On the regularity of the Hausdorff distance between spectra of perturbed   magnetic Hamiltonians
  We study the regularity properties of the Hausdorff distance between spectra of continuous Harper-like operators. As a special case we obtain H\"{o}lder continuity of this Hausdorff distance with respect to the intensity of the magnetic field for a large class of magnetic elliptic (pseudo)differential operators with long range magnetic fields. 
Horia D. Cornean, Radu Purice
math.SP math-ph math.MP