Roman Schubert (University of Bristol)

Mixing and equidistribution in wave propagation.

Abstract. We study solutions of the time dependent Schroedinger equation in the semiclassical limit $\hbar\to 0$ with oscillating initial conditions. It is well known that the propagation of quantum states in the semiclassical limit is described by the underlying Hamiltonian dynamical system. We show that if this classical system is hyperbolic and mixing, then a certain class of quantum states become equidistributed for large times. The main problem in this field is to control the two limits $\hbar\to 0$ and $t\to \infty$ simultaneously.