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Quantum unique ergodicity. (English) Zbl 1027.58024

Author’s summary: Consider a compact Riemannian manifold with ergodic geodesic flow. Quantum ergodicity is generalized from orthonormal bases of eigenfunctions of the Laplacian to packets of eigenfunctions. It is shown that this more general result is sharp. Namely, there may exist exceptional packets of eigenfunctions which concentrate on a submanifold.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
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