  We discuss the roles of the macroscopic limit and of different
system-environment interactions in the quantum-classical transition for a
chaotic system. We consider the kicked harmonic oscillator subject to
reservoirs that correspond in the classical case to purely dissipative or
purely diffusive behavior, in a situation that can be implemented in ion trap
experiments. In the dissipative case, we derive an expression for the time at
which quantum and classical predictions become different (breaking time) and
show that a complete quantum-classical correspondence is not possible in the
chaotic regime. For the diffusive environment we estimate the minimum value of
the diffusion coefficient necessary to retrieve the classical limit and also
show numerical evidence that, for diffusion below this threshold, the breaking
time behaves, essentially, as in the case of the system without a reservoir.
