Are there any considerably short examples of manifolds that are/aren't quantum ergodic, or quantum unique ergodic?
Note that a (compact) Riemannian manifold is said to be quantum ergodic if almost all of the eigenfunctions of its Laplacian operator equidistribute, while it's quantum unique ergodic if absolutely all of them do. A summary can be found here: http://www.austms.org.au/Publ/Gazette/2011/Jul11/TechPaperHassell.pdf.