On the continuity of spectra for families of magnetic pseudodifferential operators

Abstract

For families of magnetic pseudodifferential operators defined by symbols and magnetic fields depending continuously on a real parameter $\epsilon$, we show that the corresponding family of spectra also varies continuously with $\epsilon$.

22 pages

References in corpus (5)

• The Magnetic Weyl Calculus
• Magnetic Pseudodifferential Operators
• Fractal Weyl Law for Open Chaotic Maps
• Magnetic pseudodifferential operators with coefficients in C*-algebras
• Twisted Crossed Products and Magnetic Pseudodifferential Operators

Cited by in corpus (12)

• On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians
• Topological Polarization in Graphene-like Systems
• Magnetic pseudodifferential operators represented as generalized Hofstadter-like matrices
• Spectral edge regularity of magnetic Hamiltonians
• Low lying spectral gaps induced by slowly varying magnetic fields
• A Calculus for Magnetic Pseudodifferential Super Operators
• Rieffel's pseudodifferential calculus and spectral analysis of quantum Hamiltonians
• Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field
• Continuity of the spectra for families of magnetic operators on Z^d
• Peierls substitution and magnetic pseudo-differential calculus
• The Peierls-Onsager Effective Hamiltonian in a complete gauge covariant setting: Description of the spectrum
• Canonical Quantization of Constants of Motion