On the scarring of eigenstates in some arithmetic hyperbolic manifolds
Abstract
In this paper, we deal with the conjecture of 'Quantum Unique Ergodicity'. Z. Rudnick and P. Sarnak showed that there is no 'strong scarring' on closed geodesics for arithmetic congruence surfaces derived from a quaternion division algebra. We extend this result to a class of three-dimensional Riemannian manifolds X=Gamma3 that are again derived from quaternion division algebras. We show that there is no 'strong scarring' on closed geodesics or on Gamma-closed imbedded totally geodesics surfaces of X.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.