Understanding the random displacement model: From ground state properties to localization

Chapter

Abstract

  • ¬© Springer Basel 2012. All rights reserved. We give a detailed survey of results obtained in the most recent half-decade which led to a deeper understanding of the random displacement model, a model of a random Schr√∂dinger operator which describes the quantum mechanics of an electron in a structurally disordered medium. These results started by identifying configurations which characterize minimal energy, then led to Lifshitz tail bounds on the integrated density of states as well as a Wegner estimate near the spectral minimum, which ultimately resulted in a proof of spectral and dynamical localization at low energy for the multi-dimensional random displacement model.
  • Authors

    Digital Object Identifier (doi)

    International Standard Book Number (isbn) 13

  • 9783034804134
  • Start Page

  • 183
  • End Page

  • 219