Extended states in a Lifshitz tail regime for random Schrödinger operators on trees.

  title={Extended states in a Lifshitz tail regime for random Schr{\"o}dinger operators on trees.},
  author={Michael Aizenman and Simone Warzel},
  journal={Physical review letters},
  volume={106 13},
We resolve an existing question concerning the location of the mobility edge for operators with a hopping term and a random potential on the Bethe lattice. The model has been among the earliest studied for Anderson localization, and it continues to attract attention because of analogies which have been suggested with localization issues for many particle systems. We find that extended states appear through disorder enabled resonances well beyond the energy band of the operator's hopping term… 

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