Linear response theory for magnetic Schroedinger operators in disordered media
Jean-Marc Bouclet, Francois Germinet, Abel Klein, and Jeffrey H., Schenker
TL;DR
This paper establishes a rigorous foundation for linear response theory in disordered magnetic Schrödinger operators, deriving formulas for electrical conductivity and quantum Hall effects within a mathematical framework.
Contribution
It provides a rigorous justification of linear response theory and derives a Kubo formula for magnetic disordered media, including the quantum Hall conductivity at zero temperature.
Findings
Derived a Kubo formula for electric conductivity tensor.
Reproduced the Kubo-Streda formula for quantum Hall conductivity.
Constructed functional spaces for solving the Liouville equation.
Abstract
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.
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