Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions - Ludwig, Andreas W. W.; Schulz-Baldes, Hermann; Stolz, Michael (Journal of Statistical Physics, 2013)
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. © 2013 Springer Science+Business Media New York.
UnivIS-Import:2015-03-09:Pub.2013.nat.dma.pma22.lyapun
Keywords: Delocalization; Lyapunov spectrum; Symmetry classes