Two-parameter spectral averaging and localization for non-monotonic random schrödinger operators

Academic Article


  • We prove exponential localization at all energies for two types of one-dimensional random Schrödinger operators: the Poisson model and the random displacement model. As opposed to Anderson-type models, these operators are not monotonie in the random parameters. Therefore the classical one-parameter version of spectral averaging, as used in localization proofs for Anderson models, breaks down. \Ve use the new method of two-parameter spectral averaging and apply it to the Poisson as well as the displacement case. In addition, we apply results from inverse spectral theory, which show that two-parameter spectral averaging works for sufficiently many energies (all but a discrete set) to conclude localization at all energies. ©2000 American Mathematical Society.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Buschmann D; Stolz G
  • Start Page

  • 635
  • End Page

  • 653
  • Volume

  • 353
  • Issue

  • 2