Communications in Mathematical Physics

, Volume 195, Issue 3, pp 495–507

Anderson Localization for Random Schrödinger Operators with Long Range Interactions

  • Werner Kirsch
  • Peter Stollmann
  • Günter Stolz
Article

DOI: 10.1007/s002200050399

Cite this article as:
Kirsch, W., Stollmann, P. & Stolz, G. Commun. Math. Phys. (1998) 195: 495. doi:10.1007/s002200050399

Abstract:

We prove pure point spectrum with exponentially decaying eigenfunctions at all band edges for Schrödinger Operators with a periodic potential plus a random potential of the form Vw(x) = Σqi(w)f(x - i), where $f$ decays at infinity like |x|m for m>4d resp. $m>3d depending on the regularity of f. The random variables qi are supposed to be independent and identically distributed. We assume that their distribution has a bounded density of compact support.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Werner Kirsch
    • 1
  • Peter Stollmann
    • 2
  • Günter Stolz
    • 3
  1. 1.Institut für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany.¶E-mail: werner@mathphys.ruhr-uni-bochum.deGermany
  2. 2.Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany.¶E-mail: stollman@math.uni-frankfurt.deGermany
  3. 3.University of Alabama at Birmingham, Department of Mathematics, Birmingham, Alabama 35294, USA.¶E-mail: stolz@math.uab.eduUSA