Nonadiabatic dynamics in semiquantal physics

Every physical regime is some sort of approximation of reality. One lesser-known realm that is the semiquantal regime, which may be used to describe systems with both classical and quantum subcomponents. In the present review, we discuss nonadiabatic dynamics in the semiquantal regime. Our primary concern is electronic-nuclear coupling in polyatomic molecules, but we discuss several other situations as well. We begin our presentation by formulating the semiquantal approximation in quantum systems with degrees-of-freedom that evolve at different speeds. We discuss nonadiabatic phenomena, focusing on their relation to the Born-Oppenheimer approximation. We present several examples - including Jahn-Teller distortion in molecules and crystals and the dynamics of solvated electrons, buckyballs, nanotubes, atoms in a resonant cavity, SQUIDs, quantum particle-spin systems, and micromasers. We also highlight vibrating quantum billiards as a useful abstraction of semiquantal dynamics.