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We show how a classically vanishing interaction generates entanglementbetween two initially nonentangled particles, without affecting their classicaldynamics. For chaotic dynamics, the rate of entanglement is shown to saturateat the Lyapunov exponent of the classical dynamics as the interaction strengthincreases. In the saturation regime, the one-particle Wigner function followsclassical dynamics better and better as one goes deeper and deeper in thesemiclassical limit. This demonstrates that quantum-classical correspondence atthe microscopic level requires neither high temperatures, nor coupling to alarge number of external degrees of freedom

Lyapunov Generation of Entanglement and the Correspondence Principle