Decoherence and the quantum-classical limit in the presence of chaos
  We investigate how decoherence affects the short-time separation between quantum and classical dynamics for classically chaotic systems, within the framework of a specific model. For a wide range of parameters, the distance between the corresponding phase-space distributions depends on a single parameter $\chi$ that relates an effective Planck constant $\hbar_{\rm eff}$, the Lyapunov coeffficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on $\hbar_{\rm eff}$, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for $\chi\lesssim 1$, the separation remains small, going down with $\hbar_{\rm eff}^2$, so the concept of separation time loses its meaning. 
F. Toscano, R. L. de Matos Filho and L. Davidovich