Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator

We discuss the roles of the macroscopic limit and of differentsystem-environment interactions in the quantum-classical transition for achaotic system. We consider the kicked harmonic oscillator subject toreservoirs that correspond in the classical case to purely dissipative orpurely diffusive behavior, in a situation that can be implemented in ion trapexperiments. In the dissipative case, we derive an expression for the time atwhich quantum and classical predictions become different (breaking time) andshow that a complete quantum-classical correspondence is not possible in thechaotic regime. For the diffusive environment we estimate the minimum value ofthe diffusion coefficient necessary to retrieve the classical limit and alsoshow numerical evidence that, for diffusion below this threshold, the breakingtime behaves, essentially, as in the case of the system without a reservoir.Comment: 16 pages, 13 figures. Accepted for publication in Phys. Rev.