Groups and Dynamics

Quantum ergodicity describes the delocalization of most eigenfunctions of Laplace-type operators on graphs or manifolds exhibiting chaotic classical dynamics. Quantum mixing is a stronger notion, additionally controlling correlations between eigenfunctions at different energy levels. In this work, we study families of finite Schreier graphs that converge to an infinite Cayley graph and establish quantum mixing under the assumption that the limiting Cayley graph has absolutely continuous spectrum. The proof relies on a new approach to quantum ergodicity, based on trace computations, resolvent approximations and representation theory. This is a joint work with Cyril Letrouit and Mostafa Sabri.