Lyapunov Spectra for All Ten Symmetry Classes of Quasi-one-dimensional Disordered Systems of Non-interacting Fermions |
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Authors: | Andreas W. W. Ludwig Hermann Schulz-Baldes Michael Stolz |
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Affiliation: | 1. Department of Physics, University of California, Santa Barbara, CA, USA 2. Department Mathematik, Universit?t Erlangen-Nürnberg, Erlangen, Germany 3. Fakult?t für Mathematik, Ruhr-Universit?t Bochum, Bochum, Germany
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Abstract: | A random phase property is proposed for products of random matrices drawn from any one of the classical groups associated with the ten Cartan symmetry classes of non-interacting disordered Fermion systems. 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 as representatives for each of the ten symmetry classes. For those symmetry classes that correspond to two-dimensional topological insulators or superconductors, the random Dirac operators describing the one-dimensional boundaries have vanishing Lyapunov exponents and almost surely an absolutely continuous spectrum, reflecting the gapless and conducting nature of the boundary degrees of freedom. |
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