Linear response theory for magnetic Schrödinger operators in disordered media

Abstract

We justify the linear response theory for an ergodic Schrödinger operator with magnetic field within the noninteracting 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–Str˘eda formula for the quantum Hall conductivity at zero temperature.