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Remarks on quantum ergodicity

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  • We prove a generalized version of the Quantum Ergodicity Theorem on smooth compact Riemannian manifolds without boundary. We apply it to prove some asymptotic properties on the distribution of typical eigenfunctions of the Laplacian in geometric situations in which the Liouville measure is not (or not known to be) ergodic.
    Mathematics Subject Classification: Primary: 58J51, 35P20; Secondary: 37D25.


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