Role of the effective Hilbert-space size of the reservoir for the decoherence process.

We show that an environment composed by N bosons coupled through cross-Kerr interaction to an oscillator of interest can be effective at destroying quantum coherences at short times and around the revival times even if N=1 . It is analytically shown for this model that the effective Hilbert-space size is a relevant parameter for decoherence process. Based on numerical results, we investigate the long time dynamics and the classical limit. Since we are dealing with a phase reservoir, the model does not describe dissipation.

Quantum-classical transition of the open quartic oscillator: The role of the environment.

We investigate the classical and quantum dynamics of the open quartic oscillator model. Typically quantum behavior such as collapses and revivals (also squeezing) are induced by the nonlinearity of the model. We show that purely diffusive environments, as expected, attenuate such phenomena. We obtain analytical results in both regimes classical and quantum and discuss the effect of a diffusive reservoir in the two cases. We show that "separation times" as usually defined in the literature are strongly observable (and initial condition) dependent, rendering a solid definition of a unique classical limit rather difficult. In particular, the separation time for the variance can be smaller than that for the expectation value of the position of the centroid of the wave packet. We find a hierarchy of time scales which depends on the observable and the reservoir.

Quantum time scales and the classical limit: analytic results for some simple systems.

We set up a semiclassical approximation which helps us clarify by means of several simple examples the rich variety of time scale in the quantum domain. The underlying structure of quantum and classical mechanics is so completly different that it is naive to expect to reach a classical regime by counting powers of the quantum scale variant Planck's over 2pi. We show although it is possible to define a time scale for nonclassical phenomena, but it is impossible to characterize quantum dynamics through a unique time scale, such as Ehrenfest's time. We use simple systems to critically discuss and illustrate these features of the quantum-classical limit.