  The quantum and classical dynamics of particles kicked by a gaussian
attractive potential are studied. Classically, it is an open mixed system (the
motion in some parts of the phase space is chaotic, and in some parts it is
regular). The fidelity (Lochshmidt echo) is found to exhibit oscillations that
can be determined from classical considerations but are sensitive to phase
space structures that are smaller than Planck's constant. Families of
quasi-energies are determined from classical phase space structures.
Substantial differences between the classical and quantum dynamics are found
for time dependent scattering. It is argued that the system can be
experimentally realized by cold atoms kicked by a gaussian light beam.
