  Multi-channel spin-orbit quantum wires, when subjected to a magnetic field
and proximity coupled to s-wave superconductor, may support Majorana states. We
study what happens to these systems in the presence of disorder. Inspired by
the widely established theoretical methods of mesoscopic superconductivity, we
develop a la Eilenberger a quasiclassical approach to topological nanowires
valid in the limit of strong spin-orbit coupling. We find that the "Majorana
number", distinguishing between the state with Majorana fermion (symmetry class
B) and no Majorana (class D), is given by the product of two Pfaffians of
gapped quasiclassical Green's functions fixed by right and left terminals
connected to the wire. A numerical solution of the Eilenberger equations
reveals that the class D disordered quantum wires are prone to the formation of
the zero-energy anomaly (class D impurity spectral peak) in the local density
of states which shares the key features of the Majorana peak. In this way we
confirm the robustness of our previous conclusions [Phys. Rev. Lett. 109,
227005 (2012)] on a more restrictive system setup. Generally speaking, we find
that the quasiclassical approach provides a highly efficient means to address
disordered class D superconductors both in the presence and absence of
topological structures.
