How do wave packets spread? Time evolution on Ehrenfest time scales

We derive an extension of the standard time-dependent WKB theory, which can be applied
to propagate coherent states and other strongly localized states for long times. It in
particular allows us to give a uniform description of the transformation from a localized
coherent state into a delocalized Lagrangian state, which takes place at the Ehrenfest time.
The main new ingredient is a metaplectic operator that is used to modify the initial state
in a way that the standard time-dependent WKB theory can then be applied for the propagation.
This is based on joint work with Raul Vallejos and Fabricio Toscano, but in this talk we will
focus on the special case of propagation on a manifold of negative curvature.