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 χ that relates an effective Planck constant ℏ_eff, the Lyapunov coefficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on ℏ_eff, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for χ≲1, the separation remains small, going down with ℏ_eff², so the concept of separation time loses its meaning.