In this talk, I examine semiquantum chaos in vibrating quantum billiards, which may be used to explore nonadiabatic behavior in polyatomic molecules. A d-mode Galerkin expansion of a quantum billiard whose boundary has s mechanical degrees-of-freedom is interpreted physically as a molecule with s excited nuclear modes and a d-fold electronic near-degeneracy.

After motivating the problem with the example of an electron turnstile (created with a buckyball), I consider the semiquantum physical regime and its relation to the Born-Oppenheimer approximation. To establish the setting of the problems of interest (which are related to Jahn-Teller problems), I will also briefly review the notions of classical and quantum billiards.

I then consider vibrating quantum billiards and present one with spherical symmetry as an example. I will discuss some results concerning this system (and others). Finally, I will present my hopes and dreams for future work in this area.