Localization Properties of the Chalker-Coddington Model

Details Localization Properties of the Chalker-Coddington Model Localization Properties of the Chalker-Coddington Model

2010-01-20

arxiv.org/abs/1001.3625v2

Physics

Mathematical Physics

29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length a

Scientific paper

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.

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