Abstract
We derive some quantum ergodic theorems, related to microlocal behavior of eigenfunctions of a positive, self-adjoint, elliptic pseudodifferential operator Λ on a compact Riemannian manifold M, emphasizing results that hold without the hypothesis that the Hamiltonian flow generated by the symbol of Λ be ergodic. Cases treated include both integrable Hamiltonians and some associated with “soft chaos.”
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Taylor, M. Variations on Quantum Ergodic Theorems. Potential Anal 43, 625–651 (2015). https://doi.org/10.1007/s11118-015-9489-y
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DOI: https://doi.org/10.1007/s11118-015-9489-y