  We relate high-energy limits of Laplace-type and Dirac-type operators to
frame flows on the corresponding manifolds, and show that the ergodicity of
frame flows implies quantum ergodicity in an appropriate sense for those
operators. Observables for the corresponding quantum systems are matrix-valued
pseudodifferential operators and therefore the system remains non-commutative
in the high-energy limit. We discuss to what extent the space of stationary
high-energy states behaves classically.
