Wednesday, December 5, 2012

1212.0322 (Andreas W. W. Ludwig et al.)

Lyapunov spectra for all symmetry classes of quasi-one-dimensional
disordered systems

Andreas W. W. Ludwig, Hermann Schulz-Baldes, Michael Stolz
A random phase property is proposed for products of random matrices drawn from one of the classical groups associated to the 10 Cartan symmetry classes. It allows to calculate the Lyapunov spectrum explicitly in a perturbative regime. These results apply to quasi-one-dimensional random Dirac operators which can be constructed for each of the symmetry classes. For classes corresponding to quantum Hall systems, quantum spin Hall systems and $\ZM_2$-topological superconductors the random Dirac operators have vanishing Lyapunov exponents and almost surely an absolutely continuous spectrum.
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