibits discrete eigenvalues below the essential spectrum for any $a>0$. In the present work we study the effect of a magnetic filed of Aharonov-Bohm type when the magnetic field is turned on this system. Precisely we prove that in the presence of such magnetic filed there is some critical values of $a_0>0$, for which we have absence of the discrete spectrum for $\\displaystyle 0<\\frac{a}{d}<a_0$. We give a sufficient condition for the existence of discrete eigenvalues.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-10T18:27:30.000Z",
      "title": "On the spectrum of the Schrodinger Operator with Aharonov-Bohm Magnetic Field in quantum waveguide with Neumann window",
      "journal": null,
      "doi": null,
      "authors": [
        "H. Najar",
        "M. Rayssi"
      ]
    },
    {
      "version": "v2",
      "updated": "2016-02-21T19:09:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "47B80",
      "81Q15"
    ],
    "keywords": [
      "aharonov-bohm magnetic field",
      "quantum waveguide",
      "neumann window",
      "schrodinger operator",
      "discrete eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2343N"
    }
  }
}