Localization and Delocalization for Nonstationary Models

  • P. Stollmann
Conference paper
Part of the Trends in Mathematics book series (TM)


In recent years there has been considerable progress concerning mathematically rigorous results on the phenomenon of localization. We refer to the bibliography where we chose some classics, some recent articles as well as books on the subject. However, all these results provide only one part of the picture that is accepted since the groundbreaking work [4, 79] by Anderson, Mott and Twose: one expects a metal insulator transition. This effect is supposed to depend upon the dimension and the general picture is as follows: Once translated into the language of spectral theory there is a transition from a localized phase that exhibits pure point spectrum (= only bound states = no transp ort) to a delocalized phase with absolutely cont inuous spectrum (= scattering states = transport). What has been proven so far is the occurrence of the former phase, well known under the name of localization. The missing part, delocalization, has not been settled for genuine random models


Anderson Model Random Potential Anderson Localization Bethe Lattice Pure Point Spectrum 
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© Springer Basel AG 2004

Authors and Affiliations

  • P. Stollmann
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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