TY  - JOUR
A1  - Beckus, Siegfried
A1  - Bellissard, Jean
A1  - Cornean, Horia
T1  - Holder Continuity of the Spectra for Aperiodic Hamiltonians
T2  - Annales de l'Institut Henri Poincaré
N2  - 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, 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 Holder (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.
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/47962
SN  - 1424-0637
SN  - 1424-0661
VL  - 20
IS  - 11
SP  - 3603
EP  - 3631
PB  - Springer
CY  - Cham
ER  -