Linear Response Theory for Random Schroedinger Operators and Noncommutative Integration
2008, v.14, №3, 403-426
We consider an ergodic Schroedinger operator with magnetic field within the non-interacting particle approximation. Justifying the linear response theory, a rigorous derivation of a Kubo formula for the electric conductivity tensor within this context can be found in a recent work of Bouclet, Germinet, Klein and Schenker [J.M. Bouclet, F. Germinet, A. Klein and J. Schenker, Linear response theory for magnetic Schroedinger operators in disordered media. J. Func. Anal., 2005, v. 226, 301-372]. If the Fermi level falls into a region of localization, the well-known Kubo - Streda formula for the quantum Hall conductivity at zero temperature is recovered. In this review we go along the lines of the cite paper but make a more systematic use of noncommutative $L^p$-spaces, leading to a somewhat more transparent proof.
Keywords: random Schroedinger operators,Kubo formula,noncommutative integration