Dynamics of quantum-classical differences for chaotic systems

The differences between quantum and classical dynamics can be studied through the moments and correlations of the position and momentum variables in corresponding quantum and classical statistical states. In chaotic states the quantum-classical differences grow exponentially with an exponent that exceeds the classical Lyapunov exponent. It is shown analytically that the quantum-classical differences scale as ${ħ}^2,$ and that the exponent for the growth of these differences is independent of ħ. The quantum-classical difference exponent is studied for two quartic potential models, and the results are compared with previous work on the Hénon-Heiles model.