Nalini Anantharaman (U Strasbourg): Quantum ergodicity and delocalization of Schrödinger eigenfunctions

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 written by Einstein 1917. It took on its full significance after the introduction of the Schrödinger equation in 1926, and even more after the numerical simulations of the 80s, which indicate that for ‘chaotic’ classical dynamics, the associated spectrum resembles that of a class of large random matrices. Proving this is still fully open. However, we are beginning 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.