A. Joye Univ. J. Fourier – Localization Properties of the Chalker-Coddington Model

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Date(s) - 24 novembre 2010

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“Localization Properties of the Chalker-Coddington Model” Abstract: The Chalker Coddington model is an effective random unitary model designed to understand the delocalization transition of the quantum Hall effect. Despite its popularity in theoretical and computational physics, no rigorous analysis of its properties had been undertaken. After a description of the model, recent mathematical results about the localization properties of the Chalker Coddington model restricted to a cylinder of perimeter 2M will be presented: The Lyapunov spectrum is first proven to be simple, which, in particular, yields finiteness of the localization length. It is then shown that this implies spectral localization. Finally, a Thouless formula is proven and the density of states is shown to be flat. This makes it possible to compute the mean Lyapunov exponent which is independent of M. This is joint work with Joachim Asch and Olivier Bourget.