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We relate high-energy limits of Laplace-type and Dirac-type operators toframe flows on the corresponding manifolds, and show that the ergodicity offrame flows implies quantum ergodicity in an appropriate sense for thoseoperators. Observables for the corresponding quantum systems are matrix-valuedpseudodifferential operators and therefore the system remains non-commutativein the high-energy limit. We discuss to what extent the space of stationaryhigh-energy states behaves classically.Comment: 26 pages, latex2

High Energy Limits of Laplace-Type and Dirac-Type EigenFunctions and Frame Flows