Localization Properties of the Chalker-Coddington Model
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Date
2010
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BIRKHAUSER VERLAG AG
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 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 formula and compute the mean Lyapunov exponent, which is independent of M.
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Keywords
UNITARY BAND MATRICES, DENSITY-OF-STATES, INTEGRATED DENSITY, HOLDER CONTINUITY, QUANTUM, PERCOLATION, DIMENSIONS, OPERATORS, SYSTEMS