  Quantum mechanical real-time tunneling through general scattering potentials
is studied in the semiclassical limit. It is shown that the exact path integral
of the real-time propagator is dominated in the long time sector by
quasi-stationary fluctuations associated with caustics. This leads to an
extended semiclassical propagation scheme for wave packet dynamics which
accurately describes deep tunneling through static and, for the first time,
driven barrier potentials.
