Lyapunov exponents for the differences between quantum and classical dynamics

The moments and correlations of the (classical or quantum) position and momentum variables satisfy a hierarchy of coupled equations, which have been studied and solved numerically for the Hénon-Heiles model. It is found, for chaotic states of the model, that the second moments of the classical and quantum variables grow exponentially at a rate governed by the classical Lyapunov exponent. The differences between quantum and classical variables also grow exponentially, but with a larger exponent. The behavior of this quantum-classical difference exponent is studied in this paper.