Hölder Continuity of the Spectra for Aperiodic Hamiltonians

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Date
2019-02-26MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2019,05Author
Beckus, Siegfried
Bellissard, Jean
Cornean, Horia
Metadata
Show full item recordOWP-2019-05
Abstract
We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball is, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Hölder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.