# Propagation of wavepackets for large times

Author: Roman Schubert (Bristol)

### Abstract

We study the semiclassical propagation of a class of wavepackets for large times on manifolds of negative curvature. The time evolution is generated by the Laplace-Beltrami operator and the wavepackets considered are Lagrangian states. The principal result is that these wavepackets become weakly equidistributed in the joint limit $\hbar\to 0$ and $t\to\infty$ with $t<<|\ln \hbar|$. The main ingredient in the proof is hyperbolicity and mixing of the geodesic flow.