Localization Properties of the Chalker-Coddington Model
Mathematical Physics
2015-05-18 v2 Mesoscale and Nanoscale Physics
math.MP
Abstract
The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.
Keywords
Cite
@article{arxiv.1001.3625,
title = {Localization Properties of the Chalker-Coddington Model},
author = {Joachim Asch and Alain Joye and Olivier Bourget},
journal= {arXiv preprint arXiv:1001.3625},
year = {2015}
}
Comments
29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincare