Persistence under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger operators on Trees Graphs
Michael Aizenman, Simone Warzel
Abstract
We consider radial tree extensions of one-dimensional quasi-periodic Schroedinger operators and establish the stability of their absolutely continuous spectra under weak but extensive perturbations by a random potential. The sufficiency criterion for that is the existence of Bloch-Floquet states for the one dimensional operator corresponding to the radial problem.
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