Linear response theory for magnetic Schroedinger operators in disordered   media
  We justify the linear response theory for an ergodic Schroedinger operator with magnetic field within the non-interacting particle approximation, and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the Fermi level falls into a region of localization, we recover the well-known Kubo-Streda formula for the quantum Hall conductivity at zero temperature. 
Jean-Marc Bouclet, Francois Germinet, Abel Klein, and Jeffrey H.   Schenker