Spectral edge regularity of magnetic Hamiltonians

Abstract

We analyse the spectral edge regularity of a large class of magnetic Hamiltonians when the perturbation is generated by a globally bounded magnetic field. We can prove Lipschitz regularity of spectral edges if the magnetic field perturbation is either constant or slowly variable. We also recover an older result by G. Nenciu who proved Lipschitz regularity up to a logarithmic factor for general globally bounded magnetic field perturbations.

18 pages, submitted

References in corpus (1)

• On the smoothness of gap boundaries for generalized Harper operators

Cited by in corpus (6)

• Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices
• Hölder Continuity of the Spectra for Aperiodic Hamiltonians
• Low lying spectral gaps induced by slowly varying magnetic fields
• Sharp spectral stability for a class of singularly perturbed pseudo-differential operators
• Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field
• Magnetic Pseudo-differential Operators with Hörmander Symbols Dominated by Tempered Weights