Variations on Quantum Ergodic Theorems

摘要

We derive some quantum ergodic theorems, related to microlocal behavior of eigenfunctions of a positive, self-adjoint, elliptic pseudodifferential operator I > on a compact Riemannian manifold M, emphasizing results that hold without the hypothesis that the Hamiltonian flow generated by the symbol of I > be ergodic. Cases treated include both integrable Hamiltonians and some associated with "soft chaos.".