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Absolutely continuous spectrum for the Anderson model on trees

University of British Columbia

This dissertation is an examination of the absolutely continuous spectrum for the Anderson model on different types of trees. The text is divided into four chapter: an introduction, two main chapters and conclusions. In Chapter 2 the existence of purely absolutely continuous spectrum is proven for the Anderson model on a Cayley tree, or Bethe lattice, of degree K. The method used, a geometric one, is based on some properties of the hyperbolic distance. It is a simplified generalization of a result for K=3 given by R. Froese, D. Hasler and W. Spitzer. In Chapter 3 a similar result is proven for a more general tree which has vertices of degrees 2 and 3 alternating in a periodic manner. The lack of symmetry changes the analysis, making it possible to eliminate one of the steps in the proof for the Cayley tree.

Text

2010-01-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/18857

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/