{
  "id": "1009.0922",
  "version": "v2",
  "published": "2010-09-05T14:22:30.000Z",
  "updated": "2011-01-21T21:57:55.000Z",
  "title": "Defect Modes and Homogenization of Periodic Schrödinger Operators",
  "authors": [
    "M. A. Hoefer",
    "M. I. Weinstein"
  ],
  "comment": "26 pages, 3 figures, to appear SIAM J. Math. Anal",
  "journal": "SIAM J. Math. Anal., vol. 43, pp. 971-996 (2011)",
  "doi": "10.1137/100807302",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider the discrete eigenvalues of the operator $H_\\eps=-\\Delta+V(\\x)+\\eps^2Q(\\eps\\x)$, where $V(\\x)$ is periodic and $Q(\\y)$ is localized on $\\R^d,\\ \\ d\\ge1$. For $\\eps>0$ and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of the periodic Schr\\\"odinger operator, $H_0 = -\\Delta_\\x+V(\\x)$, into spectral gaps. The nature of the bifurcation depends on the homogenized Schr\\\"odinger operator $L_{A,Q}=-\\nabla_\\y\\cdot A \\nabla_\\y +\\ Q(\\y)$. Here, $A$ denotes the inverse effective mass matrix, associated with the spectral band edge, which is the site of the bifurcation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-21T21:57:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic schrödinger operators",
      "defect modes",
      "spectral band edge",
      "discrete eigenvalues",
      "homogenization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0922H"
    }
  }
}