one based on the Van Vleck propagator, the other on phase-space path integration. Leading
quantum corrections to the classical Liouville propagator take the form of a time-dependent
quantum spot. Its oscillatory structure depends on whether the underlying classical flow is
elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical
trajectories, indicating how quantum coherences are to be propagated semiclassically in …