Fokker-Planck equations and density of states in disordered quantum wires

We propose a general scheme to construct scaling equations for the density of states in disordered quantum wires for all ten pure Cartan symmetry classes. The anomalous behavior of the density of states near the Fermi level $\varepsilon =0\mathrm{}$ for the three chiral and four Bogoliubov–de Gennes universality classes is analyzed in detail by means of a mapping to a scaling equation for the reflection from a quantum wire in the presence of an imaginary potential.