  We use the Liouville-von Neumann (LvN) approach to study the dynamics and the
adiabaticity of a time-dependent driven anharmonic oscillator as an eample of
non-equilibrium 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
order of the coupling. We also show that the dynamics are governed by an
equation of motion similar to the Kepler motion which satisfies the angular
momentum conservation.
