 
Summary: Ann. Henri Poincar´e 11 (2010), 13411373
c 2010 Springer Basel AG
14240637/10/07134133
published online November 3, 2010
DOI 10.1007/s0002301000561 Annales Henri Poincar´e
Localization Properties
of the ChalkerCoddington Model
Joachim Asch, Olivier Bourget and Alain Joye
We dedicate this work to the memory of our friend and colleague Pierre Duclos
Abstract. The ChalkerCoddington quantum network percolation model
is numerically pertinent to the understanding of the delocalization tran
sition of the quantum Hall effect. We study the model restricted to a
cylinder of perimeter 2M. We prove first 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 for
mula and compute the mean Lyapunov exponent, which is independent
of M.
1. Introduction
We start with a mathematical then a physical description of the model. Fix
the parameters
