  The sensitivity of a wave field's evolution to small perturbations is of
fundamental interest. For chaotic systems, there are two distinct regimes of
either exponential or Gaussian overlap decay in time. We develop a
semiclassical approach for understanding both regimes, and give a simple
expression for the crossover time between the regimes. The wave field's
evolution is considerably more stable than the exponential instability of
chaotic trajectories seem to suggest. The resolution of this paradox lies in
the collective behavior of the appropriate set of trajectories. Results are
given for the standard map.

Chaotic Dynamics