AbstractQuantum Ergodicity (QE) is a classical topic in spectral geometry, which states that on a compact Riemannian manifold whose geodesic flow is ergodic with respect to the Liouville measure, the Laplacian has a density one subsequence of eigenfunctions that tends to be equidistributed. In this talk, we present the QE for unitary flat bundles. By using a mixture of semiclassical and geometr...
摘 要:Rapidly oscillating functions associated with Lagrangian submanifolds play a fundamental role in semiclassical analysis. In this talk I will describe how to associate classes of semiclassical oscillating functions to isotropic submanifolds of phase space, and show that these classes are invariant under the action of Fourier integral operators (modulo the usual clean intersection conditio...