Comparing two evidences of quantum chaos

We compute the evolution of Wigner distribution in the case of dissipation in a classical chaotic system to analyze the quantum chaos. We find that the quantum chaos can be denoted in two ways. First, we can use the evolutions of χ2(t) and h(ρW,t) to denote quantum chaos: in regular case, χ2(t) and h(ρW,t) oscillate with constant amplitude; in chaotic case, they exponentially increase to equilibrium values. Second, when the coupling of environment exists, we can also use the evolution the Renyi entropy to denote chaos: in regular case, Renyi entropy decreases linearly; in chaotic case, Renyi entropy decreases exponentially. Our results show that besides coupling, quantum coherence can also be disturbed by chaos.