Time-dependent driven anharmonic oscillator and adiabaticity

We use the Liouville-von Neumann approach to study the dynamics and the adiabaticity of a time-dependent driven anharmonic oscillator as an example of nonequilibrium quantum dynamics. We show that the adiabaticity is minimally broken in the sense that a Gaussian wave packet at the past infinity evolves to coherent states; however slowly the potential changes, its coherence factor is of the order of the coupling. We also show that the dynamics are governed by an equation of motion similar to the Kepler motion, which satisfies angular momentum conservation