Mathematical Physics and Harmonic Analysis Seminar

Date: April 5, 2024

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Theo McKenzie, Stanford

Title: Quantum Ergodicity for Periodic Graphs

Abstract: Quantum ergodicity (QE) is a notion of eigenfunction delocalization, that large Laplacian eigenfunction entries are “well spread” throughout a manifold or graph. Such a property is true of chaotic manifolds and graphs, such as random regular graphs and Riemannian manifolds with ergodic geodesic flow. Focusing on graphs, outside of very specific examples, QE was previously only known to hold for families of graphs with a tree local limit. In this talk we show how QE is in fact satisfied for many families of operators on periodic graphs, including Schrodinger operators with periodic potential on the discrete torus and on the honeycomb lattice.

In order to do this, we use new ideas coming from analyzing Bloch varieties and some methods coming from proofs in the continuous setting. Based on joint work with Mostafa Sabri.