Linear Response Theory for Random Schrödinger Operators and Noncommutative Integration

Details Linear Response Theory for Random Schrödinger Operators and Noncommutative Integration Linear Response Theory for Random Schrödinger Operators and Noncommutative Integration

2011-03-28

arxiv.org/abs/1103.5498v1

Physics

Mathematical Physics

Markov process and relative fields (2008)

Scientific paper

We consider an ergodic Schr\"odinger 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. 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 but make a more systematic use of noncommutative Lp-spaces, leading to a somewhat more transparent proof.

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