Mathematics Department Colloquium: Quantum ergodicity and delocalization of Schrödinger eigenfunctions

Colloquium | October 10 | 4:10-5 p.m. | 60 Evans Hall

 Nalini Anantharaman, CNRS and Université de Strasbourg

 Department of Mathematics

The question of ``quantum ergodicity'' is to understand how the ergodic properties of a classical dynamical system are translated into spectral properties of the associated quantum dynamics. This question appears already in a paper by Einstein written in 1917. It takes its full meaning after the introduction of the Schrödinger equation in 1926, and even more after the numerical simulations of the 80s that seem to indicate that, for ``chaotic'' classical dynamics, the spectrum of the associated Schrödinger operator resembles that of a class of large random matrices. Proving this is still fully open. However, we start to understand quite well how the chaotic properties of classical dynamics lead to delocalization properties of the wave functions. We will review the results on the subject and some examples.