Continuity of the spectra for families of magnetic operators on Z^d

Abstract

For families of magnetic self-adjoint operators on ${\mathbb{Z}}^d$ whose symbols and magnetic fields depend continuously on a parameter $\epsilon$, it is shown that the main spectral properties of these operators also vary continuously with respect to $\epsilon$. The proof is based on an algebraic setting involving twisted crossed product C*-algebras.

13 pages

References in corpus (1)

• On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians

Cited by in corpus (1)

• Spectral Continuity for Aperiodic Quantum Systems I. General Theory