Non-Abelian chiral symmetry controls random scattering in two-band models

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.