High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

Details High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

2006-07-25

arxiv.org/abs/math/0607616v1

Mathematics

Spectral Theory

26 pages, latex2e

Scientific paper

10.1007/s00220-006-0176-0

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.

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