A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators

Details A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators

2010-04-27

arxiv.org/abs/1004.4843v1

Physics

Mathematical Physics

Review, Alp workshop "Spectral and probabilistic properties of random walks on random graphs", St. Kathrein (2009).

Scientific paper

We review a geometric approach to proving absolutely continuous (ac) spectrum for random and deterministic Schr\"odinger operators developed in \cite{FHS1,FHS2,FHS3,FHS4}. We study decaying potentials in one dimension and present a simplified proof of ac spectrum of the Anderson model on trees. The latter implies ac spectrum for a percolation model on trees. Finally, we introduce certain loop tree models which lead to some interesting open problems.

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