Quantum-classical comparison in chaotic systems

We introduce a characteristic time of a classical chaotic dynamics, represented by the coherence time of the local maximum expansion direction. For a quantum system whose classical limit follows the above chaotic dynamics, the ratio between this time and the decorrelation time (of the order of the reciprocal of the maximum Liapunov exponent) rules the ratio between nonclassical (Moyal) and classical (Liouville) terms in the evolution of the density matrix. We show that such a ratio does not provide a complete criterion for quantum-classical correspondence.