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.