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Ann. Henri Poincare 11 (2010), 13411373 c 2010 Springer Basel AG
 

Summary: Ann. Henri Poincar´e 11 (2010), 1341­1373
c 2010 Springer Basel AG
1424-0637/10/071341-33
published online November 3, 2010
DOI 10.1007/s00023-010-0056-1 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

  

Source: Asch, Joachim - Centre De Physique Theorique, Campus de Luminy, Case 907

 

Collections: Mathematics