Jean-Marc Bouclet, Fran ois Germinet, Abel Klein, Jeffrey Schenker
Linear response theory for magnetic Schrodinger operators in disordered media
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ABSTRACT.  We justify the linear response theory for an ergodic Schrodinger 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.