Quantum decoherence due to non-linear dynamics of environment

We discuss quantum decoherence in an open system which couples with a non-linear environment with finite degrees of freedom. Even if the degrees of freedom of the environment are finite, the strong non-linearity of the environment is expected to destroy quantum coherence of the open system like a heat bath with infinite degrees of freedom. In order to demonstrate this fact, we use two-dimensional kicked rotors as the environment and investigate a master equation for a reduced density matrix which is obtained by coarse-graining the environmental degrees of freedom. Our numerical simulation shows that when the non-linearity of the environment exceeds a critical strength, quantum coherence of the open system is irreversibly destroyed. This decoherence is due to the uncorrelated response of the environment to the open system and is related to the chaotic property of the non-linear environment