A geometric approach to absolutely continuous spectrum for discrete Schrödinger operators

2010/04/27 by Froese, Richard, Hasler, David, Spitzer, Wolfgang
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1004.4843

Abstract

We review a geometric approach to proving absolutely continuous (ac) spectrum for random and deterministic Schrödinger operators developed in \citeFHS1,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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