Abstract
We prove that for a large class of Schrödinger operators on aperiodic tilings the spectrum and the integrated density of states are the same for all tilings in the local isomorphism class, i.e., for all tilings in the orbit closure of one of the tilings. This generalizes the argument in earlier work from discrete strictly ergodic operators onl 2(ℤd) to operators on thel 2-spaces of sets of vertices of strictly ergodic tilings.
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Hof, A. A remark on Schrödinger operators on aperiodic tilings. J Stat Phys 81, 851–855 (1995). https://doi.org/10.1007/BF02179262
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DOI: https://doi.org/10.1007/BF02179262