Quantum ergodicity on large graphs
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: SLMath: Eisenbud Auditorium
probabilistic methods in ergodicity
geodesic flow
compact Riemannian manifold
quantum variance of operators
negative curvature manifolds
graph-theoretic generalization
35Q60 - PDEs in connection with optics and electromagnetic theory
35Q79 - PDEs in connection with classical thermodynamics and heat transfer
35M31 - Initial value problems for mixed-type systems of PDEs
14231
We study eigenfunctions of the discrete laplacian on large regular graphs, and prove a ``quantum ergodicity'' result for these eigenfunctions : for most eigenfunctions $\psi$, the probability measure $|\psi(x)|^2$, defined on the set of vertices, is close to the uniform measure.
Although our proof is specific to regular graphs, we'll discuss possibilities of adaptation to more general models, like the Anderson model on regular graphs.
|
Ananharaman. Notes
|
Download |
14231
| H.264 Video |
14231.mp4
|
Download |
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.