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A random phase property is proposed for products of random matrices drawnfrom any one of the classical groups associated with the ten Cartan symmetryclasses of non-interacting disordered Fermion systems. It allows to calculatethe Lyapunov spectrum explicitly in a perturbative regime. These results applyto quasi-one-dimensional random Dirac operators which can be constructed asrepresentatives for each of the ten symmetry classes. For those symmetryclasses that correspond to two-dimensional topological insulators orsuperconductors, the random Dirac operators describing the one-dimensionalboundaries have vanishing Lyapunov exponents and almost surely an absolutelycontinuous spectrum, reflecting the gapless and conducting nature of theboundary degrees of freedom.

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