  We study the dynamics of non-interacting quantum particles with two bands in
the presence of random scattering. The two bands are associated with a chiral
symmetry. After breaking the latter by a potential, we still find that the
quantum dynamics is controlled by a non-Abelian chiral symmetry. The
possibility of spontaneous symmetry breaking is analyzed within a
self-consistent approach, and the instability of a symmetric solution is
discussed.
