TY - JOUR
T1 - Hölder Continuity of the Spectra for Aperiodic Hamiltonians
AU - Beckus, Siegfried
AU - Bellissard, Jean
AU - Cornean, Horia
PY - 2019/11/1
Y1 - 2019/11/1
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 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.
AB - 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 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.
KW - spectrum location
KW - aperiodic Hamiltonians
KW - operator theory
UR - http://www.scopus.com/inward/record.url?scp=85073588946&partnerID=8YFLogxK
U2 - 10.1007/s00023-019-00848-6
DO - 10.1007/s00023-019-00848-6
M3 - Journal article
SN - 1424-0637
VL - 20
SP - 3603
EP - 3631
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 11
ER -