2019
Jun
18

# Dynamics and probability: David Jerison (MIT) - Localization of eigenfunctions via an effective potential

2:00pm to 3:00pm

## Location:

Ross 70

We discuss joint work with Douglas Arnold, Guy David, Marcel Filoche and Svitlana Mayboroda.
Consider for the operator $L = -\Delta + V$ with periodic boundary conditions, and more
generally on the manifold with or without boundary. Anderson localization, a significant feature
of semiconductor physics, says that the eigenfunctions of $L$ are exponentially localized with
high probability for many classes of random potentials $V$. Filoche and Mayboroda introduced the
function $u$ solving $Lu = 1$ and showed numerically that it strongly reflects this localization.