Adiabatic Charge Transport and the Kubo Formula for Landau Type Hamiltonians

TL;DR

This paper proves that in a 2D Landau model with a spectral gap, the adiabatic charge transport aligns with the Kubo-Streda formula, using advanced mathematical techniques.

Contribution

It establishes the validity of the Kubo-Streda formula for adiabatic charge transport in Landau Hamiltonians with spectral gaps.

Findings

Adiabatic charge transport matches the Kubo-Streda formula in the model.

The proof uses Nenciu's expansion and phase space estimates.

Transport is well-defined in the spectral gap regime.

Abstract

The adiabatic charge transport is investigated in a two dimensional Landau model perturbed by a bounded potential at zero temperature. We show that if the Fermi level lies in a spectral gap then in the adiabatic limit the accumulated excess Hall transport is given by the linear response Kubo-Streda formula. The proof relies on the expansion of Nenciu, some generalized phase space estimates, and a bound on the speed of propagation.